evaluating service disciplines for ondemand mobile data collection in sensor networks

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Evaluating Service Disciplines forOn-Demand Mobile Data Collection

in Sensor NetworksLiang He, Member, IEEE , Zhe Yang, Student Member, IEEE , Jianping Pan, Senior Member, IEEE ,

Lin Cai, Senior Member, IEEE , Jingdong Xu, and Yu (Jason) Gu, Member, IEEE

Abstract Mobility-assisted data collection in sensor networks creates a new dimension to reduce and balance the energyconsumption for sensor nodes. However, it also introduces extra latency in the data collection process due to the limited mobility ofmobile elements. Therefore, how to schedule the movement of mobile elements throughout the eld is of ultimate importance. In thispaper, the on-demand scenario where data collection requests arrive at the mobile element progressively is investigated, and the datacollection process is modelled as an M=G=1=c-NJ N queuing system with an intuitive service discipline of nearest-job-next (NJN).Based on this model, the performance of data collection is evaluated through both theoretical analysis and extensive simulation. NJN isfurther extended by considering the possible requests combination (NJNC). The simulation results validate our models and offer moreinsights when compared with the rst-come-rst-serve (FCFS) discipline. In contrary to the conventional wisdom of the starvation

problem, we reveal that NJN and NJNC have better performance than FCFS, in both the average and more importantly the worstcases, which offers the much needed assurance to adopt NJN and NJNC in the design of more sophisticated data collection schemes,as well as other similar scheduling scenarios.

Index Terms Wireless ad hoc sensor networks, mobile elements, on-demand data collection

1 INTRODUCTION

M ANY applications in wireless sensor networks are dataoriented [1], [2]. Data collection in sensor networkstypically relies on the wireless communications betweensensor nodes and the sink, which may excessively consumethe limited energy supply of sensor nodes due to the super-linear path loss exponents [3]. Furthermore, sensor nodesnear the sink also tend to deplete their energy much fasterthan other nodes due to the data aggregation towards thesink, which imposes them a much heavier volume of data toforward and leads to a very unbalanced energy consump-tion in the entire network [4]. In addition, these approachesare based on a fully connected network, which requires thedense deployment of nodes and thus introduces extra costs.

Another data collection approach utilizes the often-available, controlled mobility of certain devices, referredto as mobile elements (MEs) in this paper [5], [6], [7]. Byutilizing mobile elements, not only more energy can beconserved and balanced on sensor nodes, but also thecommunications and networking become possible in verysparse networks with the store-carry-forward approach.

For example, the seabed crawler deployed in the observa-tory of the NorthEast Pacic Time-series undersea net-worked experiments (NEPTUNE) can cruise throughseveral experimentation sites, talk to experiment devi-ces, and bring the data back to the junction boxes [11].Another mobile element example is the Seaeye Sabertooth[12], a battery-powered autonomous underwater vehicle,which travels in deep water environments to collect datafrom deployed equipments, and uploads the data to thecontrol center at the docking station. Other examples of the mobility-assisted data collection include the smart buoy equipped with Seatext from WFS [13], the structuralhealth monitoring with radio-controlled helicopters [14],and so on.

Although mobile elements create a new dimension fordata collection, they also introduce extra challenges. First,the data collection latency may be large due to the rela-tively low travel speed of mobile elements [15], [18], espe-cially when compared with that of electromagnetic oracoustic waves. This large latency must be addressed forapplications with tight requirements on the timely datadelivery. Second, with a large latency, data loss mightoccur due to the buffer overow of sensor nodes, which isnot desirable for data integrity sensitive applications [16].Finally, mobile elements themselves are battery-poweredas well in most cases, e.g., the travel distance of Sabertoothis about 20-50 Km with a fully charged battery, so the datacollection must be accomplished before mobile elements

deplete their own energy.A lot of efforts have attempted to address these chal-lenges by nding the optimal data collection tour for themobile elements, under the ofine scenario where the data

L. He and Y. Gu are with the SUTD-MIT International Design Center,Singapore University of Technology and Design, 20 Dover Drive,Singapore 138682. E-mail: [email protected].

Z. Yang, J. Pan, and L. Cai are with the Department of Computer Science,University of Victoria, PO Box 3055, STN CSC, Victoria, BC V8W 3P6,Canada.

J. Xu is with the Department of Computer Science, College of InformationTechnical Science, Nankai University, 93 Weijin Road, China.

Manuscript received 28 May 2012; revised 29 Dec. 2012; accepted 16 May2013; date of publication 21 May 2013; date of current version 3 Mar. 2014.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference the Digital Object Identier below.Digital Object Identier no. 10.1109/TMC.2013.62

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in a one-dimensional space, while the sensing eld of NJN is a two-dimensional space.

The design of dynamic scheduling schemes has beenextensively explored in the scenarios such as the dynamicvehicle routing [45] and dynamic traveling salesman problem[46]. Greedy schemes similar to NJN have been explored by the research efforts on these problems [47], [48], andour queue-based analysis advances the investigation byobtaining the probability distributions of its critical per-formance metrics, such as the queue length, queuingtime, and response time. The most relevant work to oursis [49], in which the communication range between themobile elements and sensor nodes has been exploited tofacilitate the data collection, as we did in NJNC. A travel-ing salesman problem with neighbourhoods (TSPN)-basedschedule has been proposed, and the system stabilityunder it has been proved. We treat the TSPN-basedschedule as the state-of-the-art in the on-demand data

collection problem in sensor networks and adopt it as animportant benchmark in our evaluations.

3 O N-DEMAND DATA COLLECTION3.1 On-Demand Scenario versus Ofine ScenarioNumerous research efforts on the mobile data collection insensor networks exist, and most of them focus on the ofinescenario, where the mobile elements carry out the data col-lection in a periodic manner. A potential issue with this peri-odic data collection is that certain sensor nodes may nothave data to upload, and visiting these nodes just to ndout no data to collect is clearly not good for a high-efcientdata collection process.

Observing the limitation of the ofine scenario, in thispaper we consider the online scenarios, in which the datacollection is carried out by the mobile elements based on thereal-time demands from sensor nodes, i.e., the data collec-tion is carried out in an on-demand manner.

