Research ArticlePerformance Modeling of Proposed GUISET Middleware forMobile Healthcare Services in E-Marketplaces

Alaba Olu Akingbesote Mathew Olusegun Adigun Sibisuso Xulu and Edgar Jembere

Department of Computer Science University of Zululand Private Bag X1001 KwaDlangezwa 3886 South Africa

Correspondence should be addressed to Alaba Olu Akingbesote oluwamodimu2012gmailcom

Received 27 June 2014 Accepted 8 October 2014 Published 18 November 2014

Academic Editor Yuh-Rau Wang

Copyright copy 2014 Alaba Olu Akingbesote et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

GUISET is a proposed middleware engine currently under study in South Africa The goal is to provide utility services for smallmedium and macroenterprises in the context of mobile e-services Three things are important to make this engine effective andefficient the implementation performance and the pricing strategy The literature has delved richly into implementation issueof similar projects Both the performance and the pricing strategy issues have not been fully discussed especially in the contextof mobile healthcare services Some literature has addressed the performance issue using the exogenous nonpriority and thepreemptive model However with providers offering different services using that approach may prove to be difficult to implementThis work extends existing and widely adopted theories to non-preemptive model by using the queuing theory and the simulationmodel in the context of mobile healthcare services Our evaluation is based on non-preemptive priority and nonpriority disciplineOur results reveal that the unconditional average waiting time remains the same with reduction in waiting time over the non-preemptive priority model in four out of the five classes observed This is envisaged to be beneficial in mobile healthcare serviceswhere events are prioritized and urgent attention is needed to be given to urgent events

1 Introduction

The e-marketplaces are local community of service providersand requestors (service consumers) organized in verti-cal markets and gathering around portals [1] These e-marketplaces have allowed consumers to shop for bread ofservices from anywhere in the world based on pay-as-you-gomodel [2]

Onemajor improvement in these e-markets is the issue ofmobile services whereby the data processing and storage aremoved from the mobile device to powerful and centralizedcomputing platforms and then accessed over the wirelessconnection based on a thin native client or web browser onthe mobile devices [3] This improvement brought the ideaof Grid Based Utility Infrastructure Software EngineeringTechnology (GUISET) project

The basic goal of GUISET is to provide utility infras-tructure services especially in the context of mobile health-care services to small medium and microenterprise These

mobile e-services include e-health (healthcare service) e-commerce and e-learningThe idea of this project is centeredon the fact that mobile devices (eg smartphone and tabletPC) are increasingly becoming an essential part of humanlife They are the most effective and convenient communi-cation tools not bounded by time and place Mobile usersaccumulate rich experience of various services from mobileapplications (eg iPhone apps and Google apps) whichrun on their devices andor on remote servers via wirelessnetworks With rapid growth in mobile technology both inlow- andmiddle-income countries particularly in Africa andin the less affluent and rural communities mobile deviceaccess is far greater than access to computers in developingcountries For instance in South Africa about 50 millionpeople have mobile phone access and everyday experienceconfirms a near-universal mobile ownership with everyonefrom street vendors to top-level executives carrying one [4]

The report of World Health Organization (WHO) globalsurvey on e-health indicates that the dominant form of

Hindawi Publishing CorporationJournal of Applied MathematicsVolume 2014 Article ID 248293 9 pageshttpdxdoiorg1011552014248293

2 Journal of Applied Mathematics

m-health today is characterized by small-scale pilot projectsthat address single issues in information sharing and accessThis report also noted the existence of a number of applica-tions gaining attraction for mobile phone-based health issues[5]

In addition mobiles services have been attracting theattention of entrepreneurs as a profitable business optionthat reduces the development and running cost of mobileapplications of mobile users as a new technology to achieverich experience of a variety of mobile services at low costand of researchers as a promising solution for green IT [6]Three things are important to make this engine effective andefficient the GUISETs implementation performance andthe pricing strategy While the implementation and pricingstrategy process are on course see for example [7ndash9] thatof performance is yet to be fully addressed For examplein the International Data Cooperation (IDC) report theperformance challenge of Cloud which is a similar projectrose in 2008 from 631 to 829 in 2009 as reported in [10]This is an increase of 198 as against the Security challengeof about 129

One important aspect of performance is the waitingtime to respond to consumers by e-Cloud providers forproducts or requestsThis waiting time which is a key sourceof competitive advantage is so important that traditionalmarketplaces like MCDonalds in 1990s offered consumerstheir meal free of charge if the order was not served within2 minutes [11]

The focus of this research is to investigate the proposedGUISETmiddleware performance based on requests waitingtime of mobile events with different service offerings in thecontext of e-health that is we study and evaluate the servicediscipline to be adopted in the context of mobile e-healthwhere providers of service have different service offerings formobile aware requests

Most existing literature that delved into performanceimpact for example the Cloud e-marketplaces focuses onthe exogenous nonpriority model with emphasis on FirstCome First Served discipline [12ndash14] or Shortest Job Next[15] As the server farms increase with consumers demandingdifferent service disciplines some scholars like [16] use thepreemptive service discipline in the context of Cloud e-marketplaces but literature reveals that in practice pre-emption and migration of virtual machines are costly [17]Second preemption leads to increase in response time ofconsumersrsquo requests especiallywhen the requests are deadlineconstrained [18] This work extends existing and widelyadopted theories to non-preemptive model in the context ofthe proposed GUISETsmiddleware with emphasis onmobilee-health

Our assumption in this paper is that each medical pointof call is called server and we then follow that of [14 19] thatthe system consists of a number of server machines that areallocated to patientsrsquo request based on the service disciplineFurthermore each mobile event request is assigned to onlyone server and each server can only run at most one task at atime

The remainder of this paper is organized as followsSection 2 discusses the related work Section 3 introduces

our analytical model description with the numerical andsimulation setup In Section 4 we have our results anddiscussion We have the conclusion in Section 5

2 Literature Review

Since this is a proposed project and yet to be fully imple-mented we study existing literature of a similar project whichhas given us the opportunity to extend the body of knowledgeand we focus on Cloud issue on performance

In [20] the authors study the effect of queuing in relationto the time spent by patients to access clinical servicesmultiuser modelThe authors analyze the data and the resultsof the analysis show that average queue length waiting timeof patients and overutilization of doctors at the clinic couldbe reduced at an optimal server level

In [12] the authors address three things these are thelevels of QoS that can be guaranteed given service resourcesthe number of service resources that are required to ensurethat customer services can be guaranteed in terms of thepercentile and the number of customers to be supported toensure that customer services can be guaranteed in terms ofthe percentile of response time The work of [19] uses theMGc to evaluate a Cloud server firm with the assumptionthat the numbers of server machines are not restricted Theresult of the authors demonstrates the manner in whichrequest response time and number of tasks in the systemmaybe assessed with sufficient accuracy

The work of [14] uses the M[119909]Gmm+r to describea new approximate analytical model for performance eval-uation of Cloud data centers with batch task arrivals Theresults show that important performance indicators such asmean request response time waiting time in the queue queuelength blocking probability probability of immediate serviceand probability distribution of the number of tasks in thesystem can be obtained in a wide range of input parametersThis work is based on the so-called on-demand service

In [16] the authors propose a preemptive policy in Cloudmarket The idea is that when an urgent request arrives itpreempts the current request in service and such preemptedrequest is then migrated to another virtual machine if itcannot meet the deadline for completion In [18] the authorsremove the scheduling bottleneck from one-dimensional tomultidimensional resources This is done with the use ofMultidimensional Resource Integrated Scheduling (MRIS)which is an inquisitive algorithm to obtain the approximateoptimal solution

The work of [15] proposes MMm queuing model todevelop a synthetic optimization method to optimize theperformance of services in an on-demand service The simu-lation result shows that the proposed method can allow lesswaiting time and queue length and more customers to gainthe service using synthetic optimization function when thenumber of servers increases In [21] the authors model theCloud using MMcc model with different priority classeswith the main goal of studying the rejection probability fordifferent priority classes But [22] extendsKleinrockrsquos analysisto derive the stationary waiting distribution for each class

Journal of Applied Mathematics 3

WAPapplication

NETapplication

WAPapplication Applet J2EE

client

Law levelresources

Knowledgeresources Services

Enabling information bus for dynamic service selection

Request with QoS Response

Multimediainterfaces

Middlewarelayer

Gridinfrastructure

layer

SMME enablers

Utility broker

Resource repository

Figure 1 GUISET architecture

in a single server accumulating priority queue with Poissonarrival and general distribution service time

All these authors have made one or more contributionsto the existing knowledge These works have given us theopportunity to make our contribution based on the fewobservations we noticed For instance the works of [12 1415 20 22] were based on FCFS or SJN which could notwork in e-health mobile service where the e-mobile eventsare prioritized Also the generalized approach used by [12]could not reflect the real Cloud market of today The work of[16] produces a good result but [17] reveals that preemptionand migration of virtual machines are costly

Our work is closely related to [23 24] where these authorsmodel the Cloud as series of queues What differentiate ourwork are the following

(i) each of our service stations is modelled asMMcPras against the MM1 proposed by these authors

(ii) no dedicated server is given or allocated to any classthereby reducing consumersrsquo waiting time

(iii) our research is in the context of mobile services

3 The General GUISETs Architecture andthe Proposed Middleware Model

We present two architectures the first is the general archi-tecture of the proposed GUISETs in Figure 1 and the secondis our proposed performance GUISETmiddleware prototypemodel in the context of e-health in Figure 2 The second iscalved out from the first as part of the services

The GUISETs architecture has three major layers themultimodal layer the middleware and the infrastructurallayer The multimodal layer consists of SMME enablingapplications which we refer to as the client sideThis includesthe WAP Net and other applications as shown in Figure 1The clients send mobile aware requests to the GUISETmiddleware and the middleware does the service discoveryselection and composition Apart from these it checks forauthentication and authorization and resolves the issue of

pricing strategy it ensures the provisioning of good qualityof service through better service discipline The third layer isthe infrastructure layer that contains the resource repositoryThese are low level knowledge and other services like e-health service

Our research is in this middleware where we focus onthe service discipline to be adopted in the context of mobilee-health where providers of service have different serviceofferings for mobile aware requests

Our proposed prototype GUISET model is shown inFigure 2 The health-aware mobile devices are connected tothe mobile networks via a base station for example throughbase transceiver station or access point that establishes andcontrols the connections and functional interfaces betweenthe networks and mobile devices We gather our healthinformation from [25ndash27]Themobile user information (egID and location BS BP) is recorded and the risk columnfield is classified into five levels that determine the mobileevent class as shown in Table 1 For example mobile eventthat has blood sugar greater than 200mgd or blood pressureof 180110 and above is classified as severe or very high riskwith class 1 and that between 140ndash200 and 160ndash169100ndash109is classified as moderate or high risk with class 2 Thesee-health mobile events are classified under five categoriesin this research as shown in Table 1 These are transmittedto the central processor which is the dispatcher-in serverthat provides authentication authorization order of request(service discipline) and accounting services based on thehome agent and subscribersrsquo data stored in databases Afterthat the requests are delivered to the right destination wherethe e-health mobile network services will be provided andresults are then dispatched back through the dispatcher-out One assumption is that the mobile gargets and theaccess points are already in place secondly the issues ofauthentication authorization and accounting services areout of scope of this researchOur research is to prioritize theseclasses so that urgent requests get access to solution fasterthan the less urgent ones The priority is such that the orderis in the form of class 1 mobile aware event having higher

4 Journal of Applied Mathematics

Table 1 The e-health mobile aware records

ID Location Blood sugar (mgdL) Blood pressure (mmHg) Risk Mobile event classSystolic Diastolic

XXXX1 Ngoma gt200 ge180 ge110 Very high (severe) C1XXXX2 Ongoye gt140 but lt200 160ndash179 100ndash109 High (moderate) C2XXXX3 Empangeni ge126 le139 140ndash159 90ndash99 Mild C3XXXX4 Esikhawini 100 but lt126 120ndash139 80ndash89 Warning C4XXXX5 Richards Bay 110 120 80 No (normal) C5

