bouabdallah & bouabdallah (lifetime) 2013

7/29/2019 Bouabdallah & Bouabdallah (Lifetime) 2013

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The tradeoff between maximizing the sensor network lifetimeand the fastest way to report reliably an event using

reporting nodes selection

Fatma Bouabdallah *, Nizar Bouabdallah

INRIA-IRISA, Campus de Beaulieu, 35042 Rennes, France

Received 19 March 2007; received in revised form 21 November 2007; accepted 25 November 2007Available online 14 December 2007

Abstract

Energy-efficiency is one of the major concerns in wireless sensor networks since it impacts the network lifetime. In this paper, we inves-tigate the relationship between sensor networks performance, particularly its lifetime, and the number of reporting nodes Nby using bothanalytical and simulation approaches. We first show that the network lifetime and the number of correctly received reports increase whenN decreases. Moreover, we demonstrate that the average time required to report an event is a convex function of N. Based on theseresults, and as a main contribution, we prove that the optimal number of reporting nodes minimizing the energy consumption in thenetwork does not correspond to the optimal number of reporting nodes allowing the fastest way to report an event. The tradeoff betweenthese two requirements is therefore specific to each sensor application, depending on its particular needs. In this paper, we provide asimple methodology to achieve this tradeoff. 2007 Elsevier B.V. All rights reserved.

Keywords: Energy-efficiency; WSN performance; Network lifetime

1. Introduction

Energy-efficiency is a critical issue in wireless sensor net-works (WSNs) due to the limited capacity of the sensornodes batteries [1]. Indeed, once a WSN is in place, its life-time must last as long as possible based on the initially pro-vided amount of energy. In view of this, techniquesminimizing energy consumption are required to improve

the network lifetime. A widely employed mechanism is toschedule sensor nodes activity so that redundant nodesenter the sleep mode as often as possible [2,3]. Based on thisconcept, several energy-efficient MAC protocols [46] andenergy-efficient routing protocols [7,8] have been proposed.Additional solutions, based on congestion control, to

reduce energy consumption are also proposed in [9,10].These mechanisms aim at achieving further energy conser-vation by reducing the energy wastage due to the fre-quently occurring collisions in WSN networks.

The majority of previous works focused mainly on theenergy minimization problem. However, minimizing theenergy consumption must be achieved while respectingthe specific QoS requirements of sensor applications, such

as the maximum tolerable time to report an event, andthe required event reliability, etc. Indeed, the key perfor-mance metrics in WSN networks are both the network life-time and the average time required to report reliably anevent. The optimal solution must therefore take intoaccount these two metrics. In view of this, in this paper,we focus on the analysis of this tradeoff.

Moreover, the current studies handled the energy opti-mization issue without paying attention to the impact ofthe number of reporting nodes on the WSN performances.In other words, given a reporting frequency, how the

0140-3664/$ - see front matter 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.comcom.2007.11.020

* Corresponding author. Tel.: +33 6 79 84 33 78.E-mail addresses: [email protected] (F. Bouabdal-

lah), [email protected] (N. Bouabdallah).

www.elsevier.com/locate/comcom

Available online at www.sciencedirect.com

Computer Communications 31 (2008) 17631776
mailto:[email protected]:[email protected]:[email protected]:[email protected]


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network lifetime and the reporting latency evolve withrespect to the number of active reporting nodes? Our workis motivated by the results in [11,12], which highlight thesignificant energy conservation that could be achievedwhen spatial and temporal correlation is exploited toreduce the number of redundant packet transmission in

the network. Specifically, a new MAC protocol is proposedin [12] to regulate the network access by limiting the report-ing tasks of an observed event to a minimum number ofsensor nodes subject to reliability constraints.