More specically, in the on-demand mobile data collec-tion problem, we consider the scenario where mobile ele-ments travel around in the sensing eld to collect datafrom sensor nodes with wireless communication techni-ques. Sensor nodes gather sensory data according to

application requirements, and when they have gatheredenough data to report, or have captured certain eventsthat are of particular interests, sensor nodes will senddata collection requests to the MEs by adopting existing

lightweight and efcient protocols that can track andcommunicate with the MEs [3], [31].

Note that usually these tracking protocols rely on themulti-hop forwarding of messages among sensor nodes.Thus adopting these protocols to report the sensory data,which are usually of much larger size, e.g., in camera sensornetworks [32], is clearly not a good choice for the nodeenergy efciency. This is also the reason that we introducethe MEs to the network.

The ME maintains a buffer to store the received requests,and serve them according to its service discipline. As a base-line, in this paper we consider the case where only one MEis available in the network, and discussion on the case of multiple MEs is provided in Section 7.

Different from the ofine scenario, the on-demanddata collection shows great dynamics, which reside in both the temporal domain, i.e., when a new data collec-tion request will arrive, and the spatial domain, i.e.,where the new request will come from. This dynamicproperty means our objective will shift from the optimal

path planning for the ME [17], [19], [29], [30], [44], to thedesign of efcient real-time service disciplines to selectthe request to serve next. The real-time character of theon-demand scenario also impose a low computationcomplexity requirement on the service disciplines. Fig. 1summaries the differences between the on-demand datacollection and that under the ofine scenario.

3.2 Our ApproachesIn the on-demand data collection, the ME needs to selectrequest from its buffer as the next one to serve, which showsa clear queuing behavior. Inspired by this, our approach isto model the on-demand data collection process as a queu-ing system (an M=G=1=c queuing system, as will beexplained in Section 4), and theoretically analyze the perfor-mance of data collection with different service disciplines.These analytical results reveal insights on the data collectionperformance and guide the design of more sophisticatedservice schemes.

When talking about service disciplines, the rst onecomes to our mind would be the rst-come-rst-serve disci-pline, whose performance has been extensively explored by the queuing theory society [39]. However, FCFS disci-pline schedules requests based on their temporal features,

which may make the ME unnecessarily move back-and-forth, as shown in Fig. 2a. This is clearly undesirable sinceusually the travel time of the ME dominates the data col-lection latency.

Fig. 1. Differences between the on-demand data collection and the off-line data collection.

Fig. 2. Demonstration of the FCFS and NJN service disciplines. For clar-ity, only requesting sensor nodes are shown and no new requests areconsidered. The arrival order of requests is shown lexicographically.

HE ET AL.: EVALUATING SERVICE DISCIPLINES FOR ON-DEMAND MOBILE DATA COLLECTION IN SENSOR NETWORKS 799


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Noticing the inefciency of FCFS, we explore two otherdisciplines that schedule the requests according to theirspatial features. The rst service discipline we explore isthe nearest-job-next discipline (Fig. 2b), i.e., on nishing theservice of the current data collection request, the MEselects the spatially nearest requesting sensor node in itsservice queue according to its current location, and travelsto the node to collect data. Furthermore, with wirelesscommunications, it is possible for the ME to collect datafrom multiple sensor nodes at a single collection site, pro-vided that the collection site is within the communicationranges of all these nodes. Inspired by this, we extend theNJN discipline to NJN-with-combination, with which otherrequests in the queue can be combined with the nearestone and served together when possible. Analytical resultson the data collection with NJNC are also derived toquantitatively evaluate the performance improvement bythe possible requests combination.

To simplify the calculation and presentation, we assumea unit square sensing eld in this paper. This assumption

can be relaxed without violating the analysis and equiva-lent results can be obtained accordingly, although the com-putation may be more complicated. Also, we assume thatthe time from a sensor node sending out its request till theME receiving the request is negligible when comparedwith the travel time the ME takes to serve the request. Dis-cussion on how to remove these two simplications can befound in Section 7.

3.3 Denitions and SymbolsFor clarity, we list and briey explain here the denitionsused in this paper.

v: the travel speed of the ME (normalized w.r.t. theside length of the eld);

r: the wireless communication range (normalizedw.r.t. the side length of the eld) between the MEand sensor nodes;

c: the maximal number of requests that the ME canaccommodate at the same time;

S : the service time of requests, or S l for the to-be-served request selected when there are l data collec-tion requests in the service queue;

L: the size of the queuing system, i.e., the number of requests that are waiting for or under service; I : the idle period of the queuing system; B : the busy period of the queuing system; pp fp 0; p 1; . . . ; p c 1g: the system size probabilities atthe departure time of requests; ww fw0; w1; . . . ; wcg: the system size probabilities atthe arrival time of requests; uu fu0; u1; . . . ; ucg: the steady-state system sizeprobabilities of the queuing system.

4 DATA COLLECTION WITH NJNWe explore the case where the ME serves data collection

requests with the NJN discipline in this section. More spe-cically, by considering the arrival and departure pro-cesses of data collection requests, we rst model thesystem as a non-preemptive M=G=1=c-NJ N queuing

system, and then obtain the analytical results on the sys-tem measures, which offer important insights on evaluat-ing the performance of the data collection.

4.1 MM=GG=1=c-NNJN Queuing ModelThe obvious queuing behavior in the data collection processinspires us to construct a queuing model to capture its per-formance, in which the ME acts as the server and data col-lection requests are treated as clients. For any queuingmodel, the clients arrival and departure processes are thetwo most fundamental components, so we characterizethem respectively in the following.

4.1.1 Arrival Process For a particular sensor node in a stable network, the probability for it to send out a data collection request at a giventime instant is small, and the total number of sensor nodesin the network is usually expected to be relatively large.Theoretically, if the client population of a queuing system is

relatively large and the probability by which clients arriveat the queue at a given time instant is relatively small, thearrival process can be adequately modeled as a Poisson pro-cess [34]. (Similar conclusions are also obtained in [35, Prop-osition 1.12], , pp. 11). Based on this, we adopt a Poissonprocess to capture the arrival of data collection requests tothe ME, which is further veried by an event-driven simula-tor in Section 6.1.

