research article optimal qom in multichannel wireless...

Hindawi Publishing CorporationInternational Journal of Distributed Sensor NetworksVolume 2013 Article ID 120527 14 pageshttpdxdoiorg1011552013120527

Research ArticleOptimal QoM in Multichannel WirelessNetworks Based on MQICA

Na Xia12 Lina Xu1 and Chengchun Ni1

1 School of Computer and Information Hefei University of Technology Hefei 230009 China2 Engineering Research Center of Safety Critical Industrial Measurement and Control TechnologyMinistry of Education of China Hefei 230009 China

Correspondence should be addressed to Na Xia xiananawohfuteducn

Received 28 December 2012 Accepted 13 May 2013

Academic Editor Xinrong Li

Copyright copy 2013 Na Xia et al This is an open access article distributed under the Creative Commons Attribution License whichpermits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

In wireless networks wireless sniffers are distributed in a region to monitor the activities of users It can be applied for faultdiagnosis resource management and critical path analysis Due to hardware limitations wireless sniffers typically can only collectinformation on one channel at a time Therefore it is a key topic to optimize the channel selection for sniffers to maximizethe information collected so as to maximize the Quality of Monitoring (QoM) for wireless networks In this paper a Multiple-Quantum-Immune-Clone-Algorithm- (MQICA-) based solution was proposed to achieve the optimal channel allocation Theextensive simulations demonstrate thatMQICAoutperforms the related algorithms evidently with highermonitoring quality lowercomputation complexity and faster convergence The practical experiment also shows the feasibility of this algorithm

1 Introduction

With the growing application of wireless networks (egWiFiWiMax Mesh and WLAN) high quality management ofwireless device and networks is becoming more and moreimportant [1ndash3] It has been a key point to monitor networkstatus and performance accurately and in real time so as toimplement effective management

Wireless monitoring is usually realized using SimpleNetwork Management Protocol (SNMP) and base-stationlogs Since they reveal detailed PHY (eg signal strengthand spectrum density) and MAC behaviors (eg collisionand retransmission) as well as timing information theyare essential for network diagnosis and management [4ndash9] But wireless monitoring equipments are usually single-radio multichannel device [10ndash12] That is to say it hasmultioptional channels (In IEEE 80211bg WLAN thereare 3 orthogonal channels and in IEEE 80211a WLANthere are 12 orthogonal channels) So it is a key topic toallocate channels and other resources for these monitoringequipments to optimize the monitoring quality of entire

network [13ndash17] In the literature [16] it has turned out tobe a NP-hard problem in user-center mode and an effectivesolution for the problem will be with great significance to theperformance improvement of all kinds of wireless applicationnetworks

In this paper we carry out the full investigation on thecurrent wireless monitoring networks and establish a systemmonitoring model based on the undirected bipartite graphThen compared with existing algorithms we propose anoptimization solution ldquoMultiple Quantum Immune CloneAlgorithm (MQICA)rdquo to solve the problem Finally thealgorithmhas been proved to be with good performance bothin theory and experiments

The rest of the paper is organized as follows In Section 2we provide a brief review of existing work on wireless mon-itoring The problem formulation is presented in Section 3The Multiple Quantum Immune Clone channel allocationalgorithm (MQICA) is detailed in Section 4 Then we provethe validity of the proposed algorithm in Section 5 followedby extensive simulation experiments in Section 6 Finally weconclude this paper with some future work in Section 7

2 International Journal of Distributed Sensor Networks

2 Related Work

In recent years wireless monitoring networks have become ahot topic The research mainly contains monitoring devicesystem design fault diagnosis and so forth [4ndash9] In 2004ldquopassivemonitoringrdquo utilizingmulti-wireless sniffers was firstintroduced byYeo et al [4 5]He analyzed the advantages andchallenges of wireless passive monitoring and preliminarilyset up an application system which fulfilled the networkfault diagnosis based on time synchronization and datafusion of multisniffers In 2005 Rodrig et al [6] usedsniffers to capture wireless communication data and analyzethe performance characteristics of 80211 WiFi network In2006 Cheng et al [7] investigated a large-scale monitoringnetwork composed of 150 sniffers and discussed the timesynchronization method for distributed sniffers In 2007Yang and Guo et al [8] studied the lifetime model of wirelessmonitoring networks and proposed to adjust the sensing andcommunication radius of sniffers in real time to maximizethe lifetime of networks In 2010 Liu and Cao [9] researchedthe relationship between the number of monitoring sniffersand false alarm rate and put forward an algorithm based onpoller-poller structure which can limit the false alarm rate andminimize sniffers

It has become an important subject to optimize thechannel selection of monitoring sniffers so as to improvethe network monitoring quality In 2009 Shin and Bagchi[13] researched the channel selection of sniffers in Wire-less Mesh network to maximize the coverage of users Hedescribed it as a maximum coverage problem based ongroup budget constraints [14 15] and solved it using Greedyand Linear Programming (LP) algorithms which achievedgood performance Based on the previous research Chhetriet el [16] formulated the problem of channel allocationof sniffers and proved it to be NP-hard to maximize theQuality of Monitoring (QoM) of wireless network underuniversal network model Greedy and LP algorithms wereemployed to solve the problem Greedy algorithm alwaysseeks the solution with maximal current benefit during theprocess of resolution and misses the global optimal solutionor approximate of it Although LP algorithm can achievebetter solution than others its complexity is too high to meetthe real-time optimization in dynamic wireless networks In2011 we appliedGibbs Sampler theory to address the problemand proposed a distributed channel selection algorithm forsniffers to maximize QoM of network [17] This methodutilizes the local information to select the channel with lowenergy but cannot achieve the global optima in most of thecases

In [15ndash20] we can get an overview of much excellentwork in multichannel selection of wireless network itselfIn 2006 Wormsbecker and Williamson [18] studied theimpact of channel selection technique on the communicationperformance of system and applied soft channel reservationtechnique to select channels so as to reduce link layer dataframe losses and provide higher TCP throughput In 2007Kanthi and Jain [19] proposed a channel selection algorithmfor multiradio and multichannel mesh networks It is basedon Spanner conception and combinedwith network topology

The experiment results showed that it can improve datathroughput in communication link layer In 2009 You et al[20] investigated the end-to-end data transmission and theoptimal allocation of channel resource in wireless cellularnetworks and figured it out with stochastic quasi-gradientmethod In 2010 Hou andHuang [21] researched the channelselection problem in Cognitive Ratio networks describedit as a binary integer nonlinear optimization problem andproposed an algorithm based on priority order to maximizethe total channel utilization for all secondary nodes In 2011an interface-clustered channel assignment (ICCA) schemewas presented by Du et al [22] It can eliminate the colli-sion and interference to some extent enhance the networkthroughput and reduce the transmission delay

From what has been discussed previously there existgreat shortcomings in solution of wireless monitoring net-work channel allocation problems All of these studies mostfocused on the wireless network itself rather than the wire-less monitoring sniffers Existing algorithms will have highalgorithm complexity slow convergence speed and in mostcases it is difficult to get global optimal solution in the casesof large-scale networks or having more optional channelsTherefore in this paper a so-calledMultiple-QICA (MQICA)algorithm taking full advantage of the parallel characteristicsof Quantum Computing (QC) is proposed Compared withtraditional Quantum Immune Clone Algorithm (QICA)MQICA possesses lots of characteristics inherited from bothimmune and evolution algorithms Meanwhile allele andGaussian mutations are introduced in MQICA to furtherimprove the performance of the algorithm Extensive sim-ulations and practical experiments demonstrate that theproposed algorithm outperforms other algorithms not onlyin quality of solution but also in time efficiency

3 Problem Description

31 Network Model Consider a wireless network of119898moni-toring sniffers 119899 users and 119896 optional channels 119878 = 119904

1

1199042 119904

119898 is the set of sniffers 119880 = 119906

1 119906

2 119906

119899 is

the set of users and 119862 = 1198881 119888

2 119888

119896 is the set of

channels In homogeneous networks sniffers have the sametransmission characteristics They have the ability to readframe information and can analyze the information fromusers or other sniffers But at any point in time a sniffercan only observe transmissions over a single channel Let119901119906119895

denote the transmission probability of a user 119906119895(119895 =

1 2 119899) that works on channel 119888(119906119895) isin 119862 These users can

be a wireless router access point ormobile phone user and soforth If a user sends data through a channel at time 119905 it willbe called active user in time 119905

In wireless networks the relationship between sniffersand users can be described by an undirected bipartite graph119866 = (119878 119880 119864) shown in Figure 1 If 119906

119895is in themonitoring area

of 119904119894 there will be a connection between them indicated by

119890 = (119904119894 119906

119895) When 119904

119894and 119906

119895work on the same channel 119904

119894can

capture the data from 119906119895 and then we say that 119906

119895is covered

by 119904119894 119864 represents the set of all connecting edges If a user

is outside all sniffersrsquo monitoring area it is excluded from 119866

International Journal of Distributed Sensor Networks 3

S

U

E

s1 s2 si sm

u1 u2 u3 unuj

middot middot middotmiddot middot middot


Figure 1 undirected bipartite graph 119866

The vertex V in 119866 is sniffer or user namely V isin 119878 cup 119880 119873(V)denotes the neighbors of vertex V If the vertex is a user 119906

119895

119873(119906119895)means its neighbor sniffers if the vertex is a sniffer 119904

119894

119873(119904119894) is the set of neighbor users of 119904

119894 If a sniffer is inside

the communication range of another sniffer they are calledadjacent sniffers 119881(119904

119894) denotes the set of adjacent sniffers of

119904119894 and 119861

119904119894is the set of subscript of sniffers in 119881(119904

119894) In this

paper we assume that the communication radius of sniffer istwice as its monitoring radius

32 Problem Formulation a 119878 rarr 119862 represents a channelselection scheme for wireless monitoring networks and Ois the set of all possible schemes a can be expressed in theform of vector as follows a = (119886(119904

1) 119886(119904

2) 119886(119904

119898)) where

119886(119904119894) isin 119862 is the channel selected by 119904

119894 When 119904

119894selects the

channel 119886(119904119894) it can communicate with the neighbor users

who also work on channel 119886(119904119894) Given a channel selection

scheme a then 119878 = cup119896119902=1119878119888119902 119880 = cup

119896

119902=1119880119888119902 where 119878

119888119902denotes

the set of sniffers assigned to channel 119888119902 and 119880

119888119902denotes the

set of users working on channel 119888119902 Now it is able to show

the relationship between all the sniffers and users working onchannel 119888

119902in the form of undirected bipartite graph 119866

119888119902=

(119878119888119902 119880

119888119902 119864

119888119902)

Definition 1 Monitoring quality of node (MQN) when wire-less monitoring network works on channel a isin O the moni-toring quality of node 119904

119894can be defined as follows

119876119904119894(a) = sum

119906isin119873(119904119894)

119901119906sdot

1 (119888 (119906) = 119886 (119904119894))

1 + sum119905isin119861119904119894

1 (119888 (119906) = 119886 (119904119905) 119904

119905isin 119873 (119906))

(1)

where 1(sdot) is an indicator function It equals 1 when thecondition is true and 0 otherwise It is clear that the moreneighbor users work on the same channel as 119904

119894 the higher

transmission probability these users have and meanwhilethe less other sniffers cover these users the highermonitoringquality 119904

119894has MQN reflects the number of active users

available to 119904119894under the channel selection scheme a Active

users are in the state of sending data

Given a channel selection scheme a the Quality of Mon-itoring (QoM) of wireless network can be defined as follows

119876 (a) = sum119904119894isin119878

119876119904119894(a) (2)

So the higher QoM is the more active users can bemonitored in the network and the higher quality of servicethe wireless monitoring network provides

The problem of maximizing of QoM (MQM) can bedescribed as follows finding an optimal channel allocationscheme for sniffers to collect the largest amount of informa-tion transmitted by users that is tomaximize theQoMof thenetwork

The channel allocation scheme will be changed accordingto probability during different time slot So the maximalinformation collected by monitoring network in a certainperiod can be expressed as

max sum

aisinO119876 (a) times 120587 (a)

st 120587 (a) isin [0 1]

sum

aisinO120587 (a) = 1

(3)

where 120587(a) is the probability for wireless monitoring networkto work on the channel allocation scheme a

From (3) the optimal channel allocation scheme will begot as follows

alowast = argmax119876 (a) (4)