In this paper, we present an in-depth analysis of theimpact of the number of selected reporting nodes on theWSN performances (i.e., network lifetime, reportinglatency). Our ultimate goal is to determine the optimalnumber of reporting nodes that both minimizes the energyrequired to report reliably an event and respect the latencyconstraints. The obtained result can be thus used to param-eterize the MAC protocol proposed in [12], which can beseen as the feasibility demonstration of the basic access

nodes selection method, to achieve the energy-reliability-latency tradeoffs.

Moreover, in our study, we relax the minimum bound-ary constraint on the number of reporting nodes entailedby Vuran and Akyildiz [12], by allowing the selectedreporting nodes to transmit redundant information (multi-ple reports). Doing so, further flexibility and thus addi-tional energy conservation could be achieved by ourproposal. To the best of our knowledge, we are the firstto tackle the energy optimization problem from this per-spective while considering the energy-reliability-latencytradeoffs.

To achieve this, we develop new analytical models toexplore the relationship between the WSN performances(i.e., network lifetime, event reporting time) and the num-ber of active reporting nodes, given a predefined networkreporting frequency. Specifically, we analyze the basicaccess mechanism of IEEE 802.11 DCF (distributed coor-dination function) with its optional request-to-send/clear-to-send (RTS/CTS) scheme [13]. This basic protocol is usedby the currently deployed WSNs to arbitrate access, amongmultiple sensor nodes, to the shared medium in order tocommunicate with the sink node. We first derive theexpression of the collision probability and the averageenergy required to report reliably an event as functions ofthe number of reporting nodes and the reporting fre-quency. Based on these results, and as a first main contri-bution of this paper, we prove that the network lifetimeincreases when decreasing the number of active reportingnodes. We show that the maximal network lifetime isachieved when only one reporting node is activated whilethe remaining nodes undergo the sleep mode. Indeed, indoing so, collisions among reporting nodes is avoided,eliminating thus unnecessary energy consumption. We thenshow analytically that the time required to report an eventis a convex function of the number of active reportingnodes N, where the minimum is obtained for Nopt > 1.

Consequently and as a second main contribution, we dem-

onstrate that the fastest way to report reliably an eventdoes not necessarily lead to the most efficient energyconsumption. The tradeoff between these two requirements(i.e., energy consumption and reporting time) dependsmainly on the specific QoS needs of the sensor application.

Finally, in order to assess the accuracy of our proposed

analytical model, we conduct simulations. To do so, wedevelop our own evaluation environment using NS-2 [14].The results show a good match between simulations andthe analytical expressions, which confirms the accuracy ofour models. The rest of the paper is organized as follows.Section 2 discusses the related works and Section 3 presentsthe general problem statement. Communications amongsensor nodes will be outlined in Section 4. In Section 5,we introduce the mathematical models to evaluate theimpact of the number of reporting nodes on the WSN per-formances. Analytical and simulation results are discussedin Section 6. In Section 7, we provide a simple methodol-ogy to achieve the tradeoff between energy consumption

and event reporting latency. Finally, Section 8 concludesthis paper.

2. Related work

As stated before, in order to minimize the energy con-sumption in WSNs, several energy-efficient MAC proto-cols [46] and energy-efficient routing protocols [7,8]have been proposed in the literature. These schemes aimto decrease the energy consumption by using sleep sched-ules. The key idea behind this concept is to turn off com-pletely some parts of the sensor circuitry (e.g.,

microprocessor, memory, radio) when it does not receiveor transmit data, instead of keeping the sensor node inthe idle mode. This scheme simply attempts to reducewasted energy due to idle listening, i.e., lost energy whilelistening to receive possible traffic that is not sent. To doso, works in [46] suggest wake-up scheduling schemes atthe MAC layer to activate sleeping nodes when it isneeded. On the other hand, works in [7,8] address theproblem at the network layer by proposing new routingsolutions that take into account the sleep state of somenetwork nodes.