4.1.2 Departure Process The data propagation speed in sensor networks is aboutseveral hundred meters per second [30], which is much

faster than the travel speed of the ME. Thus we assumethe communication time between the ME and the sensornode to accomplish the data uploading is negligible (fur-ther discussed in Section 7). In this way, the service timeof each request can be captured by the time from the ser-vice completion of the current request to the time whenthe ME moves to the next selected requesting sensornode.

Due to the fact that the last collection site is also thestarting point of the travel when the ME serves the nextrequest, the service time of consecutively served requestsseem not to be stochastically independent. However,denote the sequence of service times as

ft1; t

2; t

3; . . .

g, and

if we examine only at every second element of the originalprocess, it is clear that ft1; t3; t5; . . .g are independent of each other, and the distribution-ergodic property of thissub-process can be easily observed [36]. The same is truefor sub-process ft2; t4; t6; . . .g. The distribution-ergodicproperty still holds if we combine these two sub-processessince their asymptotic behaviors do not change after thecombination. This means that if we can nd the time distribution when the ME travels between consecutive to-be-served sensor nodes, we can adopt it as the service timedistribution for the queuing system over a long timeperiod, i.e.,

F S x limh!1 Xh

i01h

Pr ft i xg: (1)

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One challenge in the performance analysis of NJN isits dynamic service time, in the sense that it is deter-mined by both the location of the requesting sensor nodeand that of the ME just before its service. This dynamicproperty of service time makes the existing results onthe traditional shortest-job-next discipline not applicablein our problem, which requires the service times of cli-ents are both known and xed upon their arrival to thequeue [23]. We tackle this problem by adopting existingresults on geometrical probability.

By the results in [9], the distribution of the distance between two random locations in a unit square is

f Dd

2d p 4d d 2 0 d 1;2d 2sin 1 1d 2sin 1 ffiffiffiffiffiffiffiffiffiffiffiffi1 1d 2q 4 ffiffiffiffiffiffiffiffiffiffiffiffiffid 2 1p d 2 2 1 d ffiffiffiffi2;p 0 otherwise;

8>>>>>: (2)and F Dd R d 0 f Dxdx.Based on (2), and with the constant travel speed v of theME, the travel time distribution between two uniformly and

randomly distributed sensor nodes is thus

F T t PrfD vtg0 t ffiffiffi2p =v; (3)and f T t @F T t=@t .The analysis of NJN becomes even more complicated dueto its greedy nature: the service time of the to-be-servedrequest tends to be shorter if more requests are waiting inthe system, which makes the service time state-dependent.We begin our analysis by conditioning on the system size totackle the conditional service time.

4.1.3 Finite Capacity System Note that for a specic application, certain constraints onthe maximal acceptable data collection latency exist,either because of the requirement on the timely deliveryof sensory data or the possible buffer overow of sensornodes. Thus a nite capacity queuing model is a betterchoice to capture the system behavior when comparedwith the regular M=G=1 queue. However, additionalattention is needed for those requests who arrive andnd a fully occupied system.

4.2 Service Time with a Given System SizeDenote l as the number of requests that are waiting forservice when the ME just accomplishes the service of the

current request, and is about to select the next request,i.e., the one sent by the nearest requesting sensor nodeaccording to the current location of the ME, to serve.Observing the randomness of both the current location of the ME and the requesting sensor nodes, the distancesfrom these l requesting nodes to the ME can be approxi-mately viewed as l i.i.d. random variables with distribu-tion f Dd (further veried in Section 6.3.1). Thus basedon the results on the rst-order statistic, the probability dis-tribution of the distance between the ME and the nearestrequesting node is

F D;ld 1 1 F Dd l; (4)

with probability density function (PDF) f D;ld @F D;ld =@d . The conditional service time distribution of the nearestrequest with a given system size is thus

f S lt v f D;lvt; (5)where S l represents the service time with system size l.

4.3 System Size at Departure TimeIf we record the system size every time it changes, we cansee the next system size only depends on the current one,which is exactly the Markov property. Also, the time thesystem stays at the current size is a random variable jointly determined by the arrival and the departure pro-cesses of requests. From these, we can see the evolutionprocess of system size is a semi-Markov process. Then if weonly examine the system size at the departure time of therequests, we can observe an embedded discrete-time Markovchain, which is similar to the case with FCFS [10] (Fig. 3).However, since the service time is now dependent on thecurrent system size, the chain becomes heterogeneous inits transition probabilities (Fig. 4).

With the conditional service time distribution obtained by (5), we can dene and calculate the probability of i newarrivals during the time serving a request selected from lavailable ones as

kli Z ffiffi2p =v0 e t t ii! f S ltdt; (6)where is the intensity of the arrival process. Note that forFCFS shown in Fig. 3,

ki Z ffiffi2p =v0 e t t ii! f T tdt: (7)

Fig. 3. State transition at departure time with FCFS.Fig. 4. State transition at departure time with NJN.



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The state transition matrix of the nite capacity queuewith NJN at the request departure time is then

P f pij g

k00 k01 k0c 1 1 Xc 1

i0k0i

k10 k11 k1c 1 1

X

c 1

i0k1i

0 k20 k2c 2 1 Xc 2

i0k2i

0 0 k3c 3 1 Xc 3

i0k3i

0 0 kc0 1 kc0

2666666666666666664

3777777777777777775

; (8)

and p P p . Thus p can be calculated by Pc 1i0 p i 1.4.4 General Service TimeWe have derived the conditional service time distribution in

Section 4.2, and have just obtained the system size probabili-ties at departure times in Section 4.3. Note that the servicetime of the current request is determined at the departureinstant of the previous request in most cases, and the onlyexception is when the previous departure leaves behind anempty system, in which case the service time simply followsthe distribution of f S 1t. Thus, we can obtain the generalservice time distribution of requests as

F S t p 0 Z t0 f S 1xdx Xc 1

l1p l Z t0 f S lxdx; (9)

and f S t @F S t=@t. The expected service time of the sys-tem can be calculated by