For this complicated combination optimization probleman effective heuristic algorithm is needed In 2005 Jiao andLi proposed a brand new Quantum-Inspired Immune CloneAlgorithm (QICA) [23] QICA constructs antibodies in viewof the superposition characteristics of quantum coding andenlarges the original population via clone operation thusexpanding the searching space and improving the perfor-mance of the algorithm when doing local search It isvery suitable for this complicated combination optimizationproblem because of the attributes of parallelism and provablerapid convergence But the results in QICA are expressed ina binary form [24] which are more appropriate for solvingproblems in a binary encodingThusweneed to extend it to k-resolution coding before applying the algorithm to thisMQMproblem in wireless monitoring network Then Multiple-QICA channel selection algorithm is proposed and describedin detail as follows

4 Multiple Quantum Immune Clone ChannelAllocation Algorithm (MQICA)

41 Fundamental Definitions To accurately describe theevolutionary process of the MQICA algorithm the followingfundamental definitions are proposed


Definition 2 (Channel Quantum Antibody (CQA)) Wedefine the Channel Quantum Antibody as the following trip-loid chromosome

CQA def=[

[

1199090sdot sdot sdot 119909


119898minus1



119898minus1



119898minus1

]

]

(5)

where 119898 is called the length of the chromosome that is thenumber of the monitoring sensors 119909

119894isin [0 1) represents

channel selection scheme of the 119894thmonitoring sensor 120572119894and

120573119894should meet the normalization condition |120572

119894|2+ |120573

119894|2= 1

where |120572119894|2 and |120573

119894|2 indicate respectively the nonoptimal

and optimal probability of the channel selection scheme ofthe 119894th monitoring sensor [119909119894 120572119894 120573119894]

119879 is named as an alleleof the CQA

Definition 3 (mapping between antibody to channel) Notethat in the CQA

119883 = [1199090 119909

1 119909

119894 119909

119898minus1] isin 119877

119898 (6)

where 119909119894isin [0 1) is a continuous real number If it is discrete

119883 can be mapped into integer space that

C = [1198881199040 119888

1199041 119888

119904119894 119888

119904119898minus1] isin 119885

119898 (7)

where 119888119904119894isin 0 1 119896 minus 1 and indicates the monitoring sen-

sor 119904119894to select channel 119888

119904119894 119896 is the total number of selectable

channels in the network The process described previouslyis called mapping of the CQA to channel selection schemebriefly as antibody to channel The mapping relationship isdefined as follows

119888119904119894

mapping= lfloor119896119909

119894rfloor 119894 = 0 1 119898 minus 1 (8)

Definition 4 (channel affinity) Channel affinity refers to theaffinity degree between the CQA and the channel antigenwhich is the approximate level between feasible solutionand optimal solution With the affinity value increased thefeasible solution will be much closer to the optimal one Onthe contrary the feasible solution will gradually deviate fromthe optimal oneChannel affinity is the foundation of immuneselection operation

Definition 5 (evolutionary entropy of the CQA) To measurethe extent of the evolution we introduce evolutionary entropyto the CQA

119867(119883) = 119867 (1199090 119909

1 119909

119898minus1)

= 119867 (1199090) + 119867 (119909

1| 119909

0)

+ sdot sdot sdot + 119867 (119909119898minus1

| 1199090 119909

1 119909

119898minus2)

=

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120572119894

1003816100381610038161003816

2+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120573119894

1003816100381610038161003816

2)

= minus

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816

2

+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816

2

)

= minus2

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816)

(9)

As the evolution process continues 120572119894rarr 0 120573

119894rarr 0

thus 119867(119883) rarr 0 So the evolutionary entropy can be usedto describe the extent of the evolution When the algorithmfinally comes to a convergent result the value of evolutionaryentropy is indefinitely close to zero

42 Process Design The population is denoted as 119860 = 1199031

1199032 119903

119873 where 119873 indicates the scale of the population

and 119903119894represents a CQA in it An evolution process of the

algorithm in this paper consists of three basic operationsincluding clone immune genetic variation and immuneselection Clone operation (119879

119888) clones each antibody and the

clone scale is decided by the channel affinity value of theantibody Immune genetic variation (119879

119898) will increase the

diversity of population information The immune selectionoperation (119879

119868) chooses from all antibodies generated by the

former two operations according to their channel affinity andget the optimal CQA Then compare them with the original119873 elite antibody 11990310158401015840

1198940[25] 119894 = 1 2 119873 in immune memory

set 119878119898[26] Meanwhile it forms the new population of next

generation Thus an evolution process can be described as

119860 (119905)

Clone Operation (119879119888)

997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr 1198601015840(119905)

Immune Genetic Variation (119879119898)

997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr

11986010158401015840(119905)

Immune Selection (119879119868)997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr 119860 (119905 + 1)

(10)

After this operation we need to do full interference cross tothe new operation119860(119905+1) and continue returning to the nextin case that the evolution still did not meet the terminationconditions

421 Cloning Operation A self-adaptive clone operation isproposed in [23]

119879119888(119860 (119905)) = 119879

119888(119903

1) 119879

119888(119903

2) 119879

119888(119903

119873) (11)

where 119879119888(119903

119894) = 119864

119894times 119903

119894 119894 = 1 2 119873 and 119864

119894is a unit row

vector with 119902119894columns while 119902

119894indicates the clone scale of

the CQA and is decided by the equation as follows

119902119894=[

[

[

[

119873119888times

119876 (C119894)

sum119873

119895=1119876(C

119895)

]

]

]

]

(12)


where 119873119888gt 119873 It can be concluded from (12) that if the

channel affinity of a specific CQA is greater than that ofthe others in the population then corresponding clone scalewill be larger Thus this clone strategy guarantees that themore excellent an antibody is the more resource it will getand this will obviously drive the algorithm to evolve towardsthe optimal solution much more quickly Once the cloneoperation is completed the population 119860(119905) is expanded tohave the following form

1198601015840(119905) = 119860 (119905) 119860

1015840

1(119905) 119860

1015840

119873(119905) (13)

where

1198601015840

119894(119905) = 119903

1198941(119905) 119903

1198942(119905) 119903

119894119902119894minus1(119905)

119903119894119895(119905) = 119903

119894(119905) 119895 = 1 2 119902

119894minus1

(14)

422 Immune Genetic Variation MQICA algorithm imple-ments a single-gene mutation on every triploid chromo-some during the evolution Compared with full-gene muta-tion it has been proved in the literature [27] that single-gene mutation can dramatically improve the search effi-ciency of the algorithm Denote 119903119905

119911as a CQA in 1198601015840

119894(119905) =

1199031198941(119905) 119903

1198942(119905) 119903

119894119902119894minus1(119905) which is generated by clone opera-

tion on the 119894th CQA of population119860(119905) Choose the 119895th allele[119909

119905

119911119895120572119905

119911119895120573119905

119911119895]

119879

randomly from 119903119905

119911and perform two kinds of

Gaussian mutation on it

119909119905+1120603

119911119895= 119873(120583

119905120603

119911119895 (120575

119905120603

119911119895)

2

)

=

119909119905

119911119895+ 119873(0

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

) 120603 = 120572

119909max minus 119909min2

+ 119873(0

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

120594

) 120603 = 120573

(15)

120594 is a variable After the Gaussian mutation 119909119905+1120603119911119895

mightexceed the interval [0 1) To avoid it redefine 119909119905+1120603

119911119895as fol-

lows

119909119905+1120603

119911119895=

119896 minus 1

119896

119909119905+1120603

119911119895gt 1

0 119909119905+1120603

119911119895lt 0

119873(120583119905120603

119911119895 (120575

119905120603

119911119895)

2

) others

(16)

Gaussian mutation consists of two operations one per-forms a local search around the current solution with a vari-ance of |120572119905

119911119895|

2 another performs a wide-range search aroundthe mean value with a variance of |120573119905

119911119895|

2

120594 lest the algo-rithm converges to a local optimal solution

After the Gaussian mutation indicated by (15) and (16)the algorithm will calculate the channel affinity of the newantibody and compare it with the original one that is todecide which one is better between the two feasible solutions(119909

119905+1

1199110 119909

119905+1120603

119911119895 119909

119905+1

119911119898minus1) and (119909119905

1199110 119909

119905

119911119895 119909

119905

119911119902119894minus1) If

the Gaussian mutation does improve the quality of theantibody replace 119909119905120603

119911119895with 119909119905+1120603

119911119895 and keep the probability of

0

1

minus1

minus1

120573ij

120572ij

Δ120579ij

x

y

1

Figure 2 Sketch map of QRD operation

119909119905120603

119911119895unchanged that is 120572119905+1

119911119895= 120572

119905

119911119895 120573119905+1

119911119895= 120573

119905

119911119895 Otherwise the

Gaussian mutation has no effect and the probability indica-ting that the current solution is optimal should be increasedQuantum Rotation Door (QRD) is adopted to update |120572119905

119911119895|

2

and |120573119905119911119895|

2 the former will be decreased and the latter willbe correspondingly increased after the rotation operationAssume that the step size of the rotation is Δ120579119905

119911119895 the newly

generated 120572119905+1119911119895

and 120573119905+1119911119895

are decided by (17)

[

120572119905+1

119911119895

120573119905+1

119911119895

] = [

cos (Δ120579119905119911119895) minus sin (Δ120579119905

119911119895)

sin (Δ120579119905119911119895) cos (Δ120579119905

119911119895)

] [

120572119905

119911119895

120573119905

119911119895

] (17)

During the evolution the probability of composite vector(120572

119905

119911119895 120573

119905

119911119895)will approach gradually towards 119910-axis shown as in

Figure 2

(1) If (120572119905119911119895 120573

119905

119911119895) lies in the first or the third quadrant an

anticlockwise rotation is needed and Δ120579119905119911119895is positive

(2) If (120572119905119911119895 120573

119905

119911119895) lies in the second or the fourth quadrant

a clockwise rotation is needed and Δ120579119905119911119895is negative

(3) If (120572119905119911119895 120573

119905

119911119895) lies exactly on 119910-axis the algorithm has

converged and the current feasible solution is theoptimal one

To sum up Δ120579119905119911119895is realized as follows

Δ120579119905

119911119895= sgn (120572119905

119911119895120573119905

119911119895) Δ120579 exp(minus

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

+ 119873119902119873

119904

) (18)

where sgn(sdot) is a sign function used to control the direction ofthe rotation thus to make sure that the algorithm will finallyconverge to an optimal solution Δ120579 means the maximumrotation angle in a single rotation operation Current proba-bility |120572119905

119911119895|

2 |120573119905119911119895|

2 as well as 119873119902119873

119904is employed to control


the rotation dimension or that is to say to adjust theevolutionary speed in case of precocity of an antibody 119873

119902

represents the total number of CQAs in 1198601015840(119905) that is 119873

119902=

sum119873

119894=1119902119894and 119873

119904indicates how stable the current population

119860(119905) is After every operation including Gaussian mutationand crossover whichmay update119909119905

119894119895119873

119904should be recalculate

as follows

119873119904=

119873119904+ 1 119909

119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

1 119909119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

(19)

423 Immune Selecting Operation There shall form a newpopulation

11986010158401015840(119905) = 119860 (119905) 119860

10158401015840

1(119905) 119860

10158401015840

119873(119905) (20)

after the immune genetic variation wherein

11986010158401015840

119894(119905) = 119903

10158401015840

1198941(119905) 119903

10158401015840

1198942(119905) 119903

10158401015840

119894119902119894minus1(119905) 119894 = 1 2 119873

(21)

For each CQA in population 11986010158401015840(119905) derived from

immune manipulation operation we firstly map 119883 = [1199090

1199091 119909

119898minus1] isin 119877

119898 to channel selection scheme C = [1198881199040

1198881199041 119888

119904119898minus1] isin 119885

119898 Then compare them with original 119903101584010158401198940in

119878119898on the basis of channel affinity For all 119894 = 1 2 119873 if

exists

C119887119894(119905) = C

11990310158401015840119894119895(119905) | max119876(C

11990310158401015840119894119895) 119895 = 0 1 2 119902

119894minus 1

(22)

making 119876(C119903119894) lt 119876(C

119887119894) 119894 = 1 2 119873 then 119903

10158401015840

1198940(119905 +

1) = 119887119894(119905) otherwise 11990310158401015840

1198940(119905 + 1) remains unchanged as 11990310158401015840

1198940(119905)