To maximize the network lifetime, works in [15,16] tryto use a cross-layer-based solution. Their aim is to findthe optimal setting parameters in physical, MAC androuting layers to maximize the network lifetime in thecontext of collision-free wireless sensor networks. In fact,in [15], the authors try to investigate the inherent tradeoffbetween the application layer performance and the net-work lifetime by developing a theoretical frameworkbased on an optimization problem. The proposed prob-lem aims at optimizing both the application performanceand the network lifetime in a wireless sensor networkswith orthogonal link transmissions. To do so, Namaet al. define the application layer performance as a net-work utility function which is the sum of individual node

utilities. In fact, the utility function of each node mono-

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tonically increases with the intrinsic source rate of thatnode. Resolving this cross-layer optimization problemleads to compute the optimal set of source rates, networkflows and radio resources at the transport, network andradio resource layers, respectively.

Moreover, the authors in [16] consider the joint optimal

design of physical, medium access control (MAC), androuting layers to maximize the lifetime of energy con-strained wireless sensor networks. The problem of comput-ing a lifetime-optimal routing flow, link schedule and linktransmission powers is formulated as a non-linear optimi-zation problem. In their study, the authors consider bothorthogonal and non-orthogonal link schedules. In the caseof general link schedules, the authors proposed an iterativealgorithm to approximate the optimal solution. This algo-rithm was shown to be quite accurate in linear and rhom-bus topology but not in large topologies.

Although the significant energy saving achieved by suchschemes, the WSN keeps always sending redundant data.

Typically, WSNs rely on the cooperative effort of the den-sely deployed sensor nodes to report detected events. As aresult, multiple sensor nodes may report the same event. Tofurther decrease energy consumption, several works arenow focusing on the elimination of the useless redundantinformation [11,12,17,18]. The reduction of the numberof redundant packets can be achieved either at the dataoriginator level (i.e., sensor nodes that detect the event)[11,12], by regulating their access, or at the intermediatesensor nodes routing the information to the sink, by meansof aggregation mechanisms [17,18].

In the latter case, paths from different sources to the sink

form an aggregate tree, where the redundant data at thebranching nodes are replaced by a single message. In doingso, the number of packets traversing the network is consid-erably reduced, which leads to significant energy conserva-tion [17,18]. However, such schemes affect the reliability ofthe information transmitted to the sink. The aggregationprocess at intermediate nodes must therefore be aware ofthese reliability constraints [10], which may become in caseof challenging multiple aggregation points in the route tothe sink.

Reducing the redundant information is more efficientwhen it is realized at the source nodes [12]. This isachieved by limiting the number of access reportingnodes. Specifically, [12] shows that using a small subsetof the nodes (called representative nodes) rather than allthe sensor nodes in the event area, to report the detectedevent reduces considerably the energy consumption.Indeed, limiting the number of reporting nodes alleviatesthe energy wastage caused by collisions, idle listeningand redundant packet transmission. In the optimal case,only one node will be allowed to report the detectedevent. In such case, collisions, idle listening and redun-dant packet transmission are totally eliminated. But, suchchoice may not guarantee the required reliability sinceonly one report is received by the sink regarding the

observed event.

In this paper, we analyze the impact of the number ofselected reporting nodes on the WSN performances (i.e.,network lifetime, reporting latency). We aim at derivingthe optimal numbers of reporting nodes that minimizesthe energy consumption while fulfilling the reportinglatency constraint. In this regard, as a second stage in

our optimization process, we have to make sure that theadopted number of reporting nodes ensures the maximumtolerated latency. To the best of our knowledge, this is thefirst effort that considers the triplet energy-reliability-latency constraints. It is worth noting that we will adaptthe MAC proposed in [12] to meet our specificrequirements.

To summarize, our study enables to derive the optimalsetting parameters (number of reporting nodes N and thereporting frequency f), to be used later by protocols suchas [12], in order to achieve the energy-reliability-latencytradeoffs.