E S Z ffiffi2p =v0 t f S tdt: (10)4.5 Steady-State System SizeIt is proved in [39] that with an innite system capacity,the departure time system size probabilities of the stan-dard M=G=1 queue are the same as those in the steadystate. However, this conclusion does not hold in the nite

capacity case, since we only have c states for the departuretime system size 0; 1; . . . ; c 1, while c1 states0; 1; 2; . . . ; c have to be considered for the steady statedistribution. With the level crossing methods, we canobserve the fact that the distribution of system sizes justprior to the arrival time is identical to the departure timeprobabilities as long as arrivals and departures occur indi-vidually, which clearly holds for the Poisson arrival andthe NJN disciplines. Thus

p i Prfnew request finds i in queue j request joinsg wi=1 wc0 i c 1;

so

wi 1 wcp i i 0; 1; . . . ; c 1: (11)

To obtain wc, we can equate the arrival rate with the depar-ture rate of the system,

1 wc 1 w0=E S;wc 1 1 w0= E S : (12)

Thus w can be obtained based on (11) and (12). Further-more, with the PASTA property of the Poisson arrival pro-cess, uu ww, therefore the steady state system sizedistribution is derived. The expectation of the steady statesystem size can be calculated as E L Pci0 i ui , and anew request arrives to nd a fully occupied system andthus gets dropped with probability wc. Note that certainexisting hybrid data collection protocols (i.e., using multiplehomogeneous or heterogeneous MEs) could be good choicesto address these dropped requests if the missing data areindeed needed [40].

4.6 Response TimeThe ultimate metric to evaluate the data collection perfor-mance is the response time R of requests, i.e., from the timethe request is sent to the time it is served. With the expectedsystem size and by Littles Law, we know

E R E L= 1 wc : (13)

However, similar to the case with the traditional SJN dis-cipline, the possible starvation problem needs to be investi-gated when NJN is adopted due to its greedy nature.

We argue that although NJN may suffer similar prob-lem, its severity would be much less signicant for the fol-

lowing two reasons. First, the service time of requestswith NJN cannot be arbitrarily large, which is bounded bythe maximum travel time of the ME when serving twoconsecutive requests, i.e., ffiffiffi2p =v to cross the sensing eld.Second, the service time of a specic request changes asthe ME travels in the eld, and the probability that itkeeps at a large value during a long time period is small.

However, the expected response time shown in (13) isnot enough to verify the above reasoning, and moreinsights on the distribution of response time are needed.For a given request, its response time R consists of threeparts, the residual service time S r of the request under ser-vice upon its arrival, the waiting time from the rst depar-ture after its arrival to the time it enters service W , and itsservice time S , i.e.,

R S r W S : (14)

Investigating one step further, we can see that the wait-ing time W is actually the sum of the service time of thoserequests served before the given request. Based on theresults on the general service time of the queuing system(Section 4.4) and by convolution theorem, the distribution of the waiting time when conditioning on the fact that irequests are served ahead can be obtained as

f W t; i f i

S t; (15)where f x is the x-fold convolution of f .



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Again, consider the case that l requests are waiting inthe queue for service when the ME selects the next one toserve. As mentioned above, these l distances from the MEto each of the requesting sensor nodes can be viewed as li.i.d random variables, and thus the probability for anyone of them to be selected as the next to serve is approxi-mately 1=l.

Note that it is clear that given a specic requesting node,the probability for its request to be selected as the next oneis dependent on its location in the eld, and this probabilityvaries for different requesting nodes (consider two request-ing nodes located at the corner and the center of the eld,respectively). However, if we focus on a random request inthe queue and look at its asymptotic behavior, the selectionprobability of 1=l clearly follows.

Summing over all possible l, the probability for a requestto be selected would be

ps

Xc 1

l

1

p l= l1 p 0 : (16)

Combining (15) and (16) , the distribution of the waitingtime is thus

f W t XN

i1f W t; i1 ps

i 1 ps : (17)

where N is the number of sensor nodes in the network. Fur-thermore, it is well known that the distribution of the resid-ual service time is [39]

f

S r

t

1 f

S t

=E

S: (18)

From (14), (17), and (18), we know the response time of requests follows a distribution of

f Rt f S r t f W t f S t; (19)where represents the convolution operation.With the response time distribution of requests, we candirectly obtain observations on the possible starvation prob-lem from the tail of the distribution, i.e., the longer the tail,the more serious is the starvation problem. We will examinethis again in Section 6.3.5.

The above results on the response time are obtained based on the convolution theorem. Although theoreticallysound, one potential limitation with convolution theorem isthat depending on the specic form of the functions, some-times it may not have closed-form analytical solutions. Toaddress this limitation, next we investigate the busy periodof the ME, which can serve as a stochastic upper bound of the response time when the analytical results on its distribu-tion cannot be obtained.

4.7 Busy PeriodOur approach to tackling the busy period of the ME is to

approximate its distribution based on the analytical resultsof its statistical moments with verication. Note that witha Poisson arrival, the idle period distribution of the systemis F I t 1 e t . Denote T i;j as the time the system takes

from entering state i till it entering state j , and thus T 0;0 isthe busy cycle of the system. By conditioning on the number of new arrivals when serving a request, we know

E T 0;0 E I S 1 k10 E I S 1 T 1;0 k11E I S 1 T 2;0 k12

E T 1;0 E S 1 k10 E S 1 T 1;0 k11E S 1 T 2;0 k12 E T 2;0 E S 2 T 1;0 k20 E S 2 T 2;0 k21E S 2 T 3;0 k22

with some simple arrangement, we have

E T i;0 E I E S 1 X

c

j1E T j; 0 k1 j i 0;

E S i

Xc

j

1

E T j; 0 ki j i1 i > 0:8>>>>>>>:

(20)

Thus E T 0;0 can be calculated, and the second-ordermoment of T 0;0 can be obtained with a similar approach

E T 20;0 E I S 12 k10 E I S 1 T 1;0

2 k11

E I S 1 T 2;02 k12

E T 21;0 E S 21 k10 E S 1 T 1;02 k11

E S 1 T 2;02 k12

E T 22;0 E S 2 T 1;02 k20 E S 2 T 2;0

2 k21

E S 2 T 3;02 k22 ;

and after some arrangement, we have

E T 2i;0

E I S 12 k10

Xc

j1E I S 1 T j; 02 k1 j i 0;