Immune selection operation selects the optimal CQA fromall the antibodies generated by clone operation and immunemanipulation operation as well as the immune memory set119878119898to form a brand new population After the operation is

down we can get not only new immune memory set 119878119898but

also the new generation of CQA population 119860(119905 + 1)

424 Full Interference Crossover To make full use of theinformation of all CQAs in the population thus to guaranteethat new antibodies will be generated in case of antibodyprecocity which may cause the algorithm converge to a localoptimal solution a full interference crossover strategy [28] isadopted in this paper Denote the 119895th allele in the 119894th antibodybefore and after the crossover operation to be 119860

119894119895and 119861

119894119895

respectively the relationship between119860119894119895and 119861

119894119895can then be

revealed as 119861119894119895= 119860

[(119894+119895)119873][119895] A simple example is shown in

Tables 1(a) and 1(b) to help understand when the populationscale is set to 119873 = 5 and the number of the monitoringsensors and current available channels is set to 119898 = 8 and119896 = 5 respectively

Table 1 (a) Group information before the crossing (b) Groupinformation after the crossing

(a)

NO0 11986000

11986001

11986002

11986003

11986004

11986005

11986006

11986007

NO1 11986010

11986011

11986012

11986013

11986014

11986015

11986016

11986017

NO2 11986020

11986021

11986022

11986023

11986024

11986025

11986026

11986027

NO3 11986030

11986031

11986032

11986033

11986034

11986035

11986036

11986037

NO4 11986040

11986041

11986042

11986043

11986044

11986045

11986046

11986047

(b)

NO0 11986000

11986011

11986022

11986033

11986044

11986005

11986016

11986027

NO1 11986010

11986021

11986032

11986043

11986004

11986015

11986026

11986037

NO2 11986020

11986031

11986042

11986003

11986014

11986025

11986036

11986047

NO3 11986030

11986041

11986002

11986013

11986024

11986035

11986046

11986007

NO4 11986040

11986001

11986012

11986023

11986034

11986045

11986006

11986017

43 Algorithm Description Based on the discussion theprocess of MQICA is described as follows

Step 1 Set algorithm parameters and initialize population119860(0) Calculate the initial channel affinity of each CQA in thepopulation that is the Quality of Monitoring (QoM)

Step 2 Calculate the clone scale of each CQA according to(12) and then execute clone operation After this step1198601015840

(119905) isobtained

Step 3 Do mutation operation on 1198601015840(119905) and get 11986010158401015840

(119905)

Step 4 Do immune selection and those selected antibodiesconstitute the new population 119860(119905 + 1)

Step 5 Calculate the channel affinity of each CQA in the newpopulation as well as the evolutionary entropy of the popula-tion if the former does not change any more and the lattertends to be close to zero infinitely or 119905 gt 119905max the algorithmhas already approximately converged otherwise crossoveroperation is applied to 119860(119905 + 1) and jump to Step 2

The pseudo code of the algorithm is also given inPseudocode 1

5 Performance Analysis of MQICA

We will firstly prove that MQICA just like traditional QICAhas a dramatic ability on global optimization searching Andin next chapter lots of experiments are given to furtheridentify the outstanding performance of MQICA especiallyon MQoM problems

Lemma 6 The population sequence 119860119905 119905 ge 0 generated

by the evolutionary process of MQICA is a stochastic processwith discrete parameters and constitutes a time homogeneousMarkov chain

Proof Suppose that the state space of a single CQA isΩ 119860 =119903

1 119903

2 119903

119873 represents the population where 119903

119894responds to


Input the sniffer set 119878 = 1199041 119904

2 119904

119898 channel set

119862 = 1198881 119888

2 119888

119896 user set

119880 = 1199061 119906

2 119906

119899 119888 (119906

119895) and 119901

119906119895(119895 = 1 2 119899)

the iterative terminal entropy 120576 and the maximum iterations 119905maxOutput the channel allocation vector C

(1) 119903119894(119905) larr Generate initial population 1 le 119894 le 119873 119905 = 0

(2) Domappings between antibody to channel calculate theevolutionary entropy of each CQA and get119867(119883

119903119894)

(3) 119876119894(119905) larr function(C

119903119894) lowastcompute the channel

affinity of each antibody according to (2)lowast(4) 119903

10158401015840

1198940(119905) larr 119903

119894(119905) lowastcopy the original message to 119878

119898lowast

(5) do (6) 119860

1015840(119905) larr 119860(119905) lowast clone operationlowast

(7) 11986010158401015840(119905) larr 119860

1015840(119905) lowastimmune genetic variationlowast

(8) Update immune memory set 119878119898

(9) lowastimmune selection operationlowast(10) 119860(119905 + 1) larr 119878

119898

(11) 119876lowast= max(119876

119894(119905)) lowastchoose the max valuelowast

(12) Calculate the evolutionary entropy update119867(119883119903119894)

(13) if ((119905 lt 119905max) | (sum119873

119894=1119867(119883

119903119894) gt 120576)) then

(14) 119905 = 119905 + 1(15) Do full interference cross and update 119860(119905)(16) end(17) while ((119905 lt 119905max) | (sum

119873

119894=1119867(119883

119903119894) gt 120576))

Pseudocode 1

the 119894th antibody in 119860 and 119873 is the population scale 119903119894isin Ω

119860 isin Ω119873 During the evolution process all CQAs are discrete

119883 = lfloorC119896rfloor isin 0 1119896 (119896 minus 1)119896 describes the channelselection scheme If the quantity of the CQA in population119860is119898Ω = 0 1119896 (119896 minus 1)119896

119898notin 120601 So the population state

space should be |Ω119873| = 119896

119873119898 that is the state space during theevolution is finite According to literature [29] denote 120575 tobe the minimum 120590-algebra generated by all cylinder set of Ωand 119875 to be a real-value measure function defined in (Ω 120575)and thus the probability space of an CQA can be expressedas (Ω 120575 119875) and the probability space of MQICA should bedefined as (Ω119873

120575 119875) As a result 119860(119905) 119905 ge 0 defined instate space (Ω 120575 119875) is a stochastic sequence with discreteparameter and will change with 119905 the evolutionary times ofour algorithm Obviously when the state space is replaced by(Ω

119873 120575 119875) the conclusion previously mentioned still holdsFurthermore the operations adopted in MQICA includ-

ing clone (119879119888) immune gene manipulation (119879

119898amp 119879

119890) and

immune selection (119879119868) guarantee that119860(119905 + 1) is only related

to 119860(119905) So 119860(119905) 119905 ge 0 is time homogeneous Markov chainin state space (Ω119873

120575 119875)

Definition 7 Denote alowast = Clowastas the optimal channel selectionscheme namely Clowast

= arg max119876(a) = arg 119876lowast where 119876lowast isthe QoM value corresponding to optimal channel selectionscheme MQICA will converge to global optimal solutionwhen and only when lim

119905rarrinfin119875(119876

119905= 119876

lowast) = 1

Lemma 8 The transition probability matrix 119872(119879119898) which

indicates that the probability for a CQA in clone group 1198601015840(119905)

changes its state from Λ120583 to Λ120582 after the MQICA mutationoperation 119879

119898 is strictly positive

Proof For Gaussian mutation operation 119866 shown in (15)

assume that after the mutation 119909119905+1119911119895

=

119909119905+1120572119911119895

119909119905+1120573

119911119895

the probability

for 119909119905119911119895to mutate to 119909119905+1120572

119911119895should be

119866(119909119905

119911119895 119909

119905+1120572

119911119895)

= int

119909119905+1120572119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

sdot exp(minus(119909 minus 119909

119905+1120572

119911119895)

2

120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(23)

By the same token the probability for 119909119905119911119895to mutate to 119909119905+1120573

119911119895

should be

119866(119909119905

119911119895 119909

119905+1120573

119911119895)

= int

119909119905+1120573

119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816


119905+1120573

119911119895)

2

120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(24)


Because these two Gaussian mutations are independent sothe probability of state transition from x

120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)

When the state of 120572 in a specific allele of an antibody ischanged from 119886

120582to 119886

120583by QRD operation the state transition

probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)

and obviously the transition probability matrix 119872(119879119898) is

strictly positive

Lemma 9 The state transition matrix 119875 for MQICA is aregular one

Proof The state transition process of the population inΩ119873 isdescribed by the following four operations 119879

119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890 and as a result

119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903

119894(119905)] Assume that the

state of the population was transferred from Λ120583 to Λ120582 afterthe 119905th iteration where Λ120583Λ120582 sube Ω119873 So the state transitionprobability of MQICA is

119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)

Because the full interference cross has fixed relationshipsthat is 119901119879

119890(119903

120583119894(119905 + 1)) = 1 the lemma can be proved with

the following three conditions

Condition 1 When 119876(C120583119894) lt 119876(C

120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)

Condition 2 When 119876(C120583119894) gt 119876(C

120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)

Condition 3 When 119876(C120583119894) = 119876(C

120582119894) the evolutionary

entropy of the CQA satisfies119867(119883) rarr 0 in other words thealgorithm should be converged and 119901

120583120582(119905) = 119901

120583120583(119905) = 1 and

the state transition probability ofMQICA can be summarizedas

119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)

Obviously 119875 ge 0 and exist119905 that makes 119875119905gt 0 Thus 119875 is a is

regular matrix

Lemma 10 The Markov chain derived from MQICA isergodic

Proof Lemma 9 indicates that the state transition matrix 119875for MQICA is regular and because the Markov cycle is 1based on the basic Markov limit theorem a unique limitlim

119905rarrinfin119875119905= 119875

lowast must exist Because 119875lowastgt 0 so the homo-

geneous Markov chain is nonzero and recurrent thus anystate in this chain would have an only limit distribution witha probability that is greater than zero regardless of how thepopulation is initialized As a result MQICA can start fromstate 119894 to state 119895 within limited time that is when 119905 rarr infinthis Markov chain could traverse the whole state space

Lemma 11 MQICA converges to the global optimal solutionon a probability of 1

Proof MQICA adopts a so-called survival of the fittest strat-egy which means that the channel affinities of this Markovsequence generated by the evolution are monotone and willnot decrease Λlowast sube Ω119873 represents the population containingthe global optimal antibody rlowastClowast denotes the global optimalchannel selection scheme while 119876

lowast denotes the globaloptimal channel affinity Since the evolution process wouldnot degenerate Λlowast is a closed set and will be always in anattractive state which means that for all 119894 isin Λlowast sum

119895isinΛlowast 119901

119894119895=

1 always holds So once the state of the population 119860119905is

changed to Λlowast there would be no chance for the populationto enter other state

Based on the basic Markov limit theorem MQICA willdefinitely reach state Λlowast after limited steps 119905

119888if only the state

transition matrix 119875 is regular and the corresponding Markovchain is ergodic which have been proved by Lemmas 9 and10 Thus the following equation is satisfied

lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)


Table 2 Parameters setting

119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000

This indicates that MQICA converges to the globaloptimal solution on a probability of 1

6 Experiment Results

61 Simulations In this paper we conduct extensive exper-iments to validate the effectiveness of the algorithm Theprogram is run on a PC with Intel(R) Core(TM)2 CPU240GHz 2GBmemoryThe software platform isWindowsXP Table 2 lists the parameters of MQICA

119873 is the population scales Large 119873 can promote thesearching ability of the algorithm meanwhile extend therunning time of program The other parameters are all setas the experiential value for MQICA applications and theexperiments result also shows the validity in this case

From Section 5 we have known the validity of the pro-posed algorithmMQICA in solvingmultichannel allocationproblemsNowamass of experiment results also elaborate theeffectiveness in another way Firstly we tentatively do threedifferent experiments 5 times respectively according to thesize For small scale119898 = 3 119896 = 2 119899 = 25 for medium scale119898 = 12 119896 = 6 119899 = 200 for large scale 119898 = 12 119896 = 9119899 = 1000 The experiment results are shown in Figures 3(a)3(b) and 3(c) As can be seen from the graph no matter howinitialization is MQICA will eventually well converge to thesame optimal solution

Secondly in order to validate the correctness of the algo-rithm and eliminate the possibility of local optimal solutionwe take traversal method for the small scale monitoringnetwork Ergodic results are shown as follows 11 11 080767 115 115 0767 and 075 Obviously MQICA canquickly find the optimal solution in small time For mediumand large scale we both do the test fifty times The results areexpressed in Tables 3 and 4