3. Problem statement

Let us consider the WSN as depicted in Fig. 1. Inessence, a WSN ensures the supervision of a given areaby the use of a sink node, which collects reports from thenetwork. In this analysis we consider event detection drivenwireless sensor applications. In other words, communica-tions are triggered by the occurrence of a pre-specified typeof events. Once an event occurs, it has to be reported to thesink by the sensor nodes. In such network, sensor nodes,within an event radius Rc, are the sources (i.e., reportingnodes) for the detected event. Recall that sensor nodesare characterized by their coverage range Rc (i.e., sensingrange) and transmission range Rt as shown in Fig. 1.

Henceforth, we denote by N the number of reportingnodes for a detected event. Moreover, we denote by f thenetwork reporting frequency. The network reporting fre-quency is defined as the number of packets generated perunit of time by the network to report an event. Hence,

Fig. 1. Example of a sensor network.

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given N reporting nodes, the reporting frequency of eachsensor node must be set equal to fs f=N to get the prede-fined network reporting frequency. This parameter fis gen-erally fixed by the network administrator in order toachieve required event detection reliability, R. The desiredevent reliability, R, is the number of data packets required

by the sink to consider the event as reliable [10]. Once thesink node receives R reports, it instructs the sensor nodes tostop the event reporting.

In this study, we aim at analyzing the impact of thenumber of reporting nodes N on the WSN performance.The basic idea is to let some potential reporting nodes toenter a sleep mode. In the extreme case, we only let one sen-sor node (N 1) to report a detected event with a report-ing frequency fs f. Furthermore, we evaluate thecollision probability, the average time required to reportan event and the network lifetime as a function of the num-ber of active reporting nodes N.

4. Wireless sensor networks

As stated before, communications in currently de-ployed WSN are carried using the basic IEEE 802.11DCF protocol and its optional RTS/CTS mechanism.Specifically, once an event is detected, the N active report-ing nodes compete to access the common data channel toreport the event to the sink. The IEEE 802.11 DCF accessmethod is based on the CSMA/CA technique. Accord-ingly, a host, wishing to transmit a frame, first sensesthe channel activity until an idle period equal to Distrib-

uted Inter Frame Space (DIFS) is detected. Then, the sta-tion waits for a random backoff interval beforetransmitting. The backoff time counter is decremented interms of time slots as long as the channel is sensed free.The counter is suspended once a transmission is detectedon the channel. It resumes with the old remaining backoffinterval when the channel is sensed idle again for a DIFSperiod. The station transmits its frame when the backofftime becomes zero. In this case, the host starts the processby sending a RTS frame.

If the frame is correctly received, the receiving hostsends a CTS frame after a Short Inter Frame Space(SIFS). Once the CTS frame is received, the sending hosttransmits its data frame. If the sending host does notreceive the CTS frame, a collision is assumed to haveoccurred. In this case, the sending host attempts to sendthe RTS frame again when the channel is free for a DIFSperiod augmented by the new backoff, which is calculatedas follows.

For each new transmission attempt, the backoff intervalis uniformly chosen from the range 0;CW in terms of timeslots. At the first transmission attempt of a frame, CWequals the initial backoff window size CWmin 31. Follow-ing to each unsuccessful transmission, CWis doubled untila maximum backoff window size value CWmax 1023 is

reached. Once the frame is successfully transmitted, the

CW value is reset to CWmin. Fig. 2 illustrates the IEEE802.11 DCF access mechanism.

5. Performance analysis

In this section, we present mathematical models toderive both the WSN lifetime and the average timerequired to report an event, as functions of the numberof reporting nodes N and the reporting frequency f. Toachieve this, we first calculate the collision probability in

such networks caused by the multiple reporting nodes.Then, we derive the average time required to report reliablyan event (i.e., to transmit R reports). Based on this result,we can easily obtain the associated consumed energy.Finally, using the analytic formula given in [19], we obtainthe expression of the WSN lifetime.