E S 21 k10 Xc

j1E S 1 T j; 0

2 k1 j i 1;

Xc

j1 E S i T j; 02

ki j i1 i > 1:

8>>>>>>>>>>>>>>>>>>>>>: (21)

Therefore, the rst and the second-order moments of theMEs busy period B can be calculated as

E B E T 0;0 E I; (22)

E

B 2

E

T 20;0 E

I 2 2E

BE

I: (23)

Observing the fact that the busy period of the system isactually the sum of the service times of several consecutively



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served requests, we adopt the Gamma distribution toapproximate that of the busy period as

f B t th 1e t=u = u h Gh t > 0; (24)where h 1=E B 2 =E B2 1 and u E B=h . The accu-racy of this approximation is veried in Section 6.3.6.

5 DATA COLLECTION WITH NJNCWe have theoretically analyzed the system measures whenthe NJN discipline is adopted in the previous section. Inthis section, we extend NJN by taking the wireless commu-nication properties into account: with wireless communi-cations, the ME can collect data from several requestingnodes at the same collection site, provided that the site iswithin the communication ranges of these nodes. We con-sider this NJNC discipline in the following, with whichthe ME still selects the spatially nearest requesting node asthe next one to serve, except that if there are other request-

ing nodes that are within the communication range of thenearest one, the ME will combine these requests and servethem together.

The data collection tends to fail due to the poor commu-nication quality when the distance between the ME and thecorresponding sensor node approaching the communica-tion range of adopted devices. However, it is shownthrough measurement studies that the packet receptionrates are uniformly high up to a certain transceiver distance[8]. This means the combination of requests is still reason-able since we can nd a proper value for the communica-tion range as the input of the NJNC discipline based on

empirical results or deployment measurements.The combination, if happens, can effectively reduce thesystem size, and thus shorten the response time of requests. It can also alleviate the possible starvation prob-lem, since intuitively, starvation is less likely to happenwith a smaller system size. We mainly deal with two ques-tions in this section: how likely the combination can hap-pen, and if it happens, how many requests can becombined; to what degree the combination can improvethe data collection performance.

5.1 Combination Probability

For the requests combination to happen, the collection sitemust be covered by the communication ranges of at leastanother requesting node, besides the nearest one. Same as before, assume l requests are currently available when theME selects the next request. The probability that X l request-ing nodes, including the nearest one, can be combinedtogether and served from one collection site can be captured by a binomial distribution

PrfX l xg l 1

x 1 F Drx 11 F Drl x : (25)Thus the expected number of combined requests is

E X l Xl

i1i PrfX l xg; (26)

and the probability for the combination to happen is

PrfX l > 0g 1 1 F Drl 1: (27)

Requests combination improves the system performance by effectively reducing the system size. Based on a similarM=G=1=c queuing model as that for the NJN discipline, wepresent quantitative analysis on its impact on the systemperformance in the following.

5.2 MM=G=1=c-NJNC Queuing ModelThe ME still selects the nearest request to serve with NJNC,so given the system size, the conditional service time distribution is identical to that of NJN. Following a similar ideaof the embedded Markov chain, we can derive its departuretime system size probabilities, and the results shown in (4),(5), and (6) still hold.

The difference between the heterogeneous Markovchains of NJNC and NJN is that, it is now possible to havemultiple departures after one service period, as shown inFig. 5. With the current system size l, denote an;l as the prob-ability of n arrivals during the service of the nearestrequests selected from l requests with possible requestscombination. Since the combination does not affect thearrival process, we know

an;l kln : (28)

Denote d m;l as the probability of m departures after serv-ing the nearest requests selected from l requests with possible requests combination, which means m 1 requests have been served together with the nearest one,

d m;l l 1m 1 F

Drm 1

1 F Drl m

: (29)

Thus the state transition probabilities of the embeddedMarkov chain for NJNC, i.e., the counterparts of (8) underNJNC, are

P 0 p0ij Xi

m1d m;i a j im;i" #; (30)

and p0P 0 p 0, where p0 is the departure time system sizedistribution with NJNC, and

Pc 1i0 p 0i 1. Hence, the gen-

eral service time distribution can be derived with the sameapproach as in (9) and (10).Based on (26) and p 0, we have the following result on the

system throughput with NJN and NJNC, i.e., the number of

Fig. 5. State transition at departure time with NJNC (only those for state iare shown for clarity).



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served requests during a unit time, denoted as c njnc andc njn , respectively,

c njncc njn 1 X

c 1

i1p 0i E X i 1 !: (31)

When the requests intensity in the network is heavy, i.e.,

! 1 , (31) can be simplied asc njncc njn E X c as ! 1 : (32)

The analysis on the request response time and the busyperiod of ME is much more complicated with NJNC, due tothe possible multiple departures after one service, but theidea of obtaining these results still holds. However, we can-not use (11) and (12) to precisely calculate the steady statesystem size in the NJNC case anymore, because the possiblemultiple departures after one service invalidates (11). Wecan see in this case the results obtained by (12) are essen-tially a stochastic upper bound of the arrival time systemsize probabilities, which makes the results returned by (13)also an upper bound of the expected response time.

6 P ERFORMANCE EVALUATIONSWe evaluate our modeling and analytical results on the per-formance of data collection with NJN and NJNC disciplinesin this section, and we also show the corresponding resultswith FCFS in certain cases for comparison. Note that wehave already explored the case with FCFS-with-combination

(FCFSC) in [10], whose results are not shown here due tothe space limit. We consider a 100 100 m2 square sensingeld with 100 randomly distributed sensor nodes, unlessotherwise specied. Based on the parameters from real sys-tems [30], the travel speed of ME is 1m=s. The communica-tion range r is 20 m and system capacity c is 8 by defaultunless otherwise specied.