C2

C3

C4

C5

E-health queue center 1

center n

Dispatcher-in

SMs

SMs

SMsC1

Dispatcher-out

Base station center 2

E-health queue

E-health queue

Figure 2 Proposed GUISET mobile healthcare model

priority than classes 2 3 4 and 5When an incoming requestmeets lower one on the queue it takes over that request butwhen lower request is already underprocessed that requesthas to be completed When requests of the same priorityare on the queue then the order is based on First ComeFirst Served (FCFS) All requests are sent to the dispatcher-inserver where they are then distributed to the e-health centerstations for processing The processed request then movesthrough the dispatcher-out as the outlet

Unlike most related works [16 22 24] where the non-preemptive policy is implemented at the first point of entryalone we model our non-preemptive model at every point ofqueue that is the dispatcher-in queue as MM1Pr the e-health centers as MMcPr and the dispatcher-out queueas MM1Pr This is because at every point of queue thereis likely tendency that higher priority will arrive when lowerone is on the queue

This proposed model assumes that the arrival and theservice process are exponentially distributed and due tolarge number of consumers entering the market for requestwe assume an infinite population To get our performancemeasure we follow the law of conservation of flow and thesteps stated in [28]

31 Mathematical Modelling of Dispatcher-In Queue Letmobile event with service of the 119896th priority (the smaller thenumber the higher the priority) arrive before the dispatcher-in according to Poisson distribution with parameter 120582119896 (119896 =1 2 119903) and these consumers wait on First Come FirstServed basis within their respective priorities Let the servicedistribution for the 119896th priority be exponential with mean1120583119896 As earlier said whatever the priority of a unit inservice is it has to complete its service before another itemis admitted

We define

120588119896 =120582119896

120583119896 (1 le 119896 le 119903)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 0 120590119903 equiv 120588)

(1)

The system stationary for 120590119903 = 120588 lt 1 Let an event of priority119894 arrives at time 1199050 and enters service at time 1199051 Its line wait isthus 119879119902 = 1199051 minus 1199050 At 1199050 let us say we have 1198991 of priority one inline ahead of this new arrival 1198992 of priority two 1198993 of prioritythree and so on Let 1198780 be the total time required to finish thejob already in service and 119878119896 the total time required to serve119899119896 During the new mobile request waiting time 119879119902 (say) 119899

1015840119896

mobile request of priority 119896 lt 1 will arrive and go to serviceahead of this current arrival If 1198781015840119896 is the total service time ofall 1198991015840119896 then it can be seen that

119879119902 =

119894minus1

sum119896=1

1198781015840

119896 +

119894

sum119896=1

119878119896 + 1198780 (2)

taking the expected values from both sides of the foregoingthen

1198821015840

119896 = 119864 [119879119902] =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [119878119896] + 119864 [1198780] (3)

Since 120590119894minus1 lt 120590119894 for all 119894 then 120588 lt 1 implies that 120590119894minus1 lt 1 forall 119894

To find 119864[1198780] we observe that the combined servicedistribution is the mixed exponential which is formed fromthe law of total probability as

119861 (119905) =

119894

sum119896=1

120582119896

120582(1 minus 119890

minus120583119896119905) (4)

Journal of Applied Mathematics 5

where

120582 =

119903

sum119896=1

120582119896 (5)

The random variable remaining time of service 1198780 has thevalue 0 when the system is idle hence

119864 [1198780] = Pr system is busy 119864 [1198780 | busy system] (6)But the probability that the system is busy is

120582 =

119903

sum119896=1

120582119896

120582

1

120583119896= 120588 (7)

where 120588 is the server utilization and

119864 [1198780 | busy system]

=

119903

sum119896=1

120582119896119864 [1198780 | system busy wit 119896 type cutomer]

sdot Pr mobile request has priority 119896

=

119903

sum119896=1

1

120583119896

120588119896

120588

(8)

therefore

119864 [1198780] = 120588

119903

sum119896=1

1

120583119896

120588119896

120588=

119903

sum119896=1

120588119896

120588 (9)

Since 119899119896 and the service times of individual mobile requests119878(119899)

119896are independent

119864 [119878119896] = 119864 [119899119896119878(119899)

119896] = 119864 [119899119896] 119864 [119878

(119899)

119896] =

119864 [119899119896]

120583119896 (10)

Utilizing Littlersquos formula then gives

119864 [119878119896] =120582119896119882(119896)119902

120583119896= 120588119896119882

(119896)

119902 (11)

similarly

119864 [1198781015840

119896] =119864 [1198991015840119896]

120583119896

(12)

and then utilizing the uniform properties of the Poisson wehave

119864 [1198781015840

119896] =119864 [119899119896]

120583119896

120582119896119882(119894)119902

120583119896 (13)

therefore119882(119894)119902 which is the waiting time for mobile request of119894 priority is

119882(119894)

119902 = 119882(119894)

119902

119894minus1

sum119896=1

120588119896 +

119894

sum119896=1

120588119896119882(119896)

119902 + 119864 [1198780]

119882(119894)

119902 =sum119894

119896=1 120588119896119882(119896)119902 + 119864 [1198780]

1 minus 120590119894minus1

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

(14)

Using (9) finally gives

119882(119894)

119902 =sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (15)

The above equation holds as long as 120590119894 = sum119903

119896=1 120588119896 lt 1Therefore from Littlersquos formula

119871(119894)

119902 =

119903

sum119896=1

120582119894119882(119894)

119896=

120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (16)

The total expected system size in each of the single channelsis

119871119902 =

119903

sum119894=1

119871119894

119902 =120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (17)

32 Mathematical Modelling of Mobile E-Health CenterUnlike the MM1Pr the MMcPr is governed by iden-tical exponential distributions for each priority at each of the119888 channels within a station As earlier said our service rate isequal throughout the experiment We define

120588119896 =120582119896

119888120583119896 (1 le 119896 le 119903) (18)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 120588 =120582

119888120583) (19)

where the system is stationary for 120588 lt 1 and

119882(119894)

119902 =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [1198780] (20)

where 119878119896 is the time required to serve 119899119896 mobile requests ofthe 119896th priority in the line ahead of the consumer 1198781015840119896 is theservice time of the 1198991015840119896 consumers of priority 119896 which arriveduring119882(119894)119902 1198780 is the amount of time remaining until the nextserver becomes available

Therefore

119864 [1198780]

= Pr (all servers are busy within a service station)

sdot 119864 [1198780 | all server are busy within a service station]

= (

infin

sum119899minus119888

119875119899)1

119888120583

= 1198750 (

infin

sum119899minus119888

119888120588119899

119888119899minus119888119888)1

119888120583=1198750 (119888120588)

119888

119888 (1 minus 119901)

=(119888120588)119888

119888 (1 minus 120588) (119888120583)[

119888minus1

sum119899=0

(119888120588)119899

119899+

(119888120588)119888

119888 (1 minus 120588)]

minus1

(21)

6 Journal of Applied Mathematics

but

119864 [1198780] = 120588

119903

sum119896=1

1

119906119896

120588119896

120588=

119903

sum119896=1

120588119896

119906119896

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

119882(119894)

119902 =sum119903

119896=1 (120588119896119906119896)

(1 minus 120590119894minus1) (1 minus 120590119894)

(22)

Therefore

119882(119894)

119902 =[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

119879119882(119894)

119902st =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

=[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

(23)

The expected time taken in a service station is

119882119902st =119903

sum119894=1

120582119894

120582119882(119894)

119902st (24)

The overall average time taken in 119895 service stations is

119882(ave)119902st =sum119895

119899=1 lceilsum119903

119894=1 (120582119894120582)119882(119894)119902 rceil

119895 (25)

33 Mathematical Modelling of Dispatcher-Out Ourdispatcher-out is similar to the dispatcher-in therefore thewaiting time is derived using (1) to (15) and (18) We obtain

119882119879dispout119902 =

119903

sum119894=1

119882119894

119902 (26)

The total waiting time by say class 119894 priority is

119882119894tot119902 = 119882

119894

119902din +119882119894

119902st +119882119894

119902dout (27)

while the total waiting time experienced in the queue by thewhole classes is

119908119902 =

119898

sum119899=1

119882119894tot119902

119899 (28)

34 Numerical Validation and Simulation First we validateour mathematical solution with the simulation to ascertainthe degree of correction This is done by considering fiveclasses of consumersrsquo arrival These are represented as fivearrival processes 1205821 1205822 1205823 1205824 and 1205825 where 1205821 = 1205822 =1205823 = 1205824 = 1205825 and 120582 = 1205821 + 1205822 + 1205823 + 1205824 + 1205825

Weuse theWolframMathematica 90 as themathematicaltool for our validation results and arena 145 as the simulator

Table 2 Simulation and analytical

120588 Sim Ana01 0000681 000068102 0001502 000150203 0002612 000261204 0004006 000400605 000592 00059206 0008751 0008907 0013447 001344708 0021933 002301909 0047009 00496

0

001

002

003

004

005

006

0 02 04 06 08 1

SimulationAnalytical

Server utilization (120588)

Wai

ting

time (th

r)

Figure 3 Simulation and Analytical

We set 120582 = 100 200 300 970 respectively and 119888 =2 in each of the service stations We then simulate thisexperiment using Arena discrete event simulator version 145with the same values to ascertain the degree of variabilityThis simulation was run with replication length of 1000 in 24hours per day with base time in hours and it was replicated 5times The service rate was set to 0001 for the dispatcher-inand 00005 for each of the servers in the web queue stationsand the dispatcher-out

In addition we set up a similar experiment with thesame configurations but under a nonpriority discipline usingFCFS discipline The illustration of this model is shown bynumerical examples and the impact on the five performancesof the priority classes is analyzed under the Results andDiscussion section

4 Results and Discussion

Theanalytical results and that of our simulation are comparedand the results are shown inTable 2 and Figure 3 respectivelyThe degree of variation is hardly noticed until 120588 rarr 1 but thecoefficient of variation is very small and less than unity that iswhy in Figure 3 the analytical colour overshadowed the sim-ulation colour at the initial stage Table 3 provides the results

Journal of Applied Mathematics 7

Table3Waitin

gtim

e(sec)andidleperio

d(

)

120588C1

sC2

sC3

sC4

sC5

sTo

tal

C1C2

C3C4

C5To

tal

NPP

NP

01

000

0123

000

0136

000

0137

000

0141

000

0145

000

0681

000

0131

000

0141

000

0136

000

0136

000

0135

000

0681

02

000

0255

000

0273

000

0299

000

0324

000

035

0001502

000

0302

000

0302

000

0301

000

0302

000

0295

0001502

03

000

039

000

0441

000

0513

000

0584

000

0685

0002612

000

0515

000

0515

000

0529

000

0526

000

0528

0002614

04

000

0537

000

0623

000

0756

000

0924

000116

7000

4006

000

0802

000

079

000

0798

000

0806

000

0808

000

4003

05

000

0676

000

085

0001074

0001394

0001926

000592

000117

8000118

2000119

7000118

2000118

50005923

06

000

083

0001083

0001466

0002087

0003285

0008751

0001754

000175

0001742

0001758

0001754

0008758

07

000

0993

0001354

0001954

0003155

0005991

0013447

0002695

0002677

0002688

0002694

0002697

0013451

08

000115

0001646

0002581

000

4752

0011803

0021933

000

4371

000

4366

000

4373

000

4386

000

4394

0021889

09

0001311

0002001

0003431

0007494

0032772

0047009

000

9372

000

9421

000

9384

000

9407

000

9462

0047046

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

2 Journal of Applied Mathematics

m-health today is characterized by small-scale pilot projectsthat address single issues in information sharing and accessThis report also noted the existence of a number of applica-tions gaining attraction for mobile phone-based health issues[5]

In addition mobiles services have been attracting theattention of entrepreneurs as a profitable business optionthat reduces the development and running cost of mobileapplications of mobile users as a new technology to achieverich experience of a variety of mobile services at low costand of researchers as a promising solution for green IT [6]Three things are important to make this engine effective andefficient the GUISETs implementation performance andthe pricing strategy While the implementation and pricingstrategy process are on course see for example [7ndash9] thatof performance is yet to be fully addressed For examplein the International Data Cooperation (IDC) report theperformance challenge of Cloud which is a similar projectrose in 2008 from 631 to 829 in 2009 as reported in [10]This is an increase of 198 as against the Security challengeof about 129