From Table 3 During 50-times experiment we can seethat initial channel scheme is random so the initial QoMvalue is not optimal But after a certain number of iterationsthe network monitoring quality has been converged to orclose to the optimal value of 9345 Similarly Table 4 showsthat the algorithm can still do a better performance for thedistribution of channel options under lager networks

Now we can easily conclude that MQICA will generate agood performance in channel allocation problems It can bequickly uniform convergence to the optimal solution whenthe size of monitoring networks is small or moderate Ifthe scale is large MQICA can also be better converged tothe optimal or near optimal solution in most cases Theseexperimental results have proved the effectiveness of theproposed algorithm from various scales

We also evaluate the performance of MQICA comparingthree baseline algorithms

Table 3 Result for medium scale

ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM

Initial 0767Initial 115Initial 075

Initial 075Initial 0767

(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM

Initial 24482Initial 25733 Initial 2765


(c)

Figure 3 (a) The convergence of small scale (b) The convergence of medium scale (c) The convergence of large scale

Greedy Select channel for each sniffer to maximize the sumof transmission probability of its neighbor users

Linear Programming (LP) Solve the integer programmingproblem from formula (4)

Gibbs Sampler Sniffer computes the local energy of optionalchannels and their selection probability then chooses onechannel according to the probability

We conducted four sets of experiments and the numberof optional channels is 2 6 and 9 respectively In each

experiment the four algorithms are compared in differentaspects of performance The algorithm program runs 30times to get the average result for evaluation

In the first set of experiment 1000 users are distributed in500 times 500m2 square field as shown in Figure 4 transmissionprobability 119901

119906isin [0 006] The field is partitioned in several

regular hexagon units to construct cellular framework Eachunit center is equipped with a base station (BS) working ona certain channel and users in the unit work on the samechannel as BS Every two adjacent units are on differentchannels For easy to control 25 sniffers are deployed


Table 4 Results for large scale

ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500

Figure 4 Wireless network topology Hexagonal layout with users(purple ldquo+rdquo) sniffers (solid dots) and base stations (isoscelestriangles) of each cell (different color representing working ondifferent channels)

uniformly in the field to form a network to monitor thecommunication activities of users in the field Monitoringradius of sniffer is 120 meters and 3 optional channels (inIEEE 80211bg WLAN there are 3 orthogonal channels the1st 6th and 11th with center frequency 2412MHz 2437MHzand 2462MHz) MQICA LP Greedy and Gibbs Samplerare applied separately to solve the optimal channel selectionscheme for sniffersThe quality of solution (QoM) of the fouralgorithms is shown in Figure 5

As depicted in Figure 5 after 700 iterations the pro-posedMQICA algorithm converges to the extremely optimalsolution (QoM = 28975) LP algorithm takes the secondplace with QoM up to 28105 while Gibbs Sampler andGreedy algorithm achieve the QoM of 27048 and 23893respectively It is shown that the Multiple Quantum ImmuneClone Algorithm improves the convergence rate of otheralgorithm effectively and produces a better global searchingability

Table 5 demonstrates the statistical results of the threesets of experiments Among the four algorithmsMQICA andGibbs Sampler both run 20 times in each set of experimentsto get the average optimal solution and its QoM value Asdeterministic methods LP and Greedy just run once FromTable 5 we can see that MQICA outperforms LP in three setsof experiments and evidently better than Gibbs Sampler andGreedy Furthermore MQICA converges fast with shorterrunning time than Gibbs Sample

62 Practical Network Experiment In this section we eval-uate the proposed MQICA algorithm by practical networkexperiment based on campus wireless network (IEEE 80211bWLAN) 21 WiFi sniffers were deployed in a building tocollect the user information from 1 pm to 6 pm (over 5 hours)


Table 5 Statistical results of three sets of experiments

Experiment no MQICA Gibbs sampler LP Greedy

Averageoptimal QoM

Running times(1000 iter)

AverageoptimalQoM

Running times(1000 iter) QoM Running times

(1 iter ) QoM Running times(1 iter )

1 (2 channels) 27338 10616 26052 28938 27105 0562 22872 00932 (6 channels) 26760 11695 26261 30953 26484 0812 23363 01093 (9 channels) 26263 11759 26140 35031 26088 0934 23481 0119


Active probability 0sim001 001sim002 002sim004Number of users 578 15 29

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)

Figure 5 Performance comparison of the four algorithms in the firstset of experiments (3 optional channels)

Each sniffer captured approximately 320000 MAC framesTotally 622 users were monitored working on 3 orthogonalchannels The number of users in 1st 2nd and 3rd channelsis 349 118 and 155 respectively The activity probabilities(active probability of a user is computed as the percentageof the userrsquos active time in a unit time) of these users wererecorded in Table 6 It is shown that the activity probabilitiesofmost users are less than 1The average activity probabilityis 00026

Figure 6 depicted the QoM of network with differentnumber of sniffers It is clear that the QoM (the number of

4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy

Figure 6 QoM of campus wireless network with different numberof sniffers

monitored active users) is growing up with the increment ofsniffers (from 5 to 21) Except the experiment with 21 sniffersthe other sets of experiments were conducted repeatedly withdifferent sniffers selected randomly from the 21 sniffers andthe statistical average value of QoM was recorded and shownin Figure 6 Since the average activity probability is 00026the largest number of active users is less than 17 during everytime slot By comparing with LP Gibbs Sampler and Greedythe proposed MQICA exhibits its superiority and feasibilityin the practical network environment

7 Conclusion

In this paper we investigate the channel allocation for sniffersto maximize the Quality of Monitoring (QoM) for wirelessmonitoring networks which is proved to be NP-hard AMultiple-Quantum-Immune-Clone-based channel selectionalgorithm (MQICA) is put forward to solve the problemBy theoretical proof and extensive experiments we demon-strate that MQICA can solve the channel allocation problemeffectively and outperform related algorithms evidently withfast convergence As an ongoing work we are reducingthe computation complexity and proving the convergenceperformance of algorithm in theory


Acknowledgments

This work is funded by the National Science Foundation ofUSA (CNS-0832089) the National Natural Science Fund ofChina (61100211 and 61003307) and the Postdoctoral ScienceFoundation of China (20110490084 and 2012T50569)

References

[1] J Zander S L Kim and M Almgren Radio Resource Man-agement for Wireless Networks Artech House Norwood MassUSA 2001

[2] L M Correia D Zeller O Blume et al ldquoChallenges and ena-bling technologies for energy aware mobile radio networksrdquoIEEECommunicationsMagazine vol 48 no 11 pp 66ndash72 2010

[3] Y Liu K Liu and M Li ldquoPassive diagnosis for wireless sensornetworksrdquo IEEEACM Transactions on Networking vol 18 no4 pp 1132ndash1144 2010

[4] J Yeo M Youssef and A Agrawala ldquoA framework for wirelessLAN monitoring and its applicationsrdquo in Proceedings of the3rd ACM Workshop on Wireless Security (WiSe rsquo04) pp 70ndash79ACM New York NY USA October 2004

[5] J YeoM Youssef T Henderson and A Agrawala ldquoAn accuratetechnique for measuring the wireless side of wireless networksrdquoin Proceeding of the Workshop on Wireless Traffic Measurementsand Modeling (WiTMeMo rsquo05) pp 13ndash18 USENIX AssociationBerkeley Calif USA 2005

[6] M Rodrig C Reis R Mahajan D Wetherall and J ZahorjanldquoMeasurement-based characterization of 80211 in a hotspotsettingrdquo in Proceedings of the ACM SIGCOMM Workshopon Experimental Approaches to Wireless Network Design andAnalysis pp 5ndash10 New York NY USA August 2005

[7] Y C Cheng J Bellardo P Benko A C Snoeren GM Voelkerand S Savage ldquoSolving the puzzle of enterprise 802 11 analysisrdquoin Proceedings of the Conference on Applications TechnologiesArchitectures and Protocols for Computer Communications(SIGCOMM rsquo06) pp 39ndash50 ACM New York NY USA 2006

[8] WGYang TDGuo andT Zhao ldquoOptimal lifetimemodel anditrsquos solution of a heterogeneous surveillance sensor networkrdquoChinese Journal of Computers vol 30 no 4 pp 532ndash538 2007

[9] C Liu and G Cao ldquoDistributed monitoring and aggregation inwireless sensor networksrdquo in Proceedings of the 29th Conferenceon Information Communications (INFOCOM rsquo10) pp 1ndash9 IEEEPress Piscataway NJ USA 2010

[10] J Jin B Zhao and H Zhou ldquoDLDCA a distributed link-weighted and distance-constrained channel assignment forsingle-radiomulti-channelwirelessmeshnetworksrdquo inProceed-ings of the International Conference onWireless Communicationsand Signal Processing (WCSP rsquo09) pp 1ndash5 Nanjing ChinaNovember 2009

[11] C E A Campbell K K Loo and R Comley ldquoA new MACsolution for multi-channel single radio in wireless sensornetworksrdquo in Proceedings of the 7th International Symposiumon Wireless Communication Systems (ISWCS rsquo10) pp 907ndash911York UK September 2010

[12] Z Zhang andX Yu ldquoA simple single radiomulti-channel proto-col for wireless mesh networksrdquo in Proceedings of the 2nd Inter-national Conference on Future Computer and Communication(ICFCC rsquo10) pp V3-441ndashV3-445 Wuhan China May 2010

[13] DH Shin and S Bagchi ldquoOptimalmonitoring inmulti-channelmulti-radio wireless mesh networksrdquo in Proceedings of the 10th

ACM International Symposium on Mobile Ad Hoc Networkingand Computing (MobiHoc rsquo09) pp 229ndash238 MobiHoc NewOrleans La USA May 2009

[14] B J Kim and K K Leung ldquoFrequency assignment for IEEE80211 wireless networksrdquo in Proceedings of the 58th IEEEVehicular Technology Conference (VTC rsquo03) pp 1422ndash1426Orlando Fla USA October 2003

[15] C Chekuri and A Kumar ldquoMaximum coverage problem withgroup budget constraints and applicationsrdquo in Proceedings of theInternational Workshop on Approximation Algorithms for Com-binatorial Optimization Problems pp 72ndash83 APPROX Cam-bridge Mass USA 2004

[16] A Chhetri H Nguyen G Scalosub and R Zheng ldquoOn qualityof monitoring for multi-channel wireless infrastructure net-worksrdquo in Proceedings of the 11th ACM International SymposiumonMobile AdHocNetworking andComputing (MobiHoc rsquo10) pp111ndash120 MobiHoc Chicago Ill USA September 2010

[17] P Arora N Xia and R Zheng ldquoA gibbs sampler approach foroptimal distributed monitoring of multi-channel wireless net-worksrdquo in Proceedings of IEEE GLOBECOM pp 1ndash6 IEEECommunication Society Press 2011

[18] I Wormsbecker and C Williamson ldquoOn channel selectionstrategies for multi-channel MAC protocols in wireless ad hocnetworksrdquo in Proceedings of the IEEE International Conferenceon Wireless and Mobile Computing Networking and Commu-nications (WiMob rsquo06) pp 212ndash220 IEEE Computer SocietyWashington DC USA June 2006

[19] C N Kanthi and B N Jain ldquoSpanner based distributed channelassignment inwirelessmeshnetworksrdquo inProceedings of the 2ndInternational Conference on Communication System Softwareand Middleware and Workshops (COMSWARE rsquo07) pp 1ndash10COMSWARE Bangalore India January 2007

[20] L You PWuM Song J Song andY Zhang ldquoDynamic controland resource allocation in wireless-infrastructured distributedcellular networks with OFDMArdquo in Proceedings of the 38thInternational Conference on Parallel Processing Workshops(ICPPW rsquo09) pp 337ndash343 Vienna Austria September 2009

[21] F Hou and J Huang ldquoDynamic channel selection in cognitiveradio network with channel heterogeneityrdquo in Proceedings of the53rd IEEE Global Communications Conference (GLOBECOMrsquo10) pp 6ndash12 Miami Fla USA December 2010

[22] Z G Du P L Hong W Y Zhou and K P Xue ldquoICCA Inter-face-clustered channel assignment inmulti-radio wireless meshnetworksrdquo Chinese Journal of Electronics vol 39 no 3 pp 723ndash726 2011