To deal with the inconvenience of the piecewise distancedensity function in (2), we approximate it by a polynomialfunction of order 10 using least squares tting with a veriedaccuracy [9]:

ef

Dd

0:2802d 10 2:0964d 9

2:2349d 8

24:3629d 7

106:8231d 6 194:4928d 5 182:8093d 491:8223d 3 29:3663d 2 8:2843d 0:04:

(33)

6.1 Validation of the MM=G=1=c ModelingTo validate the M=G=1=c model, we need to examine theassumptions of both the Poisson arrival of requests and thedistribution-ergodic property of their service.

We adopt a hot-spot model [37] to capture the data gen-eration in our event-driven simulator. Specically, several

hot spots ( 10 in our simulation) exist in the eld, and theprobability for an event to occur at a certain location isinverse proportional to its distance to the closest hot spot.When an event occurs, sensor nodes whose sensing range

covers it can detect the event and generate sensory data of size a e a d bits to record it, where d is the distance betweenthe node and the event, and a is set to 0:5 in our simulation.Sensor node sends out a data collection request when atotal volume of 1 KB data are accumulated in its buffer. Atotal number of 100 data collection requests are generatedand served during each simulation, which is repeated for100 times.

For each simulation run, we record the inter-arrival timeof the requests, and use an exponential distribution withthe same mean value to approximate them. We adopt theKolmogorov-Smirnov (K-S) test with a signicance level of 0:05 to verify the goodness-of-t of the approximation, andrecord the percentage of runs that pass it. We repeat thewhole process for 40 times. To verify the distribution-ergo-dic property of the service time, we also record the servicetime of each request, and calculate their one-lag autocorre-lation (as in [38]). Fig. 6a gives the results of the K-S testand the autocorrelation on the M=G=1=c model, whereeach point corresponds to one of the 100 100 simulation

runs. The x-value of the point is the percentage of simula-tion runs that pass the K-S test, and the y-value is the one-lag autocorrelation. Thus we expect that, if these points areclustered around the right bottom corner, as beingobserved from the validation results in Fig. 6a, theM=G=1=c queuing model adopted in this paper is con-rmed sound and acceptable.

6.2 Combination ProbabilityNext we evaluate our analytical results on the combinationprobability for NJNC. We explore the cases where ve, 10,and 15 requests are in the system when the ME selects the

next request to serve, respectively, and Fig. 6b shows theresults obtained with 10 requests as a representative. Threecases with a communication range of 10, 20, and 30 mrespectively are investigated. Besides the accuracy of theanalytical results, we can see that the number of combinedrequests increases with a larger r , because it is more likelyto collect data from more sensor nodes at the same collec-tion site with a longer communication range. Furthermore,the probability for the combination to happen, evenwith the shortest explored communication range of 10 m, isabout 25 percents, which increases to around 90 percentswhen r is 30 m. The high probability for requests combina-tion indicates that NJNC can improve the data collectionperformance most of the time, when compared with NJN.

6.3 System MeasuresWe evaluate the analytical results on the system measureswith NJN and NJNC in the following.

6.3.1 Service Time with a Given System Size We rst examine the results on the service time distributionwith a given system size. The conditional service time isderived based on the rst-order statistic, which assumes thedistances from requesting nodes to the current location of

the ME are independent. We start the verication by investi-gating the independence among these distances. In the sim-ulation, after the deployment of sensor nodes, we randomlyselect one as the current location of the ME. Then we select



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two other sensor nodes as the requesting sensor nodes, cal-culate their distance to the ME, and record it. We repeat thecalculation for 10;000 times, and obtain two distancessequences of size 10;000 each. Then we calculate the correla-tion coefcient of the two sequences. We repeat the wholeprocess for 20 times, and the mean square error (MSE) of the resultant correlation coefcients is 6:8010 10 5, withthe estimation of a strict independence (a correlation coef-cient of 0). This near-zero correlation supports our approxi-mation based on their independence.

For the conditional service time distribution, two caseswith a small and a large system size of 5 and 9 are exploredrespectively, and the results are shown in Fig. 6c. We cansee that the analysis and simulation agree with each other,

and the conditional service time becomes shorter with alarger system size, which is consistent with their greedynature: more queued requests in the system bring moreopportunities to have nearer ones.

6.3.2 System Size The ultimate performance metric of data collection is theresponse time of requests, which is determined by both theservice time and system size, and a shorter service time

does not necessarily lead to a shorter response time. Thus,we move on to evaluate the system size.

The average system sizes with different request arrivalrates for FCFS, NJN, and NJNC are shown in Fig. 6d. The

Fig. 6. Evaluation results on the queue-based modeling and system measures.



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system sizes under all the three disciplines are small andcomparable to each other when the trafc is light, since thepotential for both NJN and NJNC to take effect is quite lim-ited in this case. The system size for FCFS increases veryquickly when increases, and cannot keep stable anymorewhen exceeds a certain threshold ( 0:018 in Fig. 6d. In fact,the case of 0:018 in our simulation roughly corre-sponds to the case that r

E

S 1 for FCFS, where r is

the system utilization factor, and increasing further willresult in an unstable system where the steady state doesnot exist. When compared with FCFS, NJN can reduce thesystem size greatly because it tries to serve and nishnearby requests in a shorter time, and NJNC can furtherdecrease the system size as a result of possible requestscombination. Note that the capability of NJNC to furtherreduce the system size becomes more obvious when increases, since a larger system size leads to a larger poten-tial to combine already queued requests. (One thing tomention is that, not surprisingly, the resultant system sizewith FCFSC falls between those with FCFS and NJN, e.g.,

an average system size of 1:9 is resulted with the FCFSCdiscipline when is 0:018 [10].)We then explore the system size probabilities for FCFS,

NJN and NJNC with 0:018 (Fig. 6e. The maximal systemsize resultant by NJN and NJNC is around 5 to 6, but thatfor FCFS is too large to be shown clearly in the same gure(given enough system capacity, the maximal system sizewith FCFS observed in our simulation is 33). Furthermore,we can see that the requests combination shortens the queueconsistently.