One important aspect of performance is the waitingtime to respond to consumers by e-Cloud providers forproducts or requestsThis waiting time which is a key sourceof competitive advantage is so important that traditionalmarketplaces like MCDonalds in 1990s offered consumerstheir meal free of charge if the order was not served within2 minutes [11]

The focus of this research is to investigate the proposedGUISETmiddleware performance based on requests waitingtime of mobile events with different service offerings in thecontext of e-health that is we study and evaluate the servicediscipline to be adopted in the context of mobile e-healthwhere providers of service have different service offerings formobile aware requests

Most existing literature that delved into performanceimpact for example the Cloud e-marketplaces focuses onthe exogenous nonpriority model with emphasis on FirstCome First Served discipline [12ndash14] or Shortest Job Next[15] As the server farms increase with consumers demandingdifferent service disciplines some scholars like [16] use thepreemptive service discipline in the context of Cloud e-marketplaces but literature reveals that in practice pre-emption and migration of virtual machines are costly [17]Second preemption leads to increase in response time ofconsumersrsquo requests especiallywhen the requests are deadlineconstrained [18] This work extends existing and widelyadopted theories to non-preemptive model in the context ofthe proposed GUISETsmiddleware with emphasis onmobilee-health

Our assumption in this paper is that each medical pointof call is called server and we then follow that of [14 19] thatthe system consists of a number of server machines that areallocated to patientsrsquo request based on the service disciplineFurthermore each mobile event request is assigned to onlyone server and each server can only run at most one task at atime

The remainder of this paper is organized as followsSection 2 discusses the related work Section 3 introduces

our analytical model description with the numerical andsimulation setup In Section 4 we have our results anddiscussion We have the conclusion in Section 5

2 Literature Review

Since this is a proposed project and yet to be fully imple-mented we study existing literature of a similar project whichhas given us the opportunity to extend the body of knowledgeand we focus on Cloud issue on performance

In [20] the authors study the effect of queuing in relationto the time spent by patients to access clinical servicesmultiuser modelThe authors analyze the data and the resultsof the analysis show that average queue length waiting timeof patients and overutilization of doctors at the clinic couldbe reduced at an optimal server level

In [12] the authors address three things these are thelevels of QoS that can be guaranteed given service resourcesthe number of service resources that are required to ensurethat customer services can be guaranteed in terms of thepercentile and the number of customers to be supported toensure that customer services can be guaranteed in terms ofthe percentile of response time The work of [19] uses theMGc to evaluate a Cloud server firm with the assumptionthat the numbers of server machines are not restricted Theresult of the authors demonstrates the manner in whichrequest response time and number of tasks in the systemmaybe assessed with sufficient accuracy

The work of [14] uses the M[119909]Gmm+r to describea new approximate analytical model for performance eval-uation of Cloud data centers with batch task arrivals Theresults show that important performance indicators such asmean request response time waiting time in the queue queuelength blocking probability probability of immediate serviceand probability distribution of the number of tasks in thesystem can be obtained in a wide range of input parametersThis work is based on the so-called on-demand service

In [16] the authors propose a preemptive policy in Cloudmarket The idea is that when an urgent request arrives itpreempts the current request in service and such preemptedrequest is then migrated to another virtual machine if itcannot meet the deadline for completion In [18] the authorsremove the scheduling bottleneck from one-dimensional tomultidimensional resources This is done with the use ofMultidimensional Resource Integrated Scheduling (MRIS)which is an inquisitive algorithm to obtain the approximateoptimal solution

The work of [15] proposes MMm queuing model todevelop a synthetic optimization method to optimize theperformance of services in an on-demand service The simu-lation result shows that the proposed method can allow lesswaiting time and queue length and more customers to gainthe service using synthetic optimization function when thenumber of servers increases In [21] the authors model theCloud using MMcc model with different priority classeswith the main goal of studying the rejection probability fordifferent priority classes But [22] extendsKleinrockrsquos analysisto derive the stationary waiting distribution for each class

Journal of Applied Mathematics 3

WAPapplication

NETapplication

WAPapplication Applet J2EE

client

Law levelresources

Knowledgeresources Services

Enabling information bus for dynamic service selection

Request with QoS Response

Multimediainterfaces

Middlewarelayer

Gridinfrastructure

layer

SMME enablers

Utility broker

Resource repository

Figure 1 GUISET architecture

in a single server accumulating priority queue with Poissonarrival and general distribution service time

All these authors have made one or more contributionsto the existing knowledge These works have given us theopportunity to make our contribution based on the fewobservations we noticed For instance the works of [12 1415 20 22] were based on FCFS or SJN which could notwork in e-health mobile service where the e-mobile eventsare prioritized Also the generalized approach used by [12]could not reflect the real Cloud market of today The work of[16] produces a good result but [17] reveals that preemptionand migration of virtual machines are costly

Our work is closely related to [23 24] where these authorsmodel the Cloud as series of queues What differentiate ourwork are the following

(i) each of our service stations is modelled asMMcPras against the MM1 proposed by these authors

(ii) no dedicated server is given or allocated to any classthereby reducing consumersrsquo waiting time

(iii) our research is in the context of mobile services

3 The General GUISETs Architecture andthe Proposed Middleware Model

We present two architectures the first is the general archi-tecture of the proposed GUISETs in Figure 1 and the secondis our proposed performance GUISETmiddleware prototypemodel in the context of e-health in Figure 2 The second iscalved out from the first as part of the services

The GUISETs architecture has three major layers themultimodal layer the middleware and the infrastructurallayer The multimodal layer consists of SMME enablingapplications which we refer to as the client sideThis includesthe WAP Net and other applications as shown in Figure 1The clients send mobile aware requests to the GUISETmiddleware and the middleware does the service discoveryselection and composition Apart from these it checks forauthentication and authorization and resolves the issue of

pricing strategy it ensures the provisioning of good qualityof service through better service discipline The third layer isthe infrastructure layer that contains the resource repositoryThese are low level knowledge and other services like e-health service

Our research is in this middleware where we focus onthe service discipline to be adopted in the context of mobilee-health where providers of service have different serviceofferings for mobile aware requests

Our proposed prototype GUISET model is shown inFigure 2 The health-aware mobile devices are connected tothe mobile networks via a base station for example throughbase transceiver station or access point that establishes andcontrols the connections and functional interfaces betweenthe networks and mobile devices We gather our healthinformation from [25ndash27]Themobile user information (egID and location BS BP) is recorded and the risk columnfield is classified into five levels that determine the mobileevent class as shown in Table 1 For example mobile eventthat has blood sugar greater than 200mgd or blood pressureof 180110 and above is classified as severe or very high riskwith class 1 and that between 140ndash200 and 160ndash169100ndash109is classified as moderate or high risk with class 2 Thesee-health mobile events are classified under five categoriesin this research as shown in Table 1 These are transmittedto the central processor which is the dispatcher-in serverthat provides authentication authorization order of request(service discipline) and accounting services based on thehome agent and subscribersrsquo data stored in databases Afterthat the requests are delivered to the right destination wherethe e-health mobile network services will be provided andresults are then dispatched back through the dispatcher-out One assumption is that the mobile gargets and theaccess points are already in place secondly the issues ofauthentication authorization and accounting services areout of scope of this researchOur research is to prioritize theseclasses so that urgent requests get access to solution fasterthan the less urgent ones The priority is such that the orderis in the form of class 1 mobile aware event having higher

4 Journal of Applied Mathematics

Table 1 The e-health mobile aware records

ID Location Blood sugar (mgdL) Blood pressure (mmHg) Risk Mobile event classSystolic Diastolic

XXXX1 Ngoma gt200 ge180 ge110 Very high (severe) C1XXXX2 Ongoye gt140 but lt200 160ndash179 100ndash109 High (moderate) C2XXXX3 Empangeni ge126 le139 140ndash159 90ndash99 Mild C3XXXX4 Esikhawini 100 but lt126 120ndash139 80ndash89 Warning C4XXXX5 Richards Bay 110 120 80 No (normal) C5

C2

C3

C4

C5

E-health queue center 1

center n

Dispatcher-in

SMs

SMs

SMsC1

Dispatcher-out

Base station center 2

E-health queue

E-health queue

Figure 2 Proposed GUISET mobile healthcare model

priority than classes 2 3 4 and 5When an incoming requestmeets lower one on the queue it takes over that request butwhen lower request is already underprocessed that requesthas to be completed When requests of the same priorityare on the queue then the order is based on First ComeFirst Served (FCFS) All requests are sent to the dispatcher-inserver where they are then distributed to the e-health centerstations for processing The processed request then movesthrough the dispatcher-out as the outlet

Unlike most related works [16 22 24] where the non-preemptive policy is implemented at the first point of entryalone we model our non-preemptive model at every point ofqueue that is the dispatcher-in queue as MM1Pr the e-health centers as MMcPr and the dispatcher-out queueas MM1Pr This is because at every point of queue thereis likely tendency that higher priority will arrive when lowerone is on the queue

This proposed model assumes that the arrival and theservice process are exponentially distributed and due tolarge number of consumers entering the market for requestwe assume an infinite population To get our performancemeasure we follow the law of conservation of flow and thesteps stated in [28]

31 Mathematical Modelling of Dispatcher-In Queue Letmobile event with service of the 119896th priority (the smaller thenumber the higher the priority) arrive before the dispatcher-in according to Poisson distribution with parameter 120582119896 (119896 =1 2 119903) and these consumers wait on First Come FirstServed basis within their respective priorities Let the servicedistribution for the 119896th priority be exponential with mean1120583119896 As earlier said whatever the priority of a unit inservice is it has to complete its service before another itemis admitted

We define

120588119896 =120582119896

120583119896 (1 le 119896 le 119903)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 0 120590119903 equiv 120588)

(1)

The system stationary for 120590119903 = 120588 lt 1 Let an event of priority119894 arrives at time 1199050 and enters service at time 1199051 Its line wait isthus 119879119902 = 1199051 minus 1199050 At 1199050 let us say we have 1198991 of priority one inline ahead of this new arrival 1198992 of priority two 1198993 of prioritythree and so on Let 1198780 be the total time required to finish thejob already in service and 119878119896 the total time required to serve119899119896 During the new mobile request waiting time 119879119902 (say) 119899

1015840119896

mobile request of priority 119896 lt 1 will arrive and go to serviceahead of this current arrival If 1198781015840119896 is the total service time ofall 1198991015840119896 then it can be seen that

119879119902 =

119894minus1

sum119896=1

1198781015840

119896 +

119894

sum119896=1

119878119896 + 1198780 (2)

taking the expected values from both sides of the foregoingthen

1198821015840

119896 = 119864 [119879119902] =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [119878119896] + 119864 [1198780] (3)

Since 120590119894minus1 lt 120590119894 for all 119894 then 120588 lt 1 implies that 120590119894minus1 lt 1 forall 119894

To find 119864[1198780] we observe that the combined servicedistribution is the mixed exponential which is formed fromthe law of total probability as

119861 (119905) =

119894

sum119896=1

120582119896

120582(1 minus 119890

minus120583119896119905) (4)

Journal of Applied Mathematics 5

where

120582 =

119903

sum119896=1

120582119896 (5)

The random variable remaining time of service 1198780 has thevalue 0 when the system is idle hence

119864 [1198780] = Pr system is busy 119864 [1198780 | busy system] (6)But the probability that the system is busy is

120582 =

119903

sum119896=1

120582119896

120582

1

120583119896= 120588 (7)

where 120588 is the server utilization and

119864 [1198780 | busy system]

=

119903

sum119896=1

120582119896119864 [1198780 | system busy wit 119896 type cutomer]

sdot Pr mobile request has priority 119896

=

119903

sum119896=1

1

120583119896

120588119896

120588

(8)

therefore

119864 [1198780] = 120588

119903

sum119896=1

1

120583119896

120588119896

120588=

119903

sum119896=1

120588119896

120588 (9)