[23] L Jiao and Y Li ldquoQuantum-inspired immune clonal optimiza-tionrdquo in Proceedings of the International Conference on NeuralNetworks and Brain Proceedings (ICNNB rsquo05) pp 461ndash466Beijing China October 2005

[24] Y Y Li and L C Jiao ldquoQuantum-inspired immune clonal algo-rithm for SAT problemrdquo Chinese Journal of Computers vol 30no 2 pp 176ndash183 2007

[25] K A de Jong An analysis of the behavior of a class of geneticadaptive systems [PhD thesis] University of Michigan 1975

[26] Y Yu and C Z Hou ldquoA clonal selection algorithm by using lear-ning operatorrdquo in Proceedings of International Conference onMachine Learning andCybernetics pp 2924ndash2929 August 2004

[27] X Z Wang and S Y Yu ldquoImproved evolution strategies forhigh-dimensional optimizationrdquo Control Theory and Applica-tions vol 23 no 1 pp 148ndash151 2006


[28] A Narayanan and M Moore ldquoQuantum-inspired genetic algo-rithmsrdquo in Proceedings of the IEEE International Conference onEvolutionaryComputation (ICEC rsquo96) pp 61ndash66Nogaya JapanMay 1996

[29] W X Zhang and Y Liang The Mathematical Basis of GeneticAlgorithm Press of Xirsquoan Jiaotong University 2000

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics


Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of


Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks



2 Related Work

In recent years wireless monitoring networks have become ahot topic The research mainly contains monitoring devicesystem design fault diagnosis and so forth [4ndash9] In 2004ldquopassivemonitoringrdquo utilizingmulti-wireless sniffers was firstintroduced byYeo et al [4 5]He analyzed the advantages andchallenges of wireless passive monitoring and preliminarilyset up an application system which fulfilled the networkfault diagnosis based on time synchronization and datafusion of multisniffers In 2005 Rodrig et al [6] usedsniffers to capture wireless communication data and analyzethe performance characteristics of 80211 WiFi network In2006 Cheng et al [7] investigated a large-scale monitoringnetwork composed of 150 sniffers and discussed the timesynchronization method for distributed sniffers In 2007Yang and Guo et al [8] studied the lifetime model of wirelessmonitoring networks and proposed to adjust the sensing andcommunication radius of sniffers in real time to maximizethe lifetime of networks In 2010 Liu and Cao [9] researchedthe relationship between the number of monitoring sniffersand false alarm rate and put forward an algorithm based onpoller-poller structure which can limit the false alarm rate andminimize sniffers

It has become an important subject to optimize thechannel selection of monitoring sniffers so as to improvethe network monitoring quality In 2009 Shin and Bagchi[13] researched the channel selection of sniffers in Wire-less Mesh network to maximize the coverage of users Hedescribed it as a maximum coverage problem based ongroup budget constraints [14 15] and solved it using Greedyand Linear Programming (LP) algorithms which achievedgood performance Based on the previous research Chhetriet el [16] formulated the problem of channel allocationof sniffers and proved it to be NP-hard to maximize theQuality of Monitoring (QoM) of wireless network underuniversal network model Greedy and LP algorithms wereemployed to solve the problem Greedy algorithm alwaysseeks the solution with maximal current benefit during theprocess of resolution and misses the global optimal solutionor approximate of it Although LP algorithm can achievebetter solution than others its complexity is too high to meetthe real-time optimization in dynamic wireless networks In2011 we appliedGibbs Sampler theory to address the problemand proposed a distributed channel selection algorithm forsniffers to maximize QoM of network [17] This methodutilizes the local information to select the channel with lowenergy but cannot achieve the global optima in most of thecases

In [15ndash20] we can get an overview of much excellentwork in multichannel selection of wireless network itselfIn 2006 Wormsbecker and Williamson [18] studied theimpact of channel selection technique on the communicationperformance of system and applied soft channel reservationtechnique to select channels so as to reduce link layer dataframe losses and provide higher TCP throughput In 2007Kanthi and Jain [19] proposed a channel selection algorithmfor multiradio and multichannel mesh networks It is basedon Spanner conception and combinedwith network topology

The experiment results showed that it can improve datathroughput in communication link layer In 2009 You et al[20] investigated the end-to-end data transmission and theoptimal allocation of channel resource in wireless cellularnetworks and figured it out with stochastic quasi-gradientmethod In 2010 Hou andHuang [21] researched the channelselection problem in Cognitive Ratio networks describedit as a binary integer nonlinear optimization problem andproposed an algorithm based on priority order to maximizethe total channel utilization for all secondary nodes In 2011an interface-clustered channel assignment (ICCA) schemewas presented by Du et al [22] It can eliminate the colli-sion and interference to some extent enhance the networkthroughput and reduce the transmission delay

From what has been discussed previously there existgreat shortcomings in solution of wireless monitoring net-work channel allocation problems All of these studies mostfocused on the wireless network itself rather than the wire-less monitoring sniffers Existing algorithms will have highalgorithm complexity slow convergence speed and in mostcases it is difficult to get global optimal solution in the casesof large-scale networks or having more optional channelsTherefore in this paper a so-calledMultiple-QICA (MQICA)algorithm taking full advantage of the parallel characteristicsof Quantum Computing (QC) is proposed Compared withtraditional Quantum Immune Clone Algorithm (QICA)MQICA possesses lots of characteristics inherited from bothimmune and evolution algorithms Meanwhile allele andGaussian mutations are introduced in MQICA to furtherimprove the performance of the algorithm Extensive sim-ulations and practical experiments demonstrate that theproposed algorithm outperforms other algorithms not onlyin quality of solution but also in time efficiency

3 Problem Description

31 Network Model Consider a wireless network of119898moni-toring sniffers 119899 users and 119896 optional channels 119878 = 119904

1

1199042 119904

119898 is the set of sniffers 119880 = 119906

1 119906

2 119906

119899 is

the set of users and 119862 = 1198881 119888

2 119888

119896 is the set of

channels In homogeneous networks sniffers have the sametransmission characteristics They have the ability to readframe information and can analyze the information fromusers or other sniffers But at any point in time a sniffercan only observe transmissions over a single channel Let119901119906119895

denote the transmission probability of a user 119906119895(119895 =

1 2 119899) that works on channel 119888(119906119895) isin 119862 These users can

be a wireless router access point ormobile phone user and soforth If a user sends data through a channel at time 119905 it willbe called active user in time 119905

In wireless networks the relationship between sniffersand users can be described by an undirected bipartite graph119866 = (119878 119880 119864) shown in Figure 1 If 119906

119895is in themonitoring area

of 119904119894 there will be a connection between them indicated by

119890 = (119904119894 119906

119895) When 119904

119894and 119906

119895work on the same channel 119904

119894can

capture the data from 119906119895 and then we say that 119906

119895is covered

by 119904119894 119864 represents the set of all connecting edges If a user

is outside all sniffersrsquo monitoring area it is excluded from 119866


S

U

E

s1 s2 si sm

u1 u2 u3 unuj





119895


119894





119904119894 and 119861


119894) In this



1) 119886(119904

2) 119886(119904

119898)) where


119894 When 119904

119894selects the




119896

119902=1119880119888119902 where 119878

119888119902denotes






119888119902=

(119878119888119902 119880

119888119902 119864

119888119902)



119876119904119894(a) = sum

119906isin119873(119904119894)

119901119906sdot

1 (119888 (119906) = 119886 (119904119894))

1 + sum119905isin119861119904119894

1 (119888 (119906) = 119886 (119904119905) 119904

119905isin 119873 (119906))

(1)


119894 the higher






119876 (a) = sum119904119894isin119878

119876119904119894(a) (2)




max sum

aisinO119876 (a) times 120587 (a)

st 120587 (a) isin [0 1]

sum

aisinO120587 (a) = 1

(3)









CQA def=[

[



119898minus1



119898minus1



119898minus1

]

]

(5)





119894|2+ |120573

119894|2= 1

where |120572119894|2 and |120573





119883 = [1199090 119909

1 119909

119894 119909

119898minus1] isin 119877

119898 (6)



C = [1198881199040 119888

1199041 119888

119904119894 119888

119904119898minus1] isin 119885

119898 (7)





119888119904119894


119894rfloor 119894 = 0 1 119898 minus 1 (8)



119867(119883) = 119867 (1199090 119909

1 119909

119898minus1)

= 119867 (1199090) + 119867 (119909

1| 119909

0)


| 1199090 119909

1 119909

119898minus2)

=

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120572119894

1003816100381610038161003816

2+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120573119894

1003816100381610038161003816

2)

= minus

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816

2

+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816

2

)

= minus2

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816)

(9)


119894rarr 0



1199032 119903










1198940[25] 119894 = 1 2 119873 in immune memory



119860 (119905)


997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr 1198601015840(119905)


997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr

11986010158401015840(119905)


(10)



119879119888(119860 (119905)) = 119879

119888(119903

1) 119879

119888(119903

2) 119879

119888(119903

119873) (11)

where 119879119888(119903

119894) = 119864

119894times 119903

119894 119894 = 1 2 119873 and 119864

119894is a unit row




119902119894=[

[

[

[

119873119888times

119876 (C119894)

sum119873

119895=1119876(C

119895)

]

]

]

]

(12)




1198601015840(119905) = 119860 (119905) 119860

1015840

1(119905) 119860

1015840

119873(119905) (13)

where

1198601015840

119894(119905) = 119903

1198941(119905) 119903

1198942(119905) 119903

119894119902119894minus1(119905)

119903119894119895(119905) = 119903

119894(119905) 119895 = 1 2 119902

119894minus1

(14)


119911as a CQA in 1198601015840

119894(119905) =

1199031198941(119905) 119903

1198942(119905) 119903



119905

119911119895120572119905

119911119895120573119905

119911119895]

119879




119909119905+1120603

119911119895= 119873(120583

119905120603

119911119895 (120575

119905120603

119911119895)

2

)

=

119909119905

119911119895+ 119873(0

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

) 120603 = 120572


+ 119873(0

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

120594

) 120603 = 120573

(15)



119911119895as fol-

lows

119909119905+1120603

119911119895=

119896 minus 1

119896

119909119905+1120603

119911119895gt 1

0 119909119905+1120603

119911119895lt 0

119873(120583119905120603

119911119895 (120575

119905120603

119911119895)

2

) others

(16)


119911119895|


119911119895|

2



119905+1

1199110 119909

119905+1120603

119911119895 119909

119905+1

119911119898minus1) and (119909119905

1199110 119909

119905

119911119895 119909

119905

119911119902119894minus1) If


119911119895with 119909119905+1120603


0

1

minus1

minus1

120573ij

120572ij

Δ120579ij

x

y

1


119909119905120603


119911119895= 120572

119905

119911119895 120573119905+1

119911119895= 120573

119905



119911119895|

2

and |120573119905119911119895|


119911119895 the newly

generated 120572119905+1119911119895

and 120573119905+1119911119895

are decided by (17)

[

120572119905+1

119911119895

120573119905+1

119911119895

] = [

cos (Δ120579119905119911119895) minus sin (Δ120579119905

119911119895)

sin (Δ120579119905119911119895) cos (Δ120579119905

119911119895)

] [

120572119905

119911119895

120573119905

119911119895

] (17)


119905

119911119895 120573

119905


Figure 2

(1) If (120572119905119911119895 120573

119905



(2) If (120572119905119911119895 120573

119905



(3) If (120572119905119911119895 120573

119905




Δ120579119905

119911119895= sgn (120572119905

119911119895120573119905

119911119895) Δ120579 exp(minus

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

+ 119873119902119873

119904

) (18)


119911119895|

2 |120573119905119911119895|

2 as well as 119873119902119873




119902


119902=

sum119873

119894=1119902119894and 119873



119894119895119873


as follows

119873119904=

119873119904+ 1 119909

119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

1 119909119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

(19)


11986010158401015840(119905) = 119860 (119905) 119860

10158401015840

1(119905) 119860

10158401015840

119873(119905) (20)


11986010158401015840

119894(119905) = 119903

10158401015840

1198941(119905) 119903

10158401015840

1198942(119905) 119903

10158401015840

119894119902119894minus1(119905) 119894 = 1 2 119873

(21)