6.3.3 Overow Probability Data collection requests may be lost due to the limited sys-tem capacity. To gain insights on this possible data lossproblem, we explore the overow probability of the nitecapacity system in Fig. 6f, in which we consider a very smallsystem capacity ( c 3) to amplify the problem and obtain aclear observation. These three disciplines result in similaroverow probabilities when is small. However, the over-ow probability for FCFS increases dramatically and becomes much less stable as increases, and is much largerthan those achieved by NJN and NJNC. On the other hand,even with a small capacity, the overow probabilities forNJN and NJNC are very small and more stable (less than0:2 in the worst case by our simulation settings), and NJNCcan further reduce the overow probability by reducing thesystem size through possible requests combination.

6.3.4 General Service Time We then examine the general service time for both NJN andNJNC. The average service time of NJN and NJNC with dif-ferent arrival rate of requests are shown in Fig. 6g. Thedecreasing trend of the service time as increases agreeswith the greedy nature of both NJN and NJNC with morequeued requests. When comparing these two disciplines,

the service time of NJNC is slightly larger than that of NJN because of the possible combination, since NJNC reducesthe system size more aggressively and thus also reduces thepossibility of nding a closer requesting sensor node in the

future. Also note that the difference between the two becomes more obvious with a larger .

To gain more insights on the service time, Fig. 6h showsthe general service time distribution with 0:018, wherethe service time distribution for FCFS is also shown for com-parison as well. We can see that when compared with FCFS,NJN and NJNC can shorten the service time noticeably because of their nature to serve nearby requests with lesstime, and similar insights can be observed as in Fig. 6g.

6.3.5 Response Time As mentioned above, both service time and system sizeaffect the response time. Since NJN has a shorter servicetime and NJNC has a smaller system size, next we need to

examine their response time.The average response time for FCFS, NJN and NJNC isshown in Fig. 6i, from which we can see that when com-pared with FCFS, NJN and NJNC can greatly shorten theresponse time of requests, especially when is large. NJNCcan further reduce the response time as a result of possiblerequests combination, which also becomes more obvious as

increases. It shows that between a shorter service time forNJN and a smaller system size for NJNC, the system sizereduction is more dominating for the resultant responsetime. A smaller system size also indicates a lower overowprobability for a given system capacity limit. Actually, the

above observations can be inferred based on Fig. 6d and thelinear relationship between the response time and systemsize (by Littles Law). We still include Fig. 6i here for a clearand straightforward comparison.

We have derived the distribution of the response time of requests to investigate the potential starvation problemwhen the NJN (NJNC) discipline is adopted. One funda-mental part to obtain the response time distribution is theprobability for a request to be selected for service, and weverify this before moving to the response time. For eachrequest, after its arrival, we record the number of selectionsmade by the ME until the request is chosen, and comparethis to the average number of requests that are waiting forservice in the queue. If (16) holds, then we expect these tworesults to be close. We intentionally set higher trafc intensi-ties (and thus larger system sizes) for this verication tomake the observation more clear. The comparison resultsare shown in Table 1, which verify the accuracy of (16).

Next we evaluate the results on the response time distribution, which are shown in Fig. 6j ( 0:018). The responsetime by the FCFS discipline (obtained according to [39]) isalso shown for comparison. Besides the accuracy of the ana-lytical results, we can see even the worst case of NJN, interms of the longest response time experienced by requests,is much smaller than that by the FCFS discipline. This obser-

vation is a little unexpected since FCFS is known to be ableto achieve a good fairness among clients, but it also allevi-ates our concerns on the possible starvation problem withNJN (NJNC).

TABLE 1Verication of Requests Selection Probability



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To present a clear comparison between the performanceof NJN and NJNC, we presents the response time obtained by a particular run of simulation ( 0:018) in Fig. 6k,where a total number of 10; 000 requests are served (ordropped due to system overow). We sort the responsetime in an ascending order, and only plot the response timeevery 200 requests for clarity. Not surprisingly, NJNC fur-

ther reduces the response time in terms of both the averageand worst cases.

6.3.6 Busy Period Fig. 6l shows the evaluation results on the distribution of the busy period of the ME, where is set to 0:018. We can seethat although the results are obtained through approxima-tion methods, the accuracy is still good. For comparison, theresponse time distribution obtained with the FCFS disci-pline is shown here again. We can see that with NJN, evenits busy period, which is a stochastic upper bound of theresponse time, is smaller than the response time with FCFS.

6.4 Comparison with Other Scheduling SchemesIn the following, we compare the performance of NJN andNJNC with two classic scheduling schemes:

TSP: the ofine optimized TSP-based schedulingscheme, with which the mobile element carries outthe data collection according to the optimal solutionof the TSP instance formulated based on the nodedeployment. This is involved in many ofine datacollection scheme designs [17], [19], [44].

Gated-TSPN : the dynamic schedule scheme based ona TSPN instance according to the available data col-lection requests [49], which is treated as the state-of-the-art for the on-demand data collection.

The average data collection latency resultant with theGated-TSPN, NJN, and NJNC are shown in Fig. 7, with therequest arrival rate varies from 0:002 to 0:022. We cansee that the NJN (NJNC) outperforms the Gated-TSPNscheme noticeably, especially when the request arrival rateis large. However, the system stability of the Gated-TSPNscheme has been theoretically guaranteed, while our analy-sis on NJN and NJNC has not proved this property yet,which is the direction of our future work. The results with

the TSP scheme are not shown in the gure because thelatency resultant is signicantly longer, specically, around940 s when 0:006. However, the latency with the TSPscheme is relatively insensitive to the request arrival rate,

e.g., around 960 s when 0:022. This infers that the TSPscheme may be a good choice when the intensity of the datacollection tasks in the network is quite heavy.

The response time with various eld size are shown inFig. 8, where the x-axis is the side length of the square eld.The response time with the TSP scheme increases almostlinearly, which agrees with the nature of the optimal TSPtour. The NJN and NJNC outperform the Gated-TSPNscheme, and the advantage becomes more obvious with alarger eld. Again, we would like to emphasize thatalthough veried to be efcient through simulation, unlikeGated-TSPN, the system stability with NJN and NJNC hasnot be theoretically proved yet.