Since 119899119896 and the service times of individual mobile requests119878(119899)

119896are independent

119864 [119878119896] = 119864 [119899119896119878(119899)

119896] = 119864 [119899119896] 119864 [119878

(119899)

119896] =

119864 [119899119896]

120583119896 (10)

Utilizing Littlersquos formula then gives

119864 [119878119896] =120582119896119882(119896)119902

120583119896= 120588119896119882

(119896)

119902 (11)

similarly

119864 [1198781015840

119896] =119864 [1198991015840119896]

120583119896

(12)

and then utilizing the uniform properties of the Poisson wehave

119864 [1198781015840

119896] =119864 [119899119896]

120583119896

120582119896119882(119894)119902

120583119896 (13)

therefore119882(119894)119902 which is the waiting time for mobile request of119894 priority is

119882(119894)

119902 = 119882(119894)

119902

119894minus1

sum119896=1

120588119896 +

119894

sum119896=1

120588119896119882(119896)

119902 + 119864 [1198780]

119882(119894)

119902 =sum119894

119896=1 120588119896119882(119896)119902 + 119864 [1198780]

1 minus 120590119894minus1

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

(14)

Using (9) finally gives

119882(119894)

119902 =sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (15)

The above equation holds as long as 120590119894 = sum119903

119896=1 120588119896 lt 1Therefore from Littlersquos formula

119871(119894)

119902 =

119903

sum119896=1

120582119894119882(119894)

119896=

120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (16)

The total expected system size in each of the single channelsis

119871119902 =

119903

sum119894=1

119871119894

119902 =120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (17)

32 Mathematical Modelling of Mobile E-Health CenterUnlike the MM1Pr the MMcPr is governed by iden-tical exponential distributions for each priority at each of the119888 channels within a station As earlier said our service rate isequal throughout the experiment We define

120588119896 =120582119896

119888120583119896 (1 le 119896 le 119903) (18)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 120588 =120582

119888120583) (19)

where the system is stationary for 120588 lt 1 and

119882(119894)

119902 =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [1198780] (20)

where 119878119896 is the time required to serve 119899119896 mobile requests ofthe 119896th priority in the line ahead of the consumer 1198781015840119896 is theservice time of the 1198991015840119896 consumers of priority 119896 which arriveduring119882(119894)119902 1198780 is the amount of time remaining until the nextserver becomes available

Therefore

119864 [1198780]

= Pr (all servers are busy within a service station)

sdot 119864 [1198780 | all server are busy within a service station]

= (

infin

sum119899minus119888

119875119899)1

119888120583

= 1198750 (

infin

sum119899minus119888

119888120588119899

119888119899minus119888119888)1

119888120583=1198750 (119888120588)

119888

119888 (1 minus 119901)

=(119888120588)119888

119888 (1 minus 120588) (119888120583)[

119888minus1

sum119899=0

(119888120588)119899

119899+

(119888120588)119888

119888 (1 minus 120588)]

minus1

(21)

6 Journal of Applied Mathematics

but

119864 [1198780] = 120588

119903

sum119896=1

1

119906119896

120588119896

120588=

119903

sum119896=1

120588119896

119906119896

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

119882(119894)

119902 =sum119903

119896=1 (120588119896119906119896)

(1 minus 120590119894minus1) (1 minus 120590119894)

(22)

Therefore

119882(119894)

119902 =[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

119879119882(119894)

119902st =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

=[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

(23)

The expected time taken in a service station is

119882119902st =119903

sum119894=1

120582119894

120582119882(119894)

119902st (24)

The overall average time taken in 119895 service stations is

119882(ave)119902st =sum119895

119899=1 lceilsum119903

119894=1 (120582119894120582)119882(119894)119902 rceil

119895 (25)

33 Mathematical Modelling of Dispatcher-Out Ourdispatcher-out is similar to the dispatcher-in therefore thewaiting time is derived using (1) to (15) and (18) We obtain

119882119879dispout119902 =

119903

sum119894=1

119882119894

119902 (26)

The total waiting time by say class 119894 priority is

119882119894tot119902 = 119882

119894

119902din +119882119894

119902st +119882119894

119902dout (27)

while the total waiting time experienced in the queue by thewhole classes is

119908119902 =

119898

sum119899=1

119882119894tot119902

119899 (28)

34 Numerical Validation and Simulation First we validateour mathematical solution with the simulation to ascertainthe degree of correction This is done by considering fiveclasses of consumersrsquo arrival These are represented as fivearrival processes 1205821 1205822 1205823 1205824 and 1205825 where 1205821 = 1205822 =1205823 = 1205824 = 1205825 and 120582 = 1205821 + 1205822 + 1205823 + 1205824 + 1205825

Weuse theWolframMathematica 90 as themathematicaltool for our validation results and arena 145 as the simulator

Table 2 Simulation and analytical

120588 Sim Ana01 0000681 000068102 0001502 000150203 0002612 000261204 0004006 000400605 000592 00059206 0008751 0008907 0013447 001344708 0021933 002301909 0047009 00496

0

001

002

003

004

005

006

0 02 04 06 08 1

SimulationAnalytical

Server utilization (120588)

Wai

ting

time (th

r)

Figure 3 Simulation and Analytical

We set 120582 = 100 200 300 970 respectively and 119888 =2 in each of the service stations We then simulate thisexperiment using Arena discrete event simulator version 145with the same values to ascertain the degree of variabilityThis simulation was run with replication length of 1000 in 24hours per day with base time in hours and it was replicated 5times The service rate was set to 0001 for the dispatcher-inand 00005 for each of the servers in the web queue stationsand the dispatcher-out

In addition we set up a similar experiment with thesame configurations but under a nonpriority discipline usingFCFS discipline The illustration of this model is shown bynumerical examples and the impact on the five performancesof the priority classes is analyzed under the Results andDiscussion section

4 Results and Discussion

Theanalytical results and that of our simulation are comparedand the results are shown inTable 2 and Figure 3 respectivelyThe degree of variation is hardly noticed until 120588 rarr 1 but thecoefficient of variation is very small and less than unity that iswhy in Figure 3 the analytical colour overshadowed the sim-ulation colour at the initial stage Table 3 provides the results

Journal of Applied Mathematics 7

Table3Waitin

gtim

e(sec)andidleperio

d(

)

120588C1

sC2

sC3

sC4

sC5

sTo

tal

C1C2

C3C4

C5To

tal

NPP

NP

01

000

0123

000

0136

000

0137

000

0141

000

0145

000

0681

000

0131

000

0141

000

0136

000

0136

000

0135

000

0681

02

000

0255

000

0273

000

0299

000

0324

000

035

0001502

000

0302

000

0302

000

0301

000

0302

000

0295

0001502

03

000

039

000

0441

000

0513

000

0584

000

0685

0002612

000

0515

000

0515

000

0529

000

0526

000

0528

0002614

04

000

0537

000

0623

000

0756

000

0924

000116

7000

4006

000

0802

000

079

000

0798

000

0806

000

0808

000

4003

05

000

0676

000

085

0001074

0001394

0001926

000592

000117

8000118

2000119

7000118

2000118

50005923

06

000

083

0001083

0001466

0002087

0003285

0008751

0001754

000175

0001742

0001758

0001754

0008758

07

000

0993

0001354

0001954

0003155

0005991

0013447

0002695

0002677

0002688

0002694

0002697

0013451

08

000115

0001646

0002581

000

4752

0011803

0021933

000

4371

000

4366

000

4373

000

4386

000

4394

0021889

09

0001311

0002001

0003431

0007494

0032772

0047009

000

9372

000

9421

000

9384

000

9407

000

9462

0047046

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Journal of Applied Mathematics 3

WAPapplication

NETapplication

WAPapplication Applet J2EE

client

Law levelresources

Knowledgeresources Services

Enabling information bus for dynamic service selection

Request with QoS Response

Multimediainterfaces

Middlewarelayer

Gridinfrastructure

layer

SMME enablers

Utility broker

Resource repository

Figure 1 GUISET architecture

in a single server accumulating priority queue with Poissonarrival and general distribution service time

All these authors have made one or more contributionsto the existing knowledge These works have given us theopportunity to make our contribution based on the fewobservations we noticed For instance the works of [12 1415 20 22] were based on FCFS or SJN which could notwork in e-health mobile service where the e-mobile eventsare prioritized Also the generalized approach used by [12]could not reflect the real Cloud market of today The work of[16] produces a good result but [17] reveals that preemptionand migration of virtual machines are costly

Our work is closely related to [23 24] where these authorsmodel the Cloud as series of queues What differentiate ourwork are the following

(i) each of our service stations is modelled asMMcPras against the MM1 proposed by these authors

(ii) no dedicated server is given or allocated to any classthereby reducing consumersrsquo waiting time

(iii) our research is in the context of mobile services

3 The General GUISETs Architecture andthe Proposed Middleware Model

We present two architectures the first is the general archi-tecture of the proposed GUISETs in Figure 1 and the secondis our proposed performance GUISETmiddleware prototypemodel in the context of e-health in Figure 2 The second iscalved out from the first as part of the services

The GUISETs architecture has three major layers themultimodal layer the middleware and the infrastructurallayer The multimodal layer consists of SMME enablingapplications which we refer to as the client sideThis includesthe WAP Net and other applications as shown in Figure 1The clients send mobile aware requests to the GUISETmiddleware and the middleware does the service discoveryselection and composition Apart from these it checks forauthentication and authorization and resolves the issue of

pricing strategy it ensures the provisioning of good qualityof service through better service discipline The third layer isthe infrastructure layer that contains the resource repositoryThese are low level knowledge and other services like e-health service

Our research is in this middleware where we focus onthe service discipline to be adopted in the context of mobilee-health where providers of service have different serviceofferings for mobile aware requests

Our proposed prototype GUISET model is shown inFigure 2 The health-aware mobile devices are connected tothe mobile networks via a base station for example throughbase transceiver station or access point that establishes andcontrols the connections and functional interfaces betweenthe networks and mobile devices We gather our healthinformation from [25ndash27]Themobile user information (egID and location BS BP) is recorded and the risk columnfield is classified into five levels that determine the mobileevent class as shown in Table 1 For example mobile eventthat has blood sugar greater than 200mgd or blood pressureof 180110 and above is classified as severe or very high riskwith class 1 and that between 140ndash200 and 160ndash169100ndash109is classified as moderate or high risk with class 2 Thesee-health mobile events are classified under five categoriesin this research as shown in Table 1 These are transmittedto the central processor which is the dispatcher-in serverthat provides authentication authorization order of request(service discipline) and accounting services based on thehome agent and subscribersrsquo data stored in databases Afterthat the requests are delivered to the right destination wherethe e-health mobile network services will be provided andresults are then dispatched back through the dispatcher-out One assumption is that the mobile gargets and theaccess points are already in place secondly the issues ofauthentication authorization and accounting services areout of scope of this researchOur research is to prioritize theseclasses so that urgent requests get access to solution fasterthan the less urgent ones The priority is such that the orderis in the form of class 1 mobile aware event having higher

4 Journal of Applied Mathematics

Table 1 The e-health mobile aware records

ID Location Blood sugar (mgdL) Blood pressure (mmHg) Risk Mobile event classSystolic Diastolic

XXXX1 Ngoma gt200 ge180 ge110 Very high (severe) C1XXXX2 Ongoye gt140 but lt200 160ndash179 100ndash109 High (moderate) C2XXXX3 Empangeni ge126 le139 140ndash159 90ndash99 Mild C3XXXX4 Esikhawini 100 but lt126 120ndash139 80ndash89 Warning C4XXXX5 Richards Bay 110 120 80 No (normal) C5