1199091 119909

119898minus1] isin 119877


1198881199041 119888

119904119898minus1] isin 119885



exists

C119887119894(119905) = C

11990310158401015840119894119895(119905) | max119876(C

11990310158401015840119894119895) 119895 = 0 1 2 119902

119894minus 1

(22)

making 119876(C119903119894) lt 119876(C

119887119894) 119894 = 1 2 119873 then 119903

10158401015840

1198940(119905 +

1) = 119887119894(119905) otherwise 11990310158401015840


1198940(119905)





119894119895and 119861

119894119895


119894119895can then be

revealed as 119861119894119895= 119860




(a)

NO0 11986000

11986001

11986002

11986003

11986004

11986005

11986006

11986007

NO1 11986010

11986011

11986012

11986013

11986014

11986015

11986016

11986017

NO2 11986020

11986021

11986022

11986023

11986024

11986025

11986026

11986027

NO3 11986030

11986031

11986032

11986033

11986034

11986035

11986036

11986037

NO4 11986040

11986041

11986042

11986043

11986044

11986045

11986046

11986047

(b)

NO0 11986000

11986011

11986022

11986033

11986044

11986005

11986016

11986027

NO1 11986010

11986021

11986032

11986043

11986004

11986015

11986026

11986037

NO2 11986020

11986031

11986042

11986003

11986014

11986025

11986036

11986047

NO3 11986030

11986041

11986002

11986013

11986024

11986035

11986046

11986007

NO4 11986040

11986001

11986012

11986023

11986034

11986045

11986006

11986017




(119905) isobtained


(119905)









1 119903

2 119903


119894responds to



2 119904

119898 channel set

119862 = 1198881 119888

2 119888

119896 user set

119880 = 1199061 119906

2 119906

119899 119888 (119906

119895) and 119901

119906119895(119895 = 1 2 119899)




119903119894)

(3) 119876119894(119905) larr function(C



10158401015840

1198940(119905) larr 119903


119898lowast

(5) do (6) 119860


(7) 11986010158401015840(119905) larr 119860




119898

(11) 119876lowast= max(119876



(13) if ((119905 lt 119905max) | (sum119873

119894=1119867(119883

119903119894) gt 120576)) then


119873

119894=1119867(119883

119903119894) gt 120576))

Pseudocode 1










119898amp 119879

119890) and



120575 119875)



119905rarrinfin119875(119876

119905= 119876

lowast) = 1







=

119909119905+1120572119911119895

119909119905+1120573

119911119895

the probability

for 119909119905119911119895to mutate to 119909119905+1120572

119911119895should be

119866(119909119905

119911119895 119909

119905+1120572

119911119895)

= int

119909119905+1120572119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816


119905+1120572

119911119895)

2

120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(23)


119911119895

should be

119866(119909119905

119911119895 119909

119905+1120573

119911119895)

= int

119909119905+1120573

119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816


119905+1120573

119911119895)

2

120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(24)



120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)


120582to 119886


probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)


strictly positive



119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879


119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903



119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)


119890(119903




120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)


120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)




120583120582(119905) = 119901

120583120583(119905) = 1 and


119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)


regular matrix



119905rarrinfin119875119905= 119875







119894119895=






lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)



119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










S

U

E

s1 s2 si sm

u1 u2 u3 unuj





119895


119894





119904119894 and 119861


119894) In this



1) 119886(119904

2) 119886(119904

119898)) where


119894 When 119904

119894selects the




119896

119902=1119880119888119902 where 119878

119888119902denotes






119888119902=

(119878119888119902 119880

119888119902 119864

119888119902)



119876119904119894(a) = sum

119906isin119873(119904119894)

119901119906sdot

1 (119888 (119906) = 119886 (119904119894))

1 + sum119905isin119861119904119894

1 (119888 (119906) = 119886 (119904119905) 119904

119905isin 119873 (119906))

(1)


119894 the higher






119876 (a) = sum119904119894isin119878

119876119904119894(a) (2)




max sum

aisinO119876 (a) times 120587 (a)

st 120587 (a) isin [0 1]

sum

aisinO120587 (a) = 1

(3)









CQA def=[

[



119898minus1



119898minus1



119898minus1

]

]

(5)





119894|2+ |120573

119894|2= 1

where |120572119894|2 and |120573





119883 = [1199090 119909

1 119909

119894 119909

119898minus1] isin 119877

119898 (6)



C = [1198881199040 119888

1199041 119888

119904119894 119888

119904119898minus1] isin 119885

119898 (7)





119888119904119894


119894rfloor 119894 = 0 1 119898 minus 1 (8)



119867(119883) = 119867 (1199090 119909

1 119909

119898minus1)

= 119867 (1199090) + 119867 (119909

1| 119909

0)


| 1199090 119909

1 119909

119898minus2)

=

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120572119894

1003816100381610038161003816

2+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120573119894

1003816100381610038161003816

2)

= minus

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816

2

+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816

2

)

= minus2

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816)

(9)


119894rarr 0



1199032 119903










1198940[25] 119894 = 1 2 119873 in immune memory



119860 (119905)


997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr 1198601015840(119905)


997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr

11986010158401015840(119905)


(10)



119879119888(119860 (119905)) = 119879

119888(119903

1) 119879

119888(119903

2) 119879

119888(119903

119873) (11)

where 119879119888(119903

119894) = 119864

119894times 119903

119894 119894 = 1 2 119873 and 119864

119894is a unit row




119902119894=[

[

[

[

119873119888times

119876 (C119894)

sum119873

119895=1119876(C

119895)

]

]

]

]

(12)




1198601015840(119905) = 119860 (119905) 119860

1015840

1(119905) 119860

1015840

119873(119905) (13)

where

1198601015840

119894(119905) = 119903

1198941(119905) 119903

1198942(119905) 119903

119894119902119894minus1(119905)

119903119894119895(119905) = 119903

119894(119905) 119895 = 1 2 119902

119894minus1

(14)


119911as a CQA in 1198601015840

119894(119905) =

1199031198941(119905) 119903

1198942(119905) 119903



119905

119911119895120572119905

119911119895120573119905

119911119895]

119879




119909119905+1120603

119911119895= 119873(120583

119905120603

119911119895 (120575

119905120603

119911119895)

2

)

=

119909119905

119911119895+ 119873(0

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

) 120603 = 120572


+ 119873(0

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

120594

) 120603 = 120573

(15)



119911119895as fol-

lows

119909119905+1120603

119911119895=

119896 minus 1

119896

119909119905+1120603

119911119895gt 1

0 119909119905+1120603

119911119895lt 0

119873(120583119905120603

119911119895 (120575

119905120603

119911119895)

2

) others

(16)


119911119895|


119911119895|

2



119905+1

1199110 119909

119905+1120603

119911119895 119909

119905+1

119911119898minus1) and (119909119905

1199110 119909

119905

119911119895 119909

119905

119911119902119894minus1) If


119911119895with 119909119905+1120603


0

1

minus1

minus1

120573ij

120572ij

Δ120579ij

x

y

1


119909119905120603


119911119895= 120572

119905

119911119895 120573119905+1

119911119895= 120573

119905



119911119895|

2

and |120573119905119911119895|


119911119895 the newly

generated 120572119905+1119911119895

and 120573119905+1119911119895

are decided by (17)

[

120572119905+1

119911119895

120573119905+1

119911119895

] = [

cos (Δ120579119905119911119895) minus sin (Δ120579119905

119911119895)

sin (Δ120579119905119911119895) cos (Δ120579119905

119911119895)

] [

120572119905

119911119895

120573119905

119911119895

] (17)


119905

119911119895 120573

119905


Figure 2

(1) If (120572119905119911119895 120573

119905



(2) If (120572119905119911119895 120573

119905



(3) If (120572119905119911119895 120573

119905




Δ120579119905

119911119895= sgn (120572119905

119911119895120573119905

119911119895) Δ120579 exp(minus

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

+ 119873119902119873

119904

) (18)


119911119895|

2 |120573119905119911119895|

2 as well as 119873119902119873




119902


119902=

sum119873

119894=1119902119894and 119873



119894119895119873


as follows

119873119904=

119873119904+ 1 119909

119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

1 119909119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

(19)


11986010158401015840(119905) = 119860 (119905) 119860

10158401015840

1(119905) 119860

10158401015840

119873(119905) (20)


11986010158401015840

119894(119905) = 119903

10158401015840

1198941(119905) 119903

10158401015840

1198942(119905) 119903

10158401015840

119894119902119894minus1(119905) 119894 = 1 2 119873

(21)



1199091 119909

119898minus1] isin 119877


1198881199041 119888

119904119898minus1] isin 119885



exists

C119887119894(119905) = C

11990310158401015840119894119895(119905) | max119876(C

11990310158401015840119894119895) 119895 = 0 1 2 119902

119894minus 1

(22)

making 119876(C119903119894) lt 119876(C

119887119894) 119894 = 1 2 119873 then 119903

10158401015840

1198940(119905 +

1) = 119887119894(119905) otherwise 11990310158401015840


1198940(119905)





119894119895and 119861

119894119895


119894119895can then be

revealed as 119861119894119895= 119860




(a)

NO0 11986000

11986001

11986002

11986003

11986004

11986005

11986006

11986007

NO1 11986010

11986011

11986012

11986013

11986014

11986015

11986016

11986017

NO2 11986020

11986021

11986022

11986023

11986024

11986025

11986026

11986027

NO3 11986030

11986031

11986032

11986033

11986034

11986035

11986036

11986037

NO4 11986040

11986041

11986042

11986043

11986044

11986045

11986046

11986047

(b)

NO0 11986000

11986011

11986022

11986033

11986044

11986005

11986016

11986027

NO1 11986010

11986021

11986032

11986043

11986004

11986015

11986026

11986037

NO2 11986020

11986031

11986042

11986003

11986014

11986025

11986036

11986047

NO3 11986030

11986041

11986002

11986013

11986024

11986035

11986046

11986007

NO4 11986040

11986001

11986012

11986023

11986034

11986045

11986006

11986017




(119905) isobtained


(119905)









1 119903

2 119903


119894responds to



2 119904

119898 channel set

119862 = 1198881 119888

2 119888

119896 user set

119880 = 1199061 119906

2 119906

119899 119888 (119906

119895) and 119901

119906119895(119895 = 1 2 119899)




119903119894)

(3) 119876119894(119905) larr function(C



10158401015840

1198940(119905) larr 119903


119898lowast

(5) do (6) 119860


(7) 11986010158401015840(119905) larr 119860




119898

(11) 119876lowast= max(119876



(13) if ((119905 lt 119905max) | (sum119873

119894=1119867(119883

119903119894) gt 120576)) then


119873

119894=1119867(119883

119903119894) gt 120576))

Pseudocode 1










119898amp 119879

119890) and



120575 119875)



119905rarrinfin119875(119876

119905= 119876

lowast) = 1







=

119909119905+1120572119911119895

119909119905+1120573

119911119895

the probability

for 119909119905119911119895to mutate to 119909119905+1120572

119911119895should be

119866(119909119905

119911119895 119909

119905+1120572

119911119895)

= int

119909119905+1120572119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816


119905+1120572

119911119895)

2

120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(23)


119911119895

should be

119866(119909119905

119911119895 119909

119905+1120573

119911119895)

= int

119909119905+1120573

119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816


119905+1120573

119911119895)

2

120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(24)



120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)


120582to 119886


probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)


strictly positive



119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879


119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903



119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)


119890(119903




120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)


120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)




120583120582(119905) = 119901

120583120583(119905) = 1 and


119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)


regular matrix



119905rarrinfin119875119905= 119875







119894119895=






lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)



119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











CQA def=[

[



119898minus1



119898minus1



119898minus1

]

]

(5)





119894|2+ |120573

119894|2= 1

where |120572119894|2 and |120573





119883 = [1199090 119909

1 119909

119894 119909

119898minus1] isin 119877

119898 (6)



C = [1198881199040 119888

1199041 119888

119904119894 119888

119904119898minus1] isin 119885

119898 (7)





119888119904119894


119894rfloor 119894 = 0 1 119898 minus 1 (8)



119867(119883) = 119867 (1199090 119909

1 119909

119898minus1)

= 119867 (1199090) + 119867 (119909

1| 119909

0)


| 1199090 119909

1 119909

119898minus2)

=

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120572119894

1003816100381610038161003816

2+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1

1003816100381610038161003816120573119894

1003816100381610038161003816

2)

= minus

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816

2

+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816

2

)