7 DISCUSSION AND ONGOING WORKOur modeling and analysis are shown accurate but someissues need to be further explored. Here we discuss some of

these issues and the directions of ongoing work.Clearly, the assumption of a square sensing eld may nothold in practice. However, our queue-based modeling andanalysis approaches are still feasible even for general sens-ing elds, provided that the distance distribution betweenarbitrary locations in the eld can be obtained, e.g., we havealso analytically derived the random distance distributionsassociated with rhombuses and hexagons [41]. Furthermore,even if the sensing eld is of irregular shape, which may betrue in certain cases, we can adopt the polygon-approxima-tion approach to approximate the eld by the combinationof several regular shapes [42], and derive the random dis-tance distributions within and between them. Of course,more computation efforts will be needed.

Another simplication we made is that the time fortransmitting the data from sensors to the ME is negligible,which may not hold if the data volume is large. However,note that given any sensor network deployment, theknowledge on the data transmission rate and communica-tion range is available, or at least can be estimated throughexperimental measurements. Based on such knowledge,we can estimate the data volumes that can be collected if the ME travels without any stops, and then the time thatthe ME has to pause or slow down to collect the remainingdata can be calculated as well. The statistics of this addi-

tional time can be incorporated when formulating the ser-vice time distribution.

The request response time in this work does not includethe time since the request is sent by the sensor node to its

Fig. 7. Response time with request arrival rate . Fig. 8. Response time with eld size L.



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reception at the ME, which we assumed to be negligible.Observing the fact that these two times are independent toeach other, thus by the convolution theorem, we can easilytake the latter into account provided that its distributiong tcan be estimated,

1 i.e.,

f 0Rt g t f Rt: (34)

When multiple MEs are available, a straightforwardapproach is to extend the model to the multi-server case.However, in addition to the queue length and responsetime, we also need to consider the load balance among theMEs as another metric to evaluate the system performance.Some preliminary results on the on-demand data collectionwith multiple MEs can be found in [9].

8 CONCLUSIONSIn this paper, we have analytically evaluated an intuitiveservice discipline, NJN, for data collection with mobileelements in wireless sensor networks, and also exploredthe case where the ME follows NJN and combinesrequests whenever possible, i.e., NJNC. We have modeledthe system as an M=G=1=c queue, and then with differentservice disciplines (NJN and NJNC), critical system met-rics have been derived. We have veried our analyticalresults through extensive simulation, and gained moreinsights on the starvation problem that NJN and NJNCmay suffer from. Our results have showed that not onlythe average performance of NJN is much better than thatof FCFS, but also the worst-case performance of NJN isstill better than that of FCFS, even though according to

the conventional wisdom, NJN may suffer from the star-vation problem. A possible reason is that the service timeis not arbitrary for data collection applications in wirelesssensor networks. Moreover, NJNC can further improvethe performance as a result of possible requests combina-tion. We have also discussed several possible extensionsas the ongoing and future work.

ACKNOWLEDGMENTSAn early short version of this work was published at IEEEINFOCOM12, which was done when L. He was a PhD can-didate at Nankai University and a visiting research student

at University of Victoria. The work is supported in part bySingapore-MIT International Design Center IDG31000101,grant SUTD SRG ISTD 2010 002, Project GREaT IPMD13012,and grant K93-9-2010-01 from Ministry of Educations KeyLab for Computer Network and Information Integration atSoutheast University, China.

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Liang He (S09-M12) received the BEng degreein 2006 and the PhD degree in 2011 from TianjinUniversity, China, and Nankai University, China,respectively. He is currently a postdoc researchfellow at Singapore University of Technology andDesign. During October 2009 to October 2011,he was at Panlab at University of Victoria as a

visiting research student. He received the bestpaper awards of IEEE WCSP 2011 and IEEEGLOBECOM 2011. He is a member of the IEEE.

Zhe Yang (S09) received the BS degree ininformation engineering in 2005 and the MSdegree in control theory and engineering in2008, both from Xian Jiaotong University,Xian, China. He is currently working towardthe PhD degree at the Department of Electri-cal and Computer Engineering, University ofVictoria, British Columbia, Canada. His currentresearch interests include cross-layer designfor cooperative networks, scheduling and

resources allocation for wireless networks andsynchronization. He is a student member of the IEEE.

Jianping Pan (S96-M98-SM08) received thebachelors and PhD degrees in computer sciencefrom Southeast University, China, and he did hispostdoctoral research at the University of Water-loo, Canada. He is currently an associate profes-sor of computer science at the University ofVictoria, Canada. He was also at Fujitsu Labsand NTT Labs. He received the IEICE BestPaper Award in 2009, the TelecommunicationsAdvancement Foundations Telesys Award in2010, the WCSP 2011 Best Paper Award, and

the IEEE Globecom 2011 Best Paper Award, and has been serving onthe technical program committees of major computer communicationsand networking conferences including IEEE INFOCOM, ICC, Globecom,WCNC, and CCNC. He is a senior member of the IEEE.

Lin Cai (S00-M06-SM10) received the MAScand PhD degrees in electrical and computer engi-neering from the University of Waterloo, Canada,in 2002 and 2005, respectively. Since 2005, shehas been currently an associate professor withthe Department of Electrical and Computer Engi-neering, University of Victoria, Canada. She hasbeen an associate editor for IEEE Transactions on Wireless Communications , IEEE Transac- tions on Vehicular Technology , EURASIP Journal on Wireless Communications and Net-

working , the International Journal of Sensor Networks , and theJournal of Communications and Networks . She is a senior member ofthe IEEE.

Jingdong Xu received the BS, MS, and PhDdegrees from the Department of computer sci-ence from Nankai University, China, in 1988,1991, and 2002, respectively. She is currently aprofessor and the department chair of computerscience, Nankai University. His research focuseson wireless ad hoc network,wireless sensor net-work, and mobile computing.

Yu (Jason) Gu received the PhD degree fromthe Department of Computer Science and Engi-neering at the University of Minnesota in 2010.He is an assistant professor at the SingaporeUniversity of Technology and Design. He is theauthor and coauthor of more than 21 papers inpremier journals and conferences. His publica-tions have been selected as graduate coursematerials by more than 10 universities in theUnited States and other countries. He hasreceived several prestigious awards from the

University of Minnesota. He is a member of the IEEE.

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evaluating service disciplines for ondemand mobile data collection in sensor networks

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