C2

C3

C4

C5

E-health queue center 1

center n

Dispatcher-in

SMs

SMs

SMsC1

Dispatcher-out

Base station center 2

E-health queue

E-health queue

Figure 2 Proposed GUISET mobile healthcare model

priority than classes 2 3 4 and 5When an incoming requestmeets lower one on the queue it takes over that request butwhen lower request is already underprocessed that requesthas to be completed When requests of the same priorityare on the queue then the order is based on First ComeFirst Served (FCFS) All requests are sent to the dispatcher-inserver where they are then distributed to the e-health centerstations for processing The processed request then movesthrough the dispatcher-out as the outlet

Unlike most related works [16 22 24] where the non-preemptive policy is implemented at the first point of entryalone we model our non-preemptive model at every point ofqueue that is the dispatcher-in queue as MM1Pr the e-health centers as MMcPr and the dispatcher-out queueas MM1Pr This is because at every point of queue thereis likely tendency that higher priority will arrive when lowerone is on the queue

This proposed model assumes that the arrival and theservice process are exponentially distributed and due tolarge number of consumers entering the market for requestwe assume an infinite population To get our performancemeasure we follow the law of conservation of flow and thesteps stated in [28]

31 Mathematical Modelling of Dispatcher-In Queue Letmobile event with service of the 119896th priority (the smaller thenumber the higher the priority) arrive before the dispatcher-in according to Poisson distribution with parameter 120582119896 (119896 =1 2 119903) and these consumers wait on First Come FirstServed basis within their respective priorities Let the servicedistribution for the 119896th priority be exponential with mean1120583119896 As earlier said whatever the priority of a unit inservice is it has to complete its service before another itemis admitted

We define

120588119896 =120582119896

120583119896 (1 le 119896 le 119903)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 0 120590119903 equiv 120588)

(1)

The system stationary for 120590119903 = 120588 lt 1 Let an event of priority119894 arrives at time 1199050 and enters service at time 1199051 Its line wait isthus 119879119902 = 1199051 minus 1199050 At 1199050 let us say we have 1198991 of priority one inline ahead of this new arrival 1198992 of priority two 1198993 of prioritythree and so on Let 1198780 be the total time required to finish thejob already in service and 119878119896 the total time required to serve119899119896 During the new mobile request waiting time 119879119902 (say) 119899

1015840119896

mobile request of priority 119896 lt 1 will arrive and go to serviceahead of this current arrival If 1198781015840119896 is the total service time ofall 1198991015840119896 then it can be seen that

119879119902 =

119894minus1

sum119896=1

1198781015840

119896 +

119894

sum119896=1

119878119896 + 1198780 (2)

taking the expected values from both sides of the foregoingthen

1198821015840

119896 = 119864 [119879119902] =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [119878119896] + 119864 [1198780] (3)

Since 120590119894minus1 lt 120590119894 for all 119894 then 120588 lt 1 implies that 120590119894minus1 lt 1 forall 119894

To find 119864[1198780] we observe that the combined servicedistribution is the mixed exponential which is formed fromthe law of total probability as

119861 (119905) =

119894

sum119896=1

120582119896

120582(1 minus 119890

minus120583119896119905) (4)

Journal of Applied Mathematics 5

where

120582 =

119903

sum119896=1

120582119896 (5)

The random variable remaining time of service 1198780 has thevalue 0 when the system is idle hence

119864 [1198780] = Pr system is busy 119864 [1198780 | busy system] (6)But the probability that the system is busy is

120582 =

119903

sum119896=1

120582119896

120582

1

120583119896= 120588 (7)

where 120588 is the server utilization and

119864 [1198780 | busy system]

=

119903

sum119896=1

120582119896119864 [1198780 | system busy wit 119896 type cutomer]

sdot Pr mobile request has priority 119896

=

119903

sum119896=1

1

120583119896

120588119896

120588

(8)

therefore

119864 [1198780] = 120588

119903

sum119896=1

1

120583119896

120588119896

120588=

119903

sum119896=1

120588119896

120588 (9)

Since 119899119896 and the service times of individual mobile requests119878(119899)

119896are independent

119864 [119878119896] = 119864 [119899119896119878(119899)

119896] = 119864 [119899119896] 119864 [119878

(119899)

119896] =

119864 [119899119896]

120583119896 (10)

Utilizing Littlersquos formula then gives

119864 [119878119896] =120582119896119882(119896)119902

120583119896= 120588119896119882

(119896)

119902 (11)

similarly

119864 [1198781015840

119896] =119864 [1198991015840119896]

120583119896

(12)

and then utilizing the uniform properties of the Poisson wehave

119864 [1198781015840

119896] =119864 [119899119896]

120583119896

120582119896119882(119894)119902

120583119896 (13)

therefore119882(119894)119902 which is the waiting time for mobile request of119894 priority is

119882(119894)

119902 = 119882(119894)

119902

119894minus1

sum119896=1

120588119896 +

119894

sum119896=1

120588119896119882(119896)

119902 + 119864 [1198780]

119882(119894)

119902 =sum119894

119896=1 120588119896119882(119896)119902 + 119864 [1198780]

1 minus 120590119894minus1

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

(14)

Using (9) finally gives

119882(119894)

119902 =sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (15)

The above equation holds as long as 120590119894 = sum119903

119896=1 120588119896 lt 1Therefore from Littlersquos formula

119871(119894)

119902 =

119903

sum119896=1

120582119894119882(119894)

119896=

120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (16)

The total expected system size in each of the single channelsis

119871119902 =

119903

sum119894=1

119871119894

119902 =120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (17)

32 Mathematical Modelling of Mobile E-Health CenterUnlike the MM1Pr the MMcPr is governed by iden-tical exponential distributions for each priority at each of the119888 channels within a station As earlier said our service rate isequal throughout the experiment We define

120588119896 =120582119896

119888120583119896 (1 le 119896 le 119903) (18)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 120588 =120582

119888120583) (19)

where the system is stationary for 120588 lt 1 and

119882(119894)

119902 =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [1198780] (20)

where 119878119896 is the time required to serve 119899119896 mobile requests ofthe 119896th priority in the line ahead of the consumer 1198781015840119896 is theservice time of the 1198991015840119896 consumers of priority 119896 which arriveduring119882(119894)119902 1198780 is the amount of time remaining until the nextserver becomes available

Therefore

119864 [1198780]

= Pr (all servers are busy within a service station)

sdot 119864 [1198780 | all server are busy within a service station]

= (

infin

sum119899minus119888

119875119899)1

119888120583

= 1198750 (

infin

sum119899minus119888

119888120588119899

119888119899minus119888119888)1

119888120583=1198750 (119888120588)

119888

119888 (1 minus 119901)

=(119888120588)119888

119888 (1 minus 120588) (119888120583)[

119888minus1

sum119899=0

(119888120588)119899

119899+

(119888120588)119888

119888 (1 minus 120588)]

minus1

(21)

6 Journal of Applied Mathematics

but

119864 [1198780] = 120588

119903

sum119896=1

1

119906119896

120588119896

120588=

119903

sum119896=1

120588119896

119906119896

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

119882(119894)

119902 =sum119903

119896=1 (120588119896119906119896)

(1 minus 120590119894minus1) (1 minus 120590119894)

(22)

Therefore

119882(119894)

119902 =[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

119879119882(119894)

119902st =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

=[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

(23)

The expected time taken in a service station is

119882119902st =119903

sum119894=1

120582119894

120582119882(119894)

119902st (24)

The overall average time taken in 119895 service stations is

119882(ave)119902st =sum119895

119899=1 lceilsum119903

119894=1 (120582119894120582)119882(119894)119902 rceil

119895 (25)

33 Mathematical Modelling of Dispatcher-Out Ourdispatcher-out is similar to the dispatcher-in therefore thewaiting time is derived using (1) to (15) and (18) We obtain

119882119879dispout119902 =

119903

sum119894=1

119882119894

119902 (26)

The total waiting time by say class 119894 priority is

119882119894tot119902 = 119882

119894

119902din +119882119894

119902st +119882119894

119902dout (27)

while the total waiting time experienced in the queue by thewhole classes is

119908119902 =

119898

sum119899=1

119882119894tot119902

119899 (28)

34 Numerical Validation and Simulation First we validateour mathematical solution with the simulation to ascertainthe degree of correction This is done by considering fiveclasses of consumersrsquo arrival These are represented as fivearrival processes 1205821 1205822 1205823 1205824 and 1205825 where 1205821 = 1205822 =1205823 = 1205824 = 1205825 and 120582 = 1205821 + 1205822 + 1205823 + 1205824 + 1205825

Weuse theWolframMathematica 90 as themathematicaltool for our validation results and arena 145 as the simulator

Table 2 Simulation and analytical

120588 Sim Ana01 0000681 000068102 0001502 000150203 0002612 000261204 0004006 000400605 000592 00059206 0008751 0008907 0013447 001344708 0021933 002301909 0047009 00496

0

001

002

003

004

005

006

0 02 04 06 08 1

SimulationAnalytical

Server utilization (120588)

Wai

ting

time (th

r)

Figure 3 Simulation and Analytical

We set 120582 = 100 200 300 970 respectively and 119888 =2 in each of the service stations We then simulate thisexperiment using Arena discrete event simulator version 145with the same values to ascertain the degree of variabilityThis simulation was run with replication length of 1000 in 24hours per day with base time in hours and it was replicated 5times The service rate was set to 0001 for the dispatcher-inand 00005 for each of the servers in the web queue stationsand the dispatcher-out

In addition we set up a similar experiment with thesame configurations but under a nonpriority discipline usingFCFS discipline The illustration of this model is shown bynumerical examples and the impact on the five performancesof the priority classes is analyzed under the Results andDiscussion section

4 Results and Discussion

Theanalytical results and that of our simulation are comparedand the results are shown inTable 2 and Figure 3 respectivelyThe degree of variation is hardly noticed until 120588 rarr 1 but thecoefficient of variation is very small and less than unity that iswhy in Figure 3 the analytical colour overshadowed the sim-ulation colour at the initial stage Table 3 provides the results

Journal of Applied Mathematics 7

Table3Waitin

gtim

e(sec)andidleperio

d(

)

120588C1

sC2

sC3

sC4

sC5

sTo

tal

C1C2

C3C4

C5To

tal

NPP

NP

01

000

0123

000

0136

000

0137

000

0141

000

0145

000

0681

000

0131

000

0141

000

0136

000

0136

000

0135

000

0681

02

000

0255

000

0273

000

0299

000

0324

000

035

0001502

000

0302

000

0302

000

0301

000

0302

000

0295

0001502

03

000

039

000

0441

000

0513

000

0584

000

0685

0002612

000

0515

000

0515

000

0529

000

0526

000

0528

0002614

04

000

0537

000

0623

000

0756

000

0924

000116

7000

4006

000

0802

000

079

000

0798

000

0806

000

0808

000

4003

05

000

0676

000

085

0001074

0001394

0001926

000592

000117

8000118

2000119

7000118

2000118

50005923

06

000

083

0001083

0001466

0002087

0003285

0008751

0001754

000175

0001742

0001758

0001754

0008758

07

000

0993

0001354

0001954

0003155

0005991

0013447

0002695

0002677

0002688

0002694

0002697

0013451

08

000115

0001646

0002581

000

4752

0011803

0021933

000

4371

000

4366

000

4373

000

4386

000

4394

0021889

09

0001311

0002001

0003431

0007494

0032772

0047009

000

9372

000

9421

000

9384

000

9407

000

9462

0047046

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

4 Journal of Applied Mathematics

Table 1 The e-health mobile aware records

ID Location Blood sugar (mgdL) Blood pressure (mmHg) Risk Mobile event classSystolic Diastolic

XXXX1 Ngoma gt200 ge180 ge110 Very high (severe) C1XXXX2 Ongoye gt140 but lt200 160ndash179 100ndash109 High (moderate) C2XXXX3 Empangeni ge126 le139 140ndash159 90ndash99 Mild C3XXXX4 Esikhawini 100 but lt126 120ndash139 80ndash89 Warning C4XXXX5 Richards Bay 110 120 80 No (normal) C5