In this study, we distinguish between two modes of func-tioning according to the network reporting frequency f: thesaturated and unsaturated regimes. The first mode isobtained when f is high enough. In this case, each timethe channel is free for transmission, each station amongthe N reporting ones has at least one report to transmit.

In other words, for each new transmission cycle, all thereporting nodes compete to access the common channel.In contrast, in the unsaturated regime, it may happen thatthe channel remains free. This is the case when f is chosento be relatively low.

Generally, for the sake of simplicity, previous workslimited their studies to the saturated mode. The unsatu-rated mode was considered in few paper, such as in [10],using simulations. In this work, we develop an analyticalmodel for each mode. To our knowledge, we are the firstto study analytically the WSN performance under theunsaturated regime. Our aim is to analyze the impact ofthe reporting frequency f, in addition to N, on the WSNperformances.

5.1. Probability of collision in IEEE 802.11 DCF-based

MAC protocols

In this subsection, we derive the collision probability asa function of the number of reporting nodes N and thereporting frequency f considering both the saturated andunsaturated regimes. We note that collision is a key factorthat impacts the total energy consumption as well as thetime required to report an event. In fact, the more frequentthe collisions are, the more time and energy are spent to

report an event.

destination SIFS CTS SIFS ACK

source

DIFS

Contention

window

RTS SIFS DATA

Backoff Slot

RTC

destination SIFS CTS SIFS ACKdestination SIFSSIFS CTSCTS SIFSSIFS ACK

source

DIFS

Contention

window

RTS SIFS DATA

Backoff Slot

source

DIFS

Contention

window

RTS SIFSS IF S D AT A

Backoff Slot

Fig. 2. Basic access mechanism of IEEE 802.11 DCF.



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5.1.1. Probability of collision in the saturated regime

Assume N reporting stations contending to access thecommon channel. In saturation conditions, each stationhas always a report to transmit. Thus, when we reach thesaturated regime the collision probability becomes insensi-tive to the reporting frequency f. In other words,

8fP fsaturation the collision probability remains the same.In this case, a collision occurs when two or more backoffcounters Bi i 1; . . . ;N of different stations expire atthe same time.

Hereafter, we assume that the number of transmissionsthat are subject to multiple successive collisions is negligi-ble. This assumption, denoted henceforth by assumption1, is widely used in the literature to simplify the analyticalmodels. Accordingly, following to a successful transmis-sion, we can also assume that the backoff Bi i 1; . . . ;N of each reporting station takes a value in0;CWmin. This second assumption (assumption 2) holdssince we omit successive collisions occurrence as explained

in [20]. The accuracy of these approximations is justified, asit will be demonstrated in Section 6, through the perfectmatch between the analytical and simulation results.

Let us now calculate the probability of collision occur-rence Pcol satN when reporting an event, that is during aReporting Transmission Cycle (RTC). The RTC is definedas the time spent between two successive acknowledgmenttransmissions by the sink node. Recall that the sink nodesends an acknowledgment frame after the reception of eachreport. In other words, RTC is the time required by theWSN to report an event to the sink. Before we delve in cal-culations, it is important to note that our model gives sim-

ple expression and more accurate results of the collisionprobability than [20].

As we neglect multiple successive collisions occurrence,during an RTC cycle, a report can be either successfullytransmitted from the first attempt (Fig. 3a), or followingto a first collision (Fig. 3b). Hence, a collision can onlyoccur at the beginning of the RTC cycle with a probability

Pcol satN PcN, where PcN is the probability of colli-sion among Ncompeting access nodes with their associatedbackoffs Bi i 1; . . . ;N ranging between 0;CWmin.