= minus2

119898minus1

sum

119894=0

(1003816100381610038161003816120572119894

1003816100381610038161003816

2 log 1003816100381610038161003816120572119894

1003816100381610038161003816+1003816100381610038161003816120573119894

1003816100381610038161003816

2 log 1003816100381610038161003816120573119894

1003816100381610038161003816)

(9)


119894rarr 0



1199032 119903










1198940[25] 119894 = 1 2 119873 in immune memory



119860 (119905)


997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr 1198601015840(119905)


997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888997888rarr

11986010158401015840(119905)


(10)



119879119888(119860 (119905)) = 119879

119888(119903

1) 119879

119888(119903

2) 119879

119888(119903

119873) (11)

where 119879119888(119903

119894) = 119864

119894times 119903

119894 119894 = 1 2 119873 and 119864

119894is a unit row




119902119894=[

[

[

[

119873119888times

119876 (C119894)

sum119873

119895=1119876(C

119895)

]

]

]

]

(12)




1198601015840(119905) = 119860 (119905) 119860

1015840

1(119905) 119860

1015840

119873(119905) (13)

where

1198601015840

119894(119905) = 119903

1198941(119905) 119903

1198942(119905) 119903

119894119902119894minus1(119905)

119903119894119895(119905) = 119903

119894(119905) 119895 = 1 2 119902

119894minus1

(14)


119911as a CQA in 1198601015840

119894(119905) =

1199031198941(119905) 119903

1198942(119905) 119903



119905

119911119895120572119905

119911119895120573119905

119911119895]

119879




119909119905+1120603

119911119895= 119873(120583

119905120603

119911119895 (120575

119905120603

119911119895)

2

)

=

119909119905

119911119895+ 119873(0

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

) 120603 = 120572


+ 119873(0

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

120594

) 120603 = 120573

(15)



119911119895as fol-

lows

119909119905+1120603

119911119895=

119896 minus 1

119896

119909119905+1120603

119911119895gt 1

0 119909119905+1120603

119911119895lt 0

119873(120583119905120603

119911119895 (120575

119905120603

119911119895)

2

) others

(16)


119911119895|


119911119895|

2



119905+1

1199110 119909

119905+1120603

119911119895 119909

119905+1

119911119898minus1) and (119909119905

1199110 119909

119905

119911119895 119909

119905

119911119902119894minus1) If


119911119895with 119909119905+1120603


0

1

minus1

minus1

120573ij

120572ij

Δ120579ij

x

y

1


119909119905120603


119911119895= 120572

119905

119911119895 120573119905+1

119911119895= 120573

119905



119911119895|

2

and |120573119905119911119895|


119911119895 the newly

generated 120572119905+1119911119895

and 120573119905+1119911119895

are decided by (17)

[

120572119905+1

119911119895

120573119905+1

119911119895

] = [

cos (Δ120579119905119911119895) minus sin (Δ120579119905

119911119895)

sin (Δ120579119905119911119895) cos (Δ120579119905

119911119895)

] [

120572119905

119911119895

120573119905

119911119895

] (17)


119905

119911119895 120573

119905


Figure 2

(1) If (120572119905119911119895 120573

119905



(2) If (120572119905119911119895 120573

119905



(3) If (120572119905119911119895 120573

119905




Δ120579119905

119911119895= sgn (120572119905

119911119895120573119905

119911119895) Δ120579 exp(minus

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

+ 119873119902119873

119904

) (18)


119911119895|

2 |120573119905119911119895|

2 as well as 119873119902119873




119902


119902=

sum119873

119894=1119902119894and 119873



119894119895119873


as follows

119873119904=

119873119904+ 1 119909

119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

1 119909119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

(19)


11986010158401015840(119905) = 119860 (119905) 119860

10158401015840

1(119905) 119860

10158401015840

119873(119905) (20)


11986010158401015840

119894(119905) = 119903

10158401015840

1198941(119905) 119903

10158401015840

1198942(119905) 119903

10158401015840

119894119902119894minus1(119905) 119894 = 1 2 119873

(21)



1199091 119909

119898minus1] isin 119877


1198881199041 119888

119904119898minus1] isin 119885



exists

C119887119894(119905) = C

11990310158401015840119894119895(119905) | max119876(C

11990310158401015840119894119895) 119895 = 0 1 2 119902

119894minus 1

(22)

making 119876(C119903119894) lt 119876(C

119887119894) 119894 = 1 2 119873 then 119903

10158401015840

1198940(119905 +

1) = 119887119894(119905) otherwise 11990310158401015840


1198940(119905)





119894119895and 119861

119894119895


119894119895can then be

revealed as 119861119894119895= 119860




(a)

NO0 11986000

11986001

11986002

11986003

11986004

11986005

11986006

11986007

NO1 11986010

11986011

11986012

11986013

11986014

11986015

11986016

11986017

NO2 11986020

11986021

11986022

11986023

11986024

11986025

11986026

11986027

NO3 11986030

11986031

11986032

11986033

11986034

11986035

11986036

11986037

NO4 11986040

11986041

11986042

11986043

11986044

11986045

11986046

11986047

(b)

NO0 11986000

11986011

11986022

11986033

11986044

11986005

11986016

11986027

NO1 11986010

11986021

11986032

11986043

11986004

11986015

11986026

11986037

NO2 11986020

11986031

11986042

11986003

11986014

11986025

11986036

11986047

NO3 11986030

11986041

11986002

11986013

11986024

11986035

11986046

11986007

NO4 11986040

11986001

11986012

11986023

11986034

11986045

11986006

11986017




(119905) isobtained


(119905)









1 119903

2 119903


119894responds to



2 119904

119898 channel set

119862 = 1198881 119888

2 119888

119896 user set

119880 = 1199061 119906

2 119906

119899 119888 (119906

119895) and 119901

119906119895(119895 = 1 2 119899)




119903119894)

(3) 119876119894(119905) larr function(C



10158401015840

1198940(119905) larr 119903


119898lowast

(5) do (6) 119860


(7) 11986010158401015840(119905) larr 119860




119898

(11) 119876lowast= max(119876



(13) if ((119905 lt 119905max) | (sum119873

119894=1119867(119883

119903119894) gt 120576)) then


119873

119894=1119867(119883

119903119894) gt 120576))

Pseudocode 1










119898amp 119879

119890) and



120575 119875)



119905rarrinfin119875(119876

119905= 119876

lowast) = 1







=

119909119905+1120572119911119895

119909119905+1120573

119911119895

the probability

for 119909119905119911119895to mutate to 119909119905+1120572

119911119895should be

119866(119909119905

119911119895 119909

119905+1120572

119911119895)

= int

119909119905+1120572119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816


119905+1120572

119911119895)

2

120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(23)


119911119895

should be

119866(119909119905

119911119895 119909

119905+1120573

119911119895)

= int

119909119905+1120573

119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816


119905+1120573

119911119895)

2

120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(24)



120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)


120582to 119886


probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)


strictly positive



119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879


119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903



119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)


119890(119903




120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)


120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)




120583120582(119905) = 119901

120583120583(119905) = 1 and


119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)


regular matrix



119905rarrinfin119875119905= 119875







119894119895=






lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)



119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












1198601015840(119905) = 119860 (119905) 119860

1015840

1(119905) 119860

1015840

119873(119905) (13)

where

1198601015840

119894(119905) = 119903

1198941(119905) 119903

1198942(119905) 119903

119894119902119894minus1(119905)

119903119894119895(119905) = 119903

119894(119905) 119895 = 1 2 119902

119894minus1

(14)


119911as a CQA in 1198601015840

119894(119905) =

1199031198941(119905) 119903

1198942(119905) 119903



119905

119911119895120572119905

119911119895120573119905

119911119895]

119879




119909119905+1120603

119911119895= 119873(120583

119905120603

119911119895 (120575

119905120603

119911119895)

2

)

=

119909119905

119911119895+ 119873(0

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

) 120603 = 120572


+ 119873(0

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

120594

) 120603 = 120573

(15)



119911119895as fol-

lows

119909119905+1120603

119911119895=

119896 minus 1

119896

119909119905+1120603

119911119895gt 1

0 119909119905+1120603

119911119895lt 0

119873(120583119905120603

119911119895 (120575

119905120603

119911119895)

2

) others

(16)


119911119895|


119911119895|

2



119905+1

1199110 119909

119905+1120603

119911119895 119909

119905+1

119911119898minus1) and (119909119905

1199110 119909

119905

119911119895 119909

119905

119911119902119894minus1) If


119911119895with 119909119905+1120603


0

1

minus1

minus1

120573ij

120572ij

Δ120579ij

x

y

1


119909119905120603


119911119895= 120572

119905

119911119895 120573119905+1

119911119895= 120573

119905



119911119895|

2

and |120573119905119911119895|


119911119895 the newly

generated 120572119905+1119911119895

and 120573119905+1119911119895

are decided by (17)

[

120572119905+1

119911119895

120573119905+1

119911119895

] = [

cos (Δ120579119905119911119895) minus sin (Δ120579119905

119911119895)

sin (Δ120579119905119911119895) cos (Δ120579119905

119911119895)

] [

120572119905

119911119895

120573119905

119911119895

] (17)


119905

119911119895 120573

119905


Figure 2

(1) If (120572119905119911119895 120573

119905



(2) If (120572119905119911119895 120573

119905



(3) If (120572119905119911119895 120573

119905




Δ120579119905

119911119895= sgn (120572119905

119911119895120573119905

119911119895) Δ120579 exp(minus

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2

+ 119873119902119873

119904

) (18)


119911119895|

2 |120573119905119911119895|

2 as well as 119873119902119873




119902


119902=

sum119873

119894=1119902119894and 119873



119894119895119873


as follows

119873119904=

119873119904+ 1 119909

119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

1 119909119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

(19)


11986010158401015840(119905) = 119860 (119905) 119860

10158401015840

1(119905) 119860

10158401015840

119873(119905) (20)


11986010158401015840

119894(119905) = 119903

10158401015840

1198941(119905) 119903

10158401015840

1198942(119905) 119903

10158401015840

119894119902119894minus1(119905) 119894 = 1 2 119873

(21)



1199091 119909

119898minus1] isin 119877


1198881199041 119888

119904119898minus1] isin 119885



exists

C119887119894(119905) = C

11990310158401015840119894119895(119905) | max119876(C

11990310158401015840119894119895) 119895 = 0 1 2 119902

119894minus 1

(22)

making 119876(C119903119894) lt 119876(C

119887119894) 119894 = 1 2 119873 then 119903

10158401015840

1198940(119905 +

1) = 119887119894(119905) otherwise 11990310158401015840


1198940(119905)





119894119895and 119861

119894119895


119894119895can then be

revealed as 119861119894119895= 119860




(a)

NO0 11986000

11986001

11986002

11986003

11986004

11986005

11986006

11986007

NO1 11986010

11986011

11986012

11986013

11986014

11986015

11986016

11986017

NO2 11986020

11986021

11986022

11986023

11986024

11986025

11986026

11986027

NO3 11986030

11986031

11986032

11986033

11986034

11986035

11986036

11986037

NO4 11986040

11986041

11986042

11986043

11986044

11986045

11986046

11986047

(b)

NO0 11986000

11986011

11986022

11986033

11986044

11986005

11986016

11986027

NO1 11986010

11986021

11986032

11986043

11986004

11986015

11986026

11986037

NO2 11986020

11986031

11986042

11986003

11986014

11986025

11986036

11986047

NO3 11986030

11986041

11986002

11986013

11986024

11986035

11986046

11986007

NO4 11986040

11986001

11986012

11986023

11986034

11986045

11986006

11986017




(119905) isobtained


(119905)









1 119903

2 119903


119894responds to



2 119904

119898 channel set

119862 = 1198881 119888

2 119888

119896 user set

119880 = 1199061 119906

2 119906

119899 119888 (119906

119895) and 119901

119906119895(119895 = 1 2 119899)




119903119894)

(3) 119876119894(119905) larr function(C



10158401015840

1198940(119905) larr 119903


119898lowast

(5) do (6) 119860


(7) 11986010158401015840(119905) larr 119860




119898

(11) 119876lowast= max(119876



(13) if ((119905 lt 119905max) | (sum119873

119894=1119867(119883

119903119894) gt 120576)) then


119873

119894=1119867(119883

119903119894) gt 120576))

Pseudocode 1










119898amp 119879

119890) and



120575 119875)