C2

C3

C4

C5

E-health queue center 1

center n

Dispatcher-in

SMs

SMs

SMsC1

Dispatcher-out

Base station center 2

E-health queue

E-health queue

Figure 2 Proposed GUISET mobile healthcare model

priority than classes 2 3 4 and 5When an incoming requestmeets lower one on the queue it takes over that request butwhen lower request is already underprocessed that requesthas to be completed When requests of the same priorityare on the queue then the order is based on First ComeFirst Served (FCFS) All requests are sent to the dispatcher-inserver where they are then distributed to the e-health centerstations for processing The processed request then movesthrough the dispatcher-out as the outlet

Unlike most related works [16 22 24] where the non-preemptive policy is implemented at the first point of entryalone we model our non-preemptive model at every point ofqueue that is the dispatcher-in queue as MM1Pr the e-health centers as MMcPr and the dispatcher-out queueas MM1Pr This is because at every point of queue thereis likely tendency that higher priority will arrive when lowerone is on the queue

This proposed model assumes that the arrival and theservice process are exponentially distributed and due tolarge number of consumers entering the market for requestwe assume an infinite population To get our performancemeasure we follow the law of conservation of flow and thesteps stated in [28]

31 Mathematical Modelling of Dispatcher-In Queue Letmobile event with service of the 119896th priority (the smaller thenumber the higher the priority) arrive before the dispatcher-in according to Poisson distribution with parameter 120582119896 (119896 =1 2 119903) and these consumers wait on First Come FirstServed basis within their respective priorities Let the servicedistribution for the 119896th priority be exponential with mean1120583119896 As earlier said whatever the priority of a unit inservice is it has to complete its service before another itemis admitted

We define

120588119896 =120582119896

120583119896 (1 le 119896 le 119903)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 0 120590119903 equiv 120588)

(1)

The system stationary for 120590119903 = 120588 lt 1 Let an event of priority119894 arrives at time 1199050 and enters service at time 1199051 Its line wait isthus 119879119902 = 1199051 minus 1199050 At 1199050 let us say we have 1198991 of priority one inline ahead of this new arrival 1198992 of priority two 1198993 of prioritythree and so on Let 1198780 be the total time required to finish thejob already in service and 119878119896 the total time required to serve119899119896 During the new mobile request waiting time 119879119902 (say) 119899

1015840119896

mobile request of priority 119896 lt 1 will arrive and go to serviceahead of this current arrival If 1198781015840119896 is the total service time ofall 1198991015840119896 then it can be seen that

119879119902 =

119894minus1

sum119896=1

1198781015840

119896 +

119894

sum119896=1

119878119896 + 1198780 (2)

taking the expected values from both sides of the foregoingthen

1198821015840

119896 = 119864 [119879119902] =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [119878119896] + 119864 [1198780] (3)

Since 120590119894minus1 lt 120590119894 for all 119894 then 120588 lt 1 implies that 120590119894minus1 lt 1 forall 119894

To find 119864[1198780] we observe that the combined servicedistribution is the mixed exponential which is formed fromthe law of total probability as

119861 (119905) =

119894

sum119896=1

120582119896

120582(1 minus 119890

minus120583119896119905) (4)

Journal of Applied Mathematics 5

where

120582 =

119903

sum119896=1

120582119896 (5)

The random variable remaining time of service 1198780 has thevalue 0 when the system is idle hence

119864 [1198780] = Pr system is busy 119864 [1198780 | busy system] (6)But the probability that the system is busy is

120582 =

119903

sum119896=1

120582119896

120582

1

120583119896= 120588 (7)

where 120588 is the server utilization and

119864 [1198780 | busy system]

=

119903

sum119896=1

120582119896119864 [1198780 | system busy wit 119896 type cutomer]

sdot Pr mobile request has priority 119896

=

119903

sum119896=1

1

120583119896

120588119896

120588

(8)

therefore

119864 [1198780] = 120588

119903

sum119896=1

1

120583119896

120588119896

120588=

119903

sum119896=1

120588119896

120588 (9)

Since 119899119896 and the service times of individual mobile requests119878(119899)

119896are independent

119864 [119878119896] = 119864 [119899119896119878(119899)

119896] = 119864 [119899119896] 119864 [119878

(119899)

119896] =

119864 [119899119896]

120583119896 (10)

Utilizing Littlersquos formula then gives

119864 [119878119896] =120582119896119882(119896)119902

120583119896= 120588119896119882

(119896)

119902 (11)

similarly

119864 [1198781015840

119896] =119864 [1198991015840119896]

120583119896

(12)

and then utilizing the uniform properties of the Poisson wehave

119864 [1198781015840

119896] =119864 [119899119896]

120583119896

120582119896119882(119894)119902

120583119896 (13)

therefore119882(119894)119902 which is the waiting time for mobile request of119894 priority is

119882(119894)

119902 = 119882(119894)

119902

119894minus1

sum119896=1

120588119896 +

119894

sum119896=1

120588119896119882(119896)

119902 + 119864 [1198780]

119882(119894)

119902 =sum119894

119896=1 120588119896119882(119896)119902 + 119864 [1198780]

1 minus 120590119894minus1

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

(14)

Using (9) finally gives

119882(119894)

119902 =sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (15)

The above equation holds as long as 120590119894 = sum119903

119896=1 120588119896 lt 1Therefore from Littlersquos formula

119871(119894)

119902 =

119903

sum119896=1

120582119894119882(119894)

119896=

120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (16)

The total expected system size in each of the single channelsis

119871119902 =

119903

sum119894=1

119871119894

119902 =120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (17)

32 Mathematical Modelling of Mobile E-Health CenterUnlike the MM1Pr the MMcPr is governed by iden-tical exponential distributions for each priority at each of the119888 channels within a station As earlier said our service rate isequal throughout the experiment We define

120588119896 =120582119896

119888120583119896 (1 le 119896 le 119903) (18)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 120588 =120582

119888120583) (19)

where the system is stationary for 120588 lt 1 and

119882(119894)

119902 =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [1198780] (20)

where 119878119896 is the time required to serve 119899119896 mobile requests ofthe 119896th priority in the line ahead of the consumer 1198781015840119896 is theservice time of the 1198991015840119896 consumers of priority 119896 which arriveduring119882(119894)119902 1198780 is the amount of time remaining until the nextserver becomes available

Therefore

119864 [1198780]

= Pr (all servers are busy within a service station)

sdot 119864 [1198780 | all server are busy within a service station]

= (

infin

sum119899minus119888

119875119899)1

119888120583

= 1198750 (

infin

sum119899minus119888

119888120588119899

119888119899minus119888119888)1

119888120583=1198750 (119888120588)

119888

119888 (1 minus 119901)

=(119888120588)119888

119888 (1 minus 120588) (119888120583)[

119888minus1

sum119899=0

(119888120588)119899

119899+

(119888120588)119888

119888 (1 minus 120588)]

minus1

(21)

6 Journal of Applied Mathematics

but

119864 [1198780] = 120588

119903

sum119896=1

1

119906119896

120588119896

120588=

119903

sum119896=1

120588119896

119906119896

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

119882(119894)

119902 =sum119903

119896=1 (120588119896119906119896)

(1 minus 120590119894minus1) (1 minus 120590119894)

(22)

Therefore

119882(119894)

119902 =[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

119879119882(119894)

119902st =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

=[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

(23)

The expected time taken in a service station is

119882119902st =119903

sum119894=1

120582119894

120582119882(119894)

119902st (24)

The overall average time taken in 119895 service stations is

119882(ave)119902st =sum119895

119899=1 lceilsum119903

119894=1 (120582119894120582)119882(119894)119902 rceil

119895 (25)

33 Mathematical Modelling of Dispatcher-Out Ourdispatcher-out is similar to the dispatcher-in therefore thewaiting time is derived using (1) to (15) and (18) We obtain

119882119879dispout119902 =

119903

sum119894=1

119882119894

119902 (26)

The total waiting time by say class 119894 priority is

119882119894tot119902 = 119882

119894

119902din +119882119894

119902st +119882119894

119902dout (27)

while the total waiting time experienced in the queue by thewhole classes is

119908119902 =

119898

sum119899=1

119882119894tot119902

119899 (28)

34 Numerical Validation and Simulation First we validateour mathematical solution with the simulation to ascertainthe degree of correction This is done by considering fiveclasses of consumersrsquo arrival These are represented as fivearrival processes 1205821 1205822 1205823 1205824 and 1205825 where 1205821 = 1205822 =1205823 = 1205824 = 1205825 and 120582 = 1205821 + 1205822 + 1205823 + 1205824 + 1205825

Weuse theWolframMathematica 90 as themathematicaltool for our validation results and arena 145 as the simulator

Table 2 Simulation and analytical

120588 Sim Ana01 0000681 000068102 0001502 000150203 0002612 000261204 0004006 000400605 000592 00059206 0008751 0008907 0013447 001344708 0021933 002301909 0047009 00496

0

001

002

003

004

005

006

0 02 04 06 08 1

SimulationAnalytical

Server utilization (120588)

Wai

ting

time (th

r)

Figure 3 Simulation and Analytical

We set 120582 = 100 200 300 970 respectively and 119888 =2 in each of the service stations We then simulate thisexperiment using Arena discrete event simulator version 145with the same values to ascertain the degree of variabilityThis simulation was run with replication length of 1000 in 24hours per day with base time in hours and it was replicated 5times The service rate was set to 0001 for the dispatcher-inand 00005 for each of the servers in the web queue stationsand the dispatcher-out

In addition we set up a similar experiment with thesame configurations but under a nonpriority discipline usingFCFS discipline The illustration of this model is shown bynumerical examples and the impact on the five performancesof the priority classes is analyzed under the Results andDiscussion section

4 Results and Discussion

Theanalytical results and that of our simulation are comparedand the results are shown inTable 2 and Figure 3 respectivelyThe degree of variation is hardly noticed until 120588 rarr 1 but thecoefficient of variation is very small and less than unity that iswhy in Figure 3 the analytical colour overshadowed the sim-ulation colour at the initial stage Table 3 provides the results

Journal of Applied Mathematics 7

Table3Waitin

gtim

e(sec)andidleperio

d(

)

120588C1

sC2

sC3

sC4

sC5

sTo

tal

C1C2

C3C4

C5To

tal

NPP

NP

01

000

0123

000

0136

000

0137

000

0141

000

0145

000

0681

000

0131

000

0141

000

0136

000

0136

000

0135

000

0681

02

000

0255

000

0273

000

0299

000

0324

000

035

0001502

000

0302

000

0302

000

0301

000

0302

000

0295

0001502

03

000

039

000

0441

000

0513

000

0584

000

0685

0002612

000

0515

000

0515

000

0529

000

0526

000

0528

0002614

04

000

0537

000

0623

000

0756

000

0924

000116

7000

4006

000

0802

000

079

000

0798

000

0806

000

0808

000

4003

05

000

0676

000

085

0001074

0001394

0001926

000592

000117

8000118

2000119

7000118

2000118

50005923

06

000

083

0001083

0001466

0002087

0003285

0008751

0001754

000175

0001742

0001758

0001754

0008758

07

000

0993

0001354

0001954

0003155

0005991

0013447

0002695

0002677

0002688

0002694

0002697

0013451

08

000115

0001646

0002581

000

4752

0011803

0021933

000

4371

000

4366

000

4373

000

4386

000

4394

0021889

09

0001311

0002001

0003431

0007494

0032772

0047009

000

9372

000

9421

000

9384

000

9407

000

9462

0047046

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Journal of Applied Mathematics 5

where

120582 =

119903

sum119896=1

120582119896 (5)

The random variable remaining time of service 1198780 has thevalue 0 when the system is idle hence

119864 [1198780] = Pr system is busy 119864 [1198780 | busy system] (6)But the probability that the system is busy is

120582 =

119903

sum119896=1

120582119896

120582

1

120583119896= 120588 (7)

where 120588 is the server utilization and

119864 [1198780 | busy system]

=

119903

sum119896=1

120582119896119864 [1198780 | system busy wit 119896 type cutomer]

sdot Pr mobile request has priority 119896

=

119903

sum119896=1

1

120583119896

120588119896

120588

(8)

therefore

119864 [1198780] = 120588

119903

sum119896=1

1

120583119896

120588119896

120588=

119903

sum119896=1

120588119896

120588 (9)