A collision occurs when several backoff counters expireat the same time. Hence, the probability of collision PcNcan be written as follows:

PcN PrfUg XCWmink0

PrfX k;Ug 1

where the random variable X denotes mini2h1;NiBi and theevent U is defined as follows:

U f9i;j 2 h1;Ni; i 6 j;Bi Bj Xg

fCollided transmissiong 2

The event fX k;Ug simply implies that the backoff coun-ter becomes zero for the first time in kslots for at least twostations, which leads to a collision occurrence. Thus,

PrfX k;Ug can be derived as follows:

PrfX k; Ug XNi2

N

i

CWmin k

Ni

CWmin 1 N

3

5.1.2. Probability of collision in the unsaturated regime

In the unsaturated regime, the reporting frequency of

each station is relatively low. Specifically, a reporting nodemay have no report to transmit at the beginning of a newRTC cycle. Recall that previous works limited their studyto the saturated regime omitting the unsaturated one. Inother words, collision probability is always calculated con-sidering the saturated regime. So, to the best of our knowl-edge, we are the first to derive this parameter in theunsaturated regime.

In order to compute the probability of collision, weassume that all the reporting nodes detect an occurringevent exactly at the same time. Then, they will try to sendnew reports each T 1=fs units of time until the desiredevent reliability R is attained. In the unsaturated regime,

we deal with successive cycles of T units of time. We sup-pose that during each cycle, N reports are transmitted tothe sink (see Fig. 4). Each cycle of T units of time is thuscomposed of N successive RTC cycles, corresponding tothe N reports transmission, followed by an idle period.This idle period is interrupted, and thus the next cycle Tbegins, as soon as the reporting nodes generate their newreports. In this regard, T can be expressed as follows:

T XNi1

RTC i idle period 4

where RTCi corresponds to the time required by theWSN to report an event to the sink when the number of ac-tive reporting nodes (i.e., nodes that have not yet transmit-ted their reports) is i.

Specifically, at the beginning of a cycle T, all the Nreporting nodes generate new reports to transmit to thesink. Immediately, the reporting nodes leave their idlestates (see Fig. 4) and proceed according the DCF algo-rithm, described in Section 4, to transmit their reports.

Let us now calculate the collision probability amongaccess nodes trying to report the detected event. It isdefined as the probability of collision when there is at leastone packet to be sent by the Nreporting nodes. Hence, the

probability of collision can be written as follows:

Pcol unsatN PrfCollision occursjYP 1g

where Y denotes the stationary state of the stochastic pro-cess fYt; tP 0g; which represents the number of report-ing nodes still having a packet to transmit. Byconditioning on the stationary state Y, we get:

Pcol unsatN XNi1

PrfCollision occursjY ig PrfY ijYP 1g

where PrfCollision occursjY ig can be derived simply

using (1) as follows:



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where ttr is the transmission time of the data packet and tovis a constant overhead, which can be simply deduced fromFig. 2, and thus given by:

tov DIFS tRTS 3 SIFS tCTS tACK 9

Moreover, tcontN represents the average time spent in

contention procedure when N reporting nodes competefor the medium access with their associated backoffs

Bi i 1; . . . ;N ranging between 0;CW. In otherwords, it is the extra time lost due to the collision occur-rence. Hereafter, we focus on tcontN calculations. Asstated before, we neglect in our study the successive col-lisions occurrence. Doing so, we distinguish between twocases:

Case 1: The report is transmitted successfully by one ofthe reporting nodes from the first attempt (i.e., followinga successfully transmitted report) (See Fig. 3a).

Case 2: The report is transmitted successfully by one ofthe reporting hosts following to a first collision occur-rence on the medium (See Fig. 3b).