119905rarrinfin119875(119876

119905= 119876

lowast) = 1







=

119909119905+1120572119911119895

119909119905+1120573

119911119895

the probability

for 119909119905119911119895to mutate to 119909119905+1120572

119911119895should be

119866(119909119905

119911119895 119909

119905+1120572

119911119895)

= int

119909119905+1120572119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816


119905+1120572

119911119895)

2

120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(23)


119911119895

should be

119866(119909119905

119911119895 119909

119905+1120573

119911119895)

= int

119909119905+1120573

119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816


119905+1120573

119911119895)

2

120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(24)



120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)


120582to 119886


probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)


strictly positive



119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879


119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903



119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)


119890(119903




120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)


120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)




120583120582(119905) = 119901

120583120583(119905) = 1 and


119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)


regular matrix



119905rarrinfin119875119905= 119875







119894119895=






lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)



119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119902


119902=

sum119873

119894=1119902119894and 119873



119894119895119873


as follows

119873119904=

119873119904+ 1 119909

119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

1 119909119905+1

119894119895= 119909

119905

119894119895 119894 = 1 2 119873

119895 = 0 1 119898 minus 1

(19)


11986010158401015840(119905) = 119860 (119905) 119860

10158401015840

1(119905) 119860

10158401015840

119873(119905) (20)


11986010158401015840

119894(119905) = 119903

10158401015840

1198941(119905) 119903

10158401015840

1198942(119905) 119903

10158401015840

119894119902119894minus1(119905) 119894 = 1 2 119873

(21)



1199091 119909

119898minus1] isin 119877


1198881199041 119888

119904119898minus1] isin 119885



exists

C119887119894(119905) = C

11990310158401015840119894119895(119905) | max119876(C

11990310158401015840119894119895) 119895 = 0 1 2 119902

119894minus 1

(22)

making 119876(C119903119894) lt 119876(C

119887119894) 119894 = 1 2 119873 then 119903

10158401015840

1198940(119905 +

1) = 119887119894(119905) otherwise 11990310158401015840


1198940(119905)





119894119895and 119861

119894119895


119894119895can then be

revealed as 119861119894119895= 119860




(a)

NO0 11986000

11986001

11986002

11986003

11986004

11986005

11986006

11986007

NO1 11986010

11986011

11986012

11986013

11986014

11986015

11986016

11986017

NO2 11986020

11986021

11986022

11986023

11986024

11986025

11986026

11986027

NO3 11986030

11986031

11986032

11986033

11986034

11986035

11986036

11986037

NO4 11986040

11986041

11986042

11986043

11986044

11986045

11986046

11986047

(b)

NO0 11986000

11986011

11986022

11986033

11986044

11986005

11986016

11986027

NO1 11986010

11986021

11986032

11986043

11986004

11986015

11986026

11986037

NO2 11986020

11986031

11986042

11986003

11986014

11986025

11986036

11986047

NO3 11986030

11986041

11986002

11986013

11986024

11986035

11986046

11986007

NO4 11986040

11986001

11986012

11986023

11986034

11986045

11986006

11986017




(119905) isobtained


(119905)









1 119903

2 119903


119894responds to



2 119904

119898 channel set

119862 = 1198881 119888

2 119888

119896 user set

119880 = 1199061 119906

2 119906

119899 119888 (119906

119895) and 119901

119906119895(119895 = 1 2 119899)




119903119894)

(3) 119876119894(119905) larr function(C



10158401015840

1198940(119905) larr 119903


119898lowast

(5) do (6) 119860


(7) 11986010158401015840(119905) larr 119860




119898

(11) 119876lowast= max(119876



(13) if ((119905 lt 119905max) | (sum119873

119894=1119867(119883

119903119894) gt 120576)) then


119873

119894=1119867(119883

119903119894) gt 120576))

Pseudocode 1










119898amp 119879

119890) and



120575 119875)



119905rarrinfin119875(119876

119905= 119876

lowast) = 1







=

119909119905+1120572119911119895

119909119905+1120573

119911119895

the probability

for 119909119905119911119895to mutate to 119909119905+1120572

119911119895should be

119866(119909119905

119911119895 119909

119905+1120572

119911119895)

= int

119909119905+1120572119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816


119905+1120572

119911119895)

2

120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(23)


119911119895

should be

119866(119909119905

119911119895 119909

119905+1120573

119911119895)

= int

119909119905+1120573

119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816


119905+1120573

119911119895)

2

120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(24)



120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)


120582to 119886


probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)


strictly positive



119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879


119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903



119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)


119890(119903




120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)


120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)




120583120582(119905) = 119901

120583120583(119905) = 1 and


119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)


regular matrix



119905rarrinfin119875119905= 119875







119894119895=






lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)



119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











2 119904

119898 channel set

119862 = 1198881 119888

2 119888

119896 user set

119880 = 1199061 119906

2 119906

119899 119888 (119906

119895) and 119901

119906119895(119895 = 1 2 119899)




119903119894)

(3) 119876119894(119905) larr function(C



10158401015840

1198940(119905) larr 119903


119898lowast

(5) do (6) 119860


(7) 11986010158401015840(119905) larr 119860




119898

(11) 119876lowast= max(119876



(13) if ((119905 lt 119905max) | (sum119873

119894=1119867(119883

119903119894) gt 120576)) then


119873

119894=1119867(119883

119903119894) gt 120576))

Pseudocode 1










119898amp 119879

119890) and



120575 119875)



119905rarrinfin119875(119876

119905= 119876

lowast) = 1







=

119909119905+1120572119911119895

119909119905+1120573

119911119895

the probability

for 119909119905119911119895to mutate to 119909119905+1120572

119911119895should be

119866(119909119905

119911119895 119909

119905+1120572

119911119895)

= int

119909119905+1120572119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816


119905+1120572

119911119895)

2

120587

10038161003816100381610038161003816120572119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(23)


119911119895

should be

119866(119909119905

119911119895 119909

119905+1120573

119911119895)

= int

119909119905+1120573

119911119895

119909119905119911119895

(

1

radic2120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816


119905+1120573

119911119895)

2

120587

10038161003816100381610038161003816120573119905

119911119895

10038161003816100381610038161003816

2)) sdot 119889119909

gt 0

(24)



120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)


120582to 119886


probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)


strictly positive



119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879


119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903



119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)


119890(119903




120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)


120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)




120583120582(119905) = 119901

120583120583(119905) = 1 and


119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)


regular matrix



119905rarrinfin119875119905= 119875







119894119895=






lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)



119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











120583to x

120582after this

operation would be

119866(x120583 x

120582) = 119866 (119909

119905

119911119895 119909

119905+1

119911119895)

= 119866 (119909119905

119911119895 119909

119905+1120572

119911119895) sdot 119866 (119909

119905

119911119895 119909

119905+1120573

119911119895) gt 0

(25)


120582to 119886


probability 119880(119886120583 119886

120582) gt 0 Thus

119898120583120582(119879

119898) = 119866 (x

120583 x

120582) times (1 minus 119880 (119886

120583 119886

120582))

+ (1 minus 119866 (x120583 x

120582)) times 119880 (119886

120583 119886

120582) gt 0

(26)


strictly positive



119888 119879

119898 119879

119868 and

119879119890 Denote 119879 to be 119879 = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879


119903119894(119905 + 1) = 119879[119903

119894(119905)] = 119879

119888sdot 119879

119898sdot 119879

119868sdot 119879

119890[119903



119901120583120582(119905) = 119901 119860 (119905 + 1) = 119884 | 119860 (119905) = 119882 = 119901 (119884 | 119882)

=

119873

prod

119894=1

119901 119879119888(119903

119894(119905)) times

119902119894minus1

prod

119895=1

119901 119879119898(119903

119894119895(119905)) sdot 119901

119898

times

119905

prod

120578=1

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905))

times119901 119879119890(119903

120583119894(119905 + 1)) sdot 119901

119888

(27)

where

119901 119879119888(119903

119894(119905)) =

119876 (C119894)

sum119873

119895=1119876(C

119895)

gt 0

119901 119879119898(119903

119894119895(119905)) = 119898

120583120582(119879

119898) ge 0

(28)


119890(119903




120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 1 (29)


120582119894)

119901 119879119868(119903

120582119894(119905 + 1) = 119903

120583119894(119905)) = 0 (30)




120583120582(119905) = 119901

120583120583(119905) = 1 and


119901120583120582(119905) gt 0 st 119876 (C

120583119894) le 119876 (C

120582119894)

119901120583120582(119905) = 0 st 119876 (C

120583119894) gt 119876 (C

120582119894)

(31)


regular matrix



119905rarrinfin119875119905= 119875







119894119895=






lim119905rarrinfin

119875 (119876 (119905) = 119876119905119888= 119876

lowast) = 1 (32)



119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











119873 119901119898

119901119888

119873119888

120594 120576 119905max

10 05 088 15 3 10minus5 1000











ID 1198760

119876lowast Times

1 2439 9345 4732 2536 9345 4313 6304 9345 4874 9003 9345 3755 8604 9345 5106 6966 9345 4577 7444 9171 2188 8046 9345 3249 8667 9345 32110 8856 9345 7811 8871 9345 31012 2122 9345 45413 7164 9345 35614 2439 9345 40915 6304 9345 32616 2536 9345 24517 8667 9345 26518 4350 9345 35119 9345 9345 020 2122 9345 45621 7164 9345 32822 8604 9345 9123 9003 9345 10324 5438 9345 50125 2536 9171 36526 5473 9345 14127 3180 9345 26528 2439 9345 45429 8992 9345 26330 8646 9003 45331 3857 9345 26132 2122 9345 35633 7444 9345 45234 2597 9345 36535 2122 9345 53236 8367 9345 26937 6304 9345 46238 7146 9345 25439 8171 9345 5640 3200 9345 49541 9003 9345 32142 5251 9345 25643 3062 9345 51844 6304 9345 26545 6996 9345 34846 8046 9345 20647 2536 9345 52748 9345 9345 049 7164 9345 21550 8171 9345 256


5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










5 10 15 20 25 30 35 40 45 5006

07

08

09

1

11

Iterations

QoM



(a)

100 200 300 400 500 600 700 800 900 10002

3

4

5

6

7

8

9

10

Iterations

QoM



(b)

100 200 300 400 500 600 700 800 900 100023

24

25

26

27

28

29

30

Iterations

QoM



(c)












ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation











ID 1198760

119876lowast Times

1 24150 28900 6842 26367 28900 5963 27200 28850 3524 28900 28900 05 28250 28900 1526 25850 29050 7157 27417 28900 2548 24533 28900 5619 28450 28900 21510 27250 28900 32511 27200 28900 38712 28467 28900 15213 24533 28900 35614 27050 28900 26115 28700 28900 16416 28150 28850 9217 26900 28900 36418 24533 28900 25919 24750 28900 38120 25850 28900 68121 28267 28900 15422 24750 29050 29623 27200 28900 61424 25700 28900 26525 24150 28900 56226 28567 28900 24427 27800 29050 26428 25700 28900 15729 24533 28900 24630 27800 28900 10631 27417 28900 31532 28850 28900 2633 27800 29050 26834 24533 28900 65435 27200 28900 34136 25700 28900 46537 26750 28900 28738 28467 28900 38439 27900 29050 46840 27200 28900 21541 24750 28900 21642 24150 28900 65643 23587 28900 14644 25700 28900 35645 28267 28850 2146 27200 28900 26547 24533 28900 37848 27800 28900 19849 28700 28850 25450 26750 28900 394

0 50 100 150 200 250 300 350 400 450 5000

50

100

150

200

250

300

350

400

450

500









Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation












Averageoptimal QoM


AverageoptimalQoM






100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

LPMQICA

(a)

100 200 300 400 500 600 700 800 900 100020

22

24

26

28

30

Time slots

QoM

GreedyGibbs

(b)




4 6 8 10 12 14 16 18 20 2206

07

08

09

1

11

12

13

14

15

Number of nodes

Aver

age n

umbe

r of a

ctiv

e use

rs m

onito

red

MQICALP

GibbsGreedy



7 Conclusion



Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation










Acknowledgments


References


































RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation














RoboticsJournal of





Journal of



RotatingMachinery





VLSI Design



Shock and Vibration







Journal of



Volume 2014


SensorsJournal of





Propagation









research article optimal qom in multichannel wireless...

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