Since 119899119896 and the service times of individual mobile requests119878(119899)

119896are independent

119864 [119878119896] = 119864 [119899119896119878(119899)

119896] = 119864 [119899119896] 119864 [119878

(119899)

119896] =

119864 [119899119896]

120583119896 (10)

Utilizing Littlersquos formula then gives

119864 [119878119896] =120582119896119882(119896)119902

120583119896= 120588119896119882

(119896)

119902 (11)

similarly

119864 [1198781015840

119896] =119864 [1198991015840119896]

120583119896

(12)

and then utilizing the uniform properties of the Poisson wehave

119864 [1198781015840

119896] =119864 [119899119896]

120583119896

120582119896119882(119894)119902

120583119896 (13)

therefore119882(119894)119902 which is the waiting time for mobile request of119894 priority is

119882(119894)

119902 = 119882(119894)

119902

119894minus1

sum119896=1

120588119896 +

119894

sum119896=1

120588119896119882(119896)

119902 + 119864 [1198780]

119882(119894)

119902 =sum119894

119896=1 120588119896119882(119896)119902 + 119864 [1198780]

1 minus 120590119894minus1

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

(14)

Using (9) finally gives

119882(119894)

119902 =sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (15)

The above equation holds as long as 120590119894 = sum119903

119896=1 120588119896 lt 1Therefore from Littlersquos formula

119871(119894)

119902 =

119903

sum119896=1

120582119894119882(119894)

119896=

120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (16)

The total expected system size in each of the single channelsis

119871119902 =

119903

sum119894=1

119871119894

119902 =120582119894sum119903

119896=1 120588119896120583119896

(1 minus 120590119894minus1) (1 minus 120590119894) (17)

32 Mathematical Modelling of Mobile E-Health CenterUnlike the MM1Pr the MMcPr is governed by iden-tical exponential distributions for each priority at each of the119888 channels within a station As earlier said our service rate isequal throughout the experiment We define

120588119896 =120582119896

119888120583119896 (1 le 119896 le 119903) (18)

120590119896 =

119896

sum119894=1

120588119896 (1205900 equiv 120588 =120582

119888120583) (19)

where the system is stationary for 120588 lt 1 and

119882(119894)

119902 =

119894minus1

sum119896=1

119864 [1198781015840

119896] +

119894

sum119896=1

119864 [1198780] (20)

where 119878119896 is the time required to serve 119899119896 mobile requests ofthe 119896th priority in the line ahead of the consumer 1198781015840119896 is theservice time of the 1198991015840119896 consumers of priority 119896 which arriveduring119882(119894)119902 1198780 is the amount of time remaining until the nextserver becomes available

Therefore

119864 [1198780]

= Pr (all servers are busy within a service station)

sdot 119864 [1198780 | all server are busy within a service station]

= (

infin

sum119899minus119888

119875119899)1

119888120583

= 1198750 (

infin

sum119899minus119888

119888120588119899

119888119899minus119888119888)1

119888120583=1198750 (119888120588)

119888

119888 (1 minus 119901)

=(119888120588)119888

119888 (1 minus 120588) (119888120583)[

119888minus1

sum119899=0

(119888120588)119899

119899+

(119888120588)119888

119888 (1 minus 120588)]

minus1

(21)

6 Journal of Applied Mathematics

but

119864 [1198780] = 120588

119903

sum119896=1

1

119906119896

120588119896

120588=

119903

sum119896=1

120588119896

119906119896

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

119882(119894)

119902 =sum119903

119896=1 (120588119896119906119896)

(1 minus 120590119894minus1) (1 minus 120590119894)

(22)

Therefore

119882(119894)

119902 =[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

119879119882(119894)

119902st =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

=[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

(23)

The expected time taken in a service station is

119882119902st =119903

sum119894=1

120582119894

120582119882(119894)

119902st (24)

The overall average time taken in 119895 service stations is

119882(ave)119902st =sum119895

119899=1 lceilsum119903

119894=1 (120582119894120582)119882(119894)119902 rceil

119895 (25)

33 Mathematical Modelling of Dispatcher-Out Ourdispatcher-out is similar to the dispatcher-in therefore thewaiting time is derived using (1) to (15) and (18) We obtain

119882119879dispout119902 =

119903

sum119894=1

119882119894

119902 (26)

The total waiting time by say class 119894 priority is

119882119894tot119902 = 119882

119894

119902din +119882119894

119902st +119882119894

119902dout (27)

while the total waiting time experienced in the queue by thewhole classes is

119908119902 =

119898

sum119899=1

119882119894tot119902

119899 (28)

34 Numerical Validation and Simulation First we validateour mathematical solution with the simulation to ascertainthe degree of correction This is done by considering fiveclasses of consumersrsquo arrival These are represented as fivearrival processes 1205821 1205822 1205823 1205824 and 1205825 where 1205821 = 1205822 =1205823 = 1205824 = 1205825 and 120582 = 1205821 + 1205822 + 1205823 + 1205824 + 1205825

Weuse theWolframMathematica 90 as themathematicaltool for our validation results and arena 145 as the simulator

Table 2 Simulation and analytical

120588 Sim Ana01 0000681 000068102 0001502 000150203 0002612 000261204 0004006 000400605 000592 00059206 0008751 0008907 0013447 001344708 0021933 002301909 0047009 00496

0

001

002

003

004

005

006

0 02 04 06 08 1

SimulationAnalytical

Server utilization (120588)

Wai

ting

time (th

r)

Figure 3 Simulation and Analytical

We set 120582 = 100 200 300 970 respectively and 119888 =2 in each of the service stations We then simulate thisexperiment using Arena discrete event simulator version 145with the same values to ascertain the degree of variabilityThis simulation was run with replication length of 1000 in 24hours per day with base time in hours and it was replicated 5times The service rate was set to 0001 for the dispatcher-inand 00005 for each of the servers in the web queue stationsand the dispatcher-out

In addition we set up a similar experiment with thesame configurations but under a nonpriority discipline usingFCFS discipline The illustration of this model is shown bynumerical examples and the impact on the five performancesof the priority classes is analyzed under the Results andDiscussion section

4 Results and Discussion

Theanalytical results and that of our simulation are comparedand the results are shown inTable 2 and Figure 3 respectivelyThe degree of variation is hardly noticed until 120588 rarr 1 but thecoefficient of variation is very small and less than unity that iswhy in Figure 3 the analytical colour overshadowed the sim-ulation colour at the initial stage Table 3 provides the results

Journal of Applied Mathematics 7

Table3Waitin

gtim

e(sec)andidleperio

d(

)

120588C1

sC2

sC3

sC4

sC5

sTo

tal

C1C2

C3C4

C5To

tal

NPP

NP

01

000

0123

000

0136

000

0137

000

0141

000

0145

000

0681

000

0131

000

0141

000

0136

000

0136

000

0135

000

0681

02

000

0255

000

0273

000

0299

000

0324

000

035

0001502

000

0302

000

0302

000

0301

000

0302

000

0295

0001502

03

000

039

000

0441

000

0513

000

0584

000

0685

0002612

000

0515

000

0515

000

0529

000

0526

000

0528

0002614

04

000

0537

000

0623

000

0756

000

0924

000116

7000

4006

000

0802

000

079

000

0798

000

0806

000

0808

000

4003

05

000

0676

000

085

0001074

0001394

0001926

000592

000117

8000118

2000119

7000118

2000118

50005923

06

000

083

0001083

0001466

0002087

0003285

0008751

0001754

000175

0001742

0001758

0001754

0008758

07

000

0993

0001354

0001954

0003155

0005991

0013447

0002695

0002677

0002688

0002694

0002697

0013451

08

000115

0001646

0002581

000

4752

0011803

0021933

000

4371

000

4366

000

4373

000

4386

000

4394

0021889

09

0001311

0002001

0003431

0007494

0032772

0047009

000

9372

000

9421

000

9384

000

9407

000

9462

0047046

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

6 Journal of Applied Mathematics

but

119864 [1198780] = 120588

119903

sum119896=1

1

119906119896

120588119896

120588=

119903

sum119896=1

120588119896

119906119896

119882(119894)

119902 =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

119882(119894)

119902 =sum119903

119896=1 (120588119896119906119896)

(1 minus 120590119894minus1) (1 minus 120590119894)

(22)

Therefore

119882(119894)

119902 =[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

119879119882(119894)

119902st =119864 [1198780]

(1 minus 120590119894minus1) (1 minus 120590119894)

=[119888 (1 minus 120588) (119888120583)sum

119888minus1

119899=0 (119888120588)(119899minus119888)119899

+ 119888120583]minus1

(1 minus 120590119894minus1) (1 minus 120590119894)

(23)

The expected time taken in a service station is

119882119902st =119903

sum119894=1

120582119894

120582119882(119894)

119902st (24)

The overall average time taken in 119895 service stations is

119882(ave)119902st =sum119895

119899=1 lceilsum119903

119894=1 (120582119894120582)119882(119894)119902 rceil

119895 (25)

33 Mathematical Modelling of Dispatcher-Out Ourdispatcher-out is similar to the dispatcher-in therefore thewaiting time is derived using (1) to (15) and (18) We obtain

119882119879dispout119902 =

119903

sum119894=1

119882119894

119902 (26)

The total waiting time by say class 119894 priority is

119882119894tot119902 = 119882

119894

119902din +119882119894

119902st +119882119894

119902dout (27)

while the total waiting time experienced in the queue by thewhole classes is

119908119902 =

119898

sum119899=1

119882119894tot119902

119899 (28)

34 Numerical Validation and Simulation First we validateour mathematical solution with the simulation to ascertainthe degree of correction This is done by considering fiveclasses of consumersrsquo arrival These are represented as fivearrival processes 1205821 1205822 1205823 1205824 and 1205825 where 1205821 = 1205822 =1205823 = 1205824 = 1205825 and 120582 = 1205821 + 1205822 + 1205823 + 1205824 + 1205825

Weuse theWolframMathematica 90 as themathematicaltool for our validation results and arena 145 as the simulator

Table 2 Simulation and analytical

120588 Sim Ana01 0000681 000068102 0001502 000150203 0002612 000261204 0004006 000400605 000592 00059206 0008751 0008907 0013447 001344708 0021933 002301909 0047009 00496

0

001

002

003

004

005

006

0 02 04 06 08 1

SimulationAnalytical

Server utilization (120588)

Wai

ting

time (th

r)

Figure 3 Simulation and Analytical

We set 120582 = 100 200 300 970 respectively and 119888 =2 in each of the service stations We then simulate thisexperiment using Arena discrete event simulator version 145with the same values to ascertain the degree of variabilityThis simulation was run with replication length of 1000 in 24hours per day with base time in hours and it was replicated 5times The service rate was set to 0001 for the dispatcher-inand 00005 for each of the servers in the web queue stationsand the dispatcher-out

In addition we set up a similar experiment with thesame configurations but under a nonpriority discipline usingFCFS discipline The illustration of this model is shown bynumerical examples and the impact on the five performancesof the priority classes is analyzed under the Results andDiscussion section

4 Results and Discussion

Theanalytical results and that of our simulation are comparedand the results are shown inTable 2 and Figure 3 respectivelyThe degree of variation is hardly noticed until 120588 rarr 1 but thecoefficient of variation is very small and less than unity that iswhy in Figure 3 the analytical colour overshadowed the sim-ulation colour at the initial stage Table 3 provides the results

Journal of Applied Mathematics 7

Table3Waitin

gtim

e(sec)andidleperio

d(

)

120588C1

sC2

sC3

sC4

sC5

sTo

tal

C1C2

C3C4

C5To

tal

NPP

NP

01

000

0123

000

0136

000

0137

000

0141

000

0145

000

0681

000

0131

000

0141

000

0136

000

0136

000

0135

000

0681

02

000

0255

000

0273

000

0299

000

0324

000

035

0001502

000

0302

000

0302

000

0301

000

0302

000

0295

0001502

03

000

039

000

0441

000

0513

000

0584

000

0685

0002612

000

0515

000

0515

000

0529

000

0526

000

0528

0002614

04

000

0537

000

0623

000

0756

000

0924

000116

7000

4006

000

0802

000

079

000

0798

000

0806

000

0808

000

4003

05

000

0676

000

085

0001074

0001394

0001926

000592

000117

8000118

2000119

7000118

2000118

50005923

06

000

083

0001083

0001466

0002087

0003285

0008751

0001754

000175

0001742

0001758

0001754

0008758

07

000

0993

0001354

0001954

0003155

0005991

0013447

0002695

0002677

0002688

0002694

0002697

0013451

08

000115

0001646

0002581

000

4752

0011803

0021933

000

4371

000

4366

000

4373

000

4386

000

4394

0021889

09

0001311

0002001

0003431

0007494

0032772

0047009

000

9372

000

9421

000

9384

000

9407

000

9462

0047046

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Journal of Applied Mathematics 7

Table3Waitin

gtim

e(sec)andidleperio

d(

)

120588C1

sC2

sC3

sC4

sC5

sTo

tal

C1C2

C3C4

C5To

tal

NPP

NP

01

000

0123

000

0136

000

0137

000

0141

000

0145

000

0681

000

0131

000

0141

000

0136

000

0136

000

0135

000

0681

02

000

0255

000

0273

000

0299

000

0324

000

035

0001502

000

0302

000

0302

000

0301

000

0302

000

0295

0001502

03

000

039

000

0441

000

0513

000

0584

000

0685

0002612

000

0515

000

0515

000

0529

000

0526

000

0528

0002614

04

000

0537

000

0623

000

0756

000

0924

000116

7000

4006

000

0802

000

079

000

0798

000

0806

000

0808

000

4003

05

000

0676

000

085

0001074

0001394

0001926

000592

000117

8000118

2000119

7000118

2000118

50005923

06

000

083

0001083

0001466

0002087

0003285

0008751

0001754

000175

0001742

0001758

0001754

0008758

07

000

0993

0001354

0001954

0003155

0005991

0013447

0002695

0002677

0002688

0002694

0002697

0013451

08

000115

0001646

0002581

000

4752

0011803

0021933

000

4371

000

4366

000

4373

000

4386

000

4394

0021889

09

0001311

0002001

0003431

0007494

0032772

0047009

000

9372

000

9421

000

9384

000

9407

000

9462

0047046

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

8 Journal of Applied Mathematics

0

0005

001

0015

002

0025

003

0035

004

0045

005

0 02 04 06 08 1

C1C2C3

C4C5Total waiting time

Server utilization (120588)

Wai

ting

time (th

r)

Figure 4 Performance of the five classes waiting with the totalwaiting time

of our waiting time distributions of our simulation underthe non-preemptive priority and the exogenous nonprioritywhere we use the FCFS policy We represent the simulationresults of non-preemptive as C1sndashC5s and the nonpriority(FCFS) ones as C1ndashC5 Our first observation reveals that thetotal waiting time simulation results of both are the sameThis implies that the total waiting time on the queue isindependent of the service discipline Second the waitingtime distributions of the classes in the non-preemptive differwhile those of nonpriority have equal distributions

Figure 4 is the performance result of our simulation thatwe obtained from Table 3 of our non-preemptive priorityAt the initial state when the server utilization is below05 the performance difference of these five classes is notfully noticed As the server utilization increases that is thenumber of mobile events increases in the proposed GUISETse-marketplace the performance differentiation becomes wellnoticed with class 1 priority having the minimum waitingtime followed by class two while class five has the highestwaiting time All these four classes have better performanceat the expense of the fifth class

In Figure 5 we compare this model with that of nonpri-ority model using the First Come First Served policy Bothof them have an unnoticeable performance differentiationbelow 04 but as the 120588 rarr 1 where 120588 lt 1 four classesout of the five classes observed have better waiting timeperformances over the conventional exogenous nonprioritymodel Though the fifth class has higher waiting time thisclass can be dedicated to requests that do not pose much risk

00005

0010015

0020025

0030035

0040045

005

0 02 04 06 08 1

C1sC2sC3sC4s

C5sN PPFCFS

Server utilization (120588)

Wai

ting

time (th

r)

Figure 5 Performance of non-preemptive priority and nonpriority

like checking information whose waiting time does not poserisk for example the issue of blood pressure request with12080 which is normal in this experiment This implies thaturgent e-health mobile requests have better response timethan noncritical requests We envisage this proposed systemto be good in the mobile e-health sector where patients withurgent request equipment need urgent attention Also it willbe good to the e-health provider if the costs paid per class areprioritized since they have the same overall average waitingtime

5 Conclusion

One of the objectives of the proposed GUISET engine isthe provisioning of mobile e-services to clients In thisresearch we model a typical GUISET mobile healthcaremiddleware and evaluate the performance impact of mobilehealthcare device requestsrsquo waiting time using the non-preemptive priority and the nonpriority service disciplineIn our evaluation we recorded the same average time forboth disciplines but the waiting time distributions of eachclass in the non-preemptive priority differ with the lowestclass having the minimum waiting time Four out of thefive classes observed perform better in the non-preemptivediscipline than nonpriority discipline This prototype systemwill be a good service in the mobile healthcare environmentwhere urgent requests are given higher priority than lowerrequests For example request of severe risk should havehigher priority than that of moderate or mild risk

More can still be done to have better consumers waitingtime performance for the whole class For example onecan consider the case where the lowest priority consumersrepresent a scheduled task and the highest appear at random

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Journal of Applied Mathematics 9

Acknowledgments

This work is based on the research supported in part by theNational Research Foundation of South Africa-Grant UIDTP11062500001 (2012ndash2014) The authors also acknowledgefunds received from industry partners Telkom SA LtdHuawei Technologies SA (Pty) Ltd and Dynatech Informa-tion Systems South Africa in support of this research

References

[1] P M Papazoglou Web Services Principle and TechnologyPearson Education Edinburgh Gate UK 2008

[2] A O Akingbesote M O Adigun J Oladosu E Jembere andI Kaseeram ldquoThe Trade-off between consumerrsquos satisfactionand resource service level by e-market providers in e-marketplacesrdquo in Proceedings of the International Conference ElectricalEngineering and Computer Sciences (EECS rsquo13) Hong Kong2013

[3] H T Dinh C Lee D Niyato and P Wang ldquoA survey of mobilecloud computing architecture applications and approachesrdquoWireless Communications andMobile Computing vol 13 no 18pp 1587ndash1611 2013

[4] June 2014 http wwwwhointbulletinvolumes90512-020512en

[5] World Health Organization ldquomHealth new horizons for healththroughmobile technologiesrdquo inGlobal Observatory for eHealthServices vol 3 WHO 2011 httpwwwwhoint20goe20publicationseHealth series vol3en

[6] M Ali ldquoGreen cloud on the horizonrdquo in Proceedings of the 1stInternational Conference on Cloud Computing (CloudCom 09)pp 451ndash459 Manila Philippines 2009

[7] T Shezi E Jembere and M Adigun ldquoTowards developingfailure tolerant communication framework for GUISET ser-vicesrdquo in Proceedings of the Southern Africa TelecommunicationNetworks and Applications Conference (SATNACT rsquo11) 2011

[8] E K Olatunji M O Adigun E Jembere J Oladosu and PTarwire ldquoA privacy-as-a-service model for securing data inGUISET environmentrdquo in Southern Africa TelecommunicationNetworks and Applications Conference (SATNAC rsquo13) Septem-ber 2013

[9] M E Buthelezi M O Adigun O O Ekabua and J SIyilade ldquoAccounting pricing and charging service models fora GUISET grid-based service provisioning environmentrdquo inProceedings of the International Conference on e-Learning e-Business Enterprise Information Systems and e-Government(EEE rsquo08) pp 350ndash355 July 2008

[10] S O Kuyoro F Ibikunle and O Awodele ldquoCloud computingsecurity issues and challengesrdquo International Journal of Com-puter Networks vol 3 no 5 2011

[11] C C Kim L Smith H Thorne and R W Hilton ldquoManagingcosts and time for customer valuerdquo inManagement AccountingInformation for Managing and Creating Value chapter 15 pp726ndash728 McGraw-Hill Maidenhead UK 2008

[12] K Xiong and H Perros ldquoService performance and analysis incloud computingrdquo in Proceedings of the World Conference onServicesmdashI pp 693ndash700 Los Angeles Calif USA July 2009

[13] H Khazaei J Misic and V B Misic ldquoPerformance analysis ofcloud centers under burst arrivals and total rejection policyrdquoin Proceedings of the Global Telecommunications Conference(GLOBECOM rsquo11) pp 1ndash6 IEEEHouston Tex USADecember2011

[14] H Khazaei M Jelena and B M Vojislav ldquoPerformanceevaluation of cloud data centers with batch task arrivalsrdquo inCommunication Infrastructures for Cloud Computing pp 199ndash223 2013

[15] L Guo T Yan S Zhao and C Jiang ldquoDynamic performanceoptimization for cloud computing using MMm queueingsystemrdquo Journal of Applied Mathematics vol 2014 Article ID756592 8 pages 2014

[16] R Santhosh and T Ravichandran ldquoPre-emptive scheduling ofon-line real time services with taskmigration for cloud comput-ingrdquo in Proceedings of the International Conference on PatternRecognition Informatics and Mobile Engineering (PRIME rsquo13)pp 271ndash276 February 2013

[17] S T Maguluri R Srikant and L Ying ldquoStochastic models ofload balancing and scheduling in cloud computing clustersrdquo inProceedings of the IEEE Conference on Computer Communica-tions (INFOCOM rsquo12) pp 702ndash710 March 2012

[18] S Nagendram J V Lakshmi D V N Rao and C N JyothihildquoEfficient resource scheduling in data centers using MRISrdquoIndian Journal of Computer Science and Engineering vol 2 no5 2011

[19] P Ehsan and P Massoud ldquoMinimizing data center coolingand server power costsrdquo in Proceedings of the 14th ACMIEEEInternational Symposium on Low Power Electronics and Designpp 145ndash150 New York NY USA 2009

[20] M M Kembe E S Onah and S Iorkegh ldquoA study of waitingand service costs of a multi-server queuing model in a spe-cialist hospitalrdquo International Journal of Scientific amp TechnologyResearch vol 1 no 8 pp 19ndash23 2012

[21] W Ellens M Zivkovic J Akkerboom R Litjens and HVan Den Berg ldquoPerformance of cloud computing centerswith multiple priority classesrdquo in Proceedings of the IEEE 5thInternational Conference on Cloud Computing (CLOUD rsquo12) pp245ndash252 Honolulu Hawaii USA June 2012

[22] D A Stanford P Taylor and I Ziedins ldquoWaiting time distri-butions in the accumulating priority queuerdquo Queueing Systemsvol 77 no 3 pp 297ndash330 2014

[23] X Nan Y He and L Guan ldquoOptimal resource allocation formultimedia cloud based on queuing modelrdquo in Proceedings ofthe 13th InternationalWorkshop onMultimedia Signal Processing(MMSP rsquo11) pp 1ndash6 IEEE Hangzhou China October 2011

[24] F Kamoun ldquoPerformance analysis of a non-preemptive priorityqueuing system subjected to a correlated Markovian interrup-tion processrdquo Computers amp Operations Research vol 35 no 12pp 3969ndash3988 2008

[25] httpwwwnhlbinihgovhbpdetectcateghtm[26] httpwwwidphstateiaushpcdpcommonpdfdiabetesclass-

finalpdf[27] Primary health care Standard Treatment Guidelines and Essen-

tail Medicines List Health Department Western Cape SouthAfrica 2008 httpwwwkznhealthgovzaedlphc2008pdf

[28] G Donald and M H Carl Fundamentals of Queueing TheoryJohn Wiley amp Sons 2nd edition 1985

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Algebra

Discrete Dynamics in Nature and Society

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Decision SciencesAdvances in

Discrete MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom

Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Mathematical PhysicsAdvances in

Complex AnalysisJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

OptimizationJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Operations ResearchAdvances in

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences

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The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Algebra

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Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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