(a) Case 1: This case happens with a probability1 Pcol satN. In this case, tcontN t1contN is simplythe average backoff time spent by the transmitting node,denoted by node j, before accessing to the data channel(See Fig. 3a). According to assumption 2 (Refer to Section5.1.1), all the reporting nodes backoff counters take valuesin 0;CWmin at the beginning of an RTC cycle. Moreover,as the report is successfully transmitted, the transmittingnode j has certainly the minimum backoff value among

the N competing access nodes (i.e., X Bj). In addition8i 6 j, we have Bi > Bj. Let U denote that event:

U f9!j 2 h1;Ni;Bj Xg fSuccessful transmissiong

10

Note that

PrfUg 1 PrfUg 11

Doing so, t1contN can be expressed as follows:

t1contN EXjU Slots 12

whereEXjU EX;U=PrfUg 13

Moreover, EX;U can be written as follows:

EX;U XCWmink0

kPrfX k;Ug 14

where PrfX k;Ug can be simply derived based on (3):

PrfX k;Ug PrfX kg PrfX k;Ug

N

1

CWmin k N1

CWmin 1 N

15

(b) Case 2: In this case, the report is successfully trans-mitted by one of the reporting nodes after a first failedattempt. Such case happens with a probability Pcol satN.tcontN t2contN is therefore the sum of the time spentfrom the beginning of the RTC cycle until the end of thetransmission of the collided RTS frame t02N and the

average backoff time required by the new transmittingnode j to access to the channel in order to transmit cor-rectly another RTS frame t002N (See Fig. 3b). Hence,we get:

t2cont N t02 N t

002 N 16

And we have:

t02 N DIFS tRTS EXjU Slots 17

where EX j U is the average backoff time of the collidedstations. It can be simply derived using the fact that

EX j U EX;U=PrfUg: Doing so, we have:

Bc N EX;U XCWmink0

kPrfX k;Ug 18

where PrfX k; Ug is given by (3).Let us now focus on the calculation of t002N. As we

mentioned before, a collision can occur only whenNc Nc P 2 stations send RTS requests at the same time.The Nc collided stations perceive the collision as they donot receive the CTS frame from the sink aftertCTS SIFS twait units of time. On the other side, theremaining N Nc nodes, which did not participate in thecollision, detect immediately the collision occurrence asthey receive a collided RTS frame and they will wait fora period of time equal to EIFS twait2 Slots beforeattempting again to access the channel. In this case, start-ing from the collision occurrence backoff counters of these

N Nc nodes take values in twait2; twait2 CWmin.On the other hand, the backoff windows of the Nc col-

lided stations double. Accordingly, the backoff countersof the collided stations take values in 0; 2 CWmin.However, these stations have to wait for a period of timeapproximately equal to 11 slots corresponding totwait tCTS SIFS before they try again to access to thedata channel. Hence, starting from the collision

occurrence, the backoff counters of the Nc collided stationsvary between twait; twait 2 CWmin, whereas theremaining nodes backoff counters vary betweentwait2; twait2 CWmin.

Let the random variable X0 denote mini2h1;NiBi and U0

be the following event:

U0 f9!j 2 h1;Ni;Bj X0g

fSuccessful transmissiong 19

We recall that we aim at calculating t002N, which is theaverage backoff time required by the WSN to successfullytransmit a new report after a first failed attempt. t002N

can be therefore written as:



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t002 N EX0;U0jU 20

which leads to:

t002 N Xtwait 2CWmin 1

ktwait

kPrfX0 k;U0jUg 21

In order to calculate t002N, we have first to derive the

expression of PrfX0 k;U0 j Ug. To achieve this, threecases are to be distinguished according to the value of X0

(in term of time slots).(i) twait 6 X

0 k< twait2In this case, the host jthat accesses the medium is one of

the Nc collided stations. Using the theorem of total proba-bility, we get:

PrfX0 k;U0jUg XNn2

PrfX0 k;U0;Nc njUg 22

This yields to

PrfX0 k;U0jUg XNn2

PrfX0 k;U0jNc n;Ug PrfNc njUg

23

Since the transmitting node j participate in the previouscollision, we have:

PrfX0 k;U0jNc n;Ug

n

1

2 CWmin twait k

Nn1

2 CWmin 1 Nn 24

Moreover, we have:

PrfNc njUg PrfNc n;Ug

PrfUg PrfNc ng

PrfUg 25

where

PrfNc ng XCWmink0

N

n

CWmin k

Nn

CWmin 1 N

26

(ii) twait2 6 X0 k6 twait2 CWmin

In this case the host j that accesses the channel may beeither one of the Nc stations, which already participatedin the first collision, or belongs to the N Nc remainingones. Accordingly, we distinguish between two sub-cases:

Sub-case (b.1): The transmitting host j already partici-

pated in the first collision. Such event is denoted by C. Inthis case, we have:

PrfX0 k;U0;CjUg XNn2

PrfX0 k;U0;CjNc n;Ug

PrfNc njUg 27

where


n

1

CWmin twait2 k

Nn 2 CWmin twait k n1

CWmin 1 Nn 2 CWmin 1

n

28

And PrfNc n j Ug is already given by (25).Sub-case (b.2): The transmitting host j did not partici-

pate in the first collision. Such event is denoted by C. Inthis case, we have:

PrfX0 k;U0;CjUg XN

n2


PrfNc njUg 29

where


N n

1

CWmin twait2 k

Nn1 2 CWmin twait k n

CWmin 1 Nn 2 CWmin 1

n

30

Putting both sub-cases together, we get the expression ofPrfX0 k;U0 j Ug when twait 6 X

0 k6 CWmin asfollows:

PrfX0

k;U0

jUg PrfX0

k;U0

;CjUg PrfX0

k;U0

;CjUg31

(iii) CWmin twait2 < X0 k< twait 2 CWmin

This case happens only when all the N reporting nodesparticipated in the first collision (i.e., Nc N). Thus, wehave:

PrfX0 k;U0jUg PrfX0 k;U0;Nc NjUg 32

This leads to

PrfX0 k;U0jUg PrfX0 k;U0jNc N;Ug

PrfNc NjUg 33

where

PrfX0 k;U0jNc N;Ug

N

1

2 CWmin twait k

N1

2 CWmin 1 N

34

And PrfNc NjUg is already given by (25).Moreover, using (21), (22), (31) and (33), we simply

derive t002N and thus we get the expression of t2contNby means of(16). Doing so, we finally derive the expressionof tcontN, which is given by:

tcont N 1 Pc N t1cont N Pc N t2cont N 35

By substituting (35) in (8), we get the average timerequired to report an event in the saturated regime whenthe number of reporting nodes is N. Hence, the averagetime needed to report reliably an event is: Tsat reliablyN

R TsatN:

5.2.2. Average time to report an event in the unsaturated

regime

In the unsaturated regime, the reporting frequency ofeach station is low enough so that the medium remains freefor a period of time after the transmission of Nreports. As

stated before, we deal with successive cycles of T 1f units



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of time. During each cycle Nreports are transmitted to thesink (see Fig. 4). Specifically, at the beginning of a cycle, allthe N reporting nodes compete to access the channel, sim-ilarly to the saturated regime. Once the first report is suc-cessfully transmitted, the remaining N 1 nodescompete again to access the data channel. Then, once the

next report is transmitted successfully, the N 2 remain-ing nodes compete once more to access the medium, and soon and so forth until all the reports are transmitted. Hencewe get:

Tunsat N 1

N

XNi1

Tsati 36

The average time required to report reliably an event inthe unsaturated regime can be therefore written as follows:

Tunsat reliably N;f 1

f b

R

Nc R b

R

NcN

Tunsat N

37

5.3. Sensor network lifetime

In this paper, the network lifetime Tnetwork lifetimeN,when considering Nreporting nodes are activate, is definedas the time spent from the deployment until the networkbecomes unable to report events due to the lack of energy.Typically, Tnetwork lifetimeN depends on the total initiallyprovided amount of energy Einitial, the rate of event occur-rence M, the reporting frequency f and the desired reliabil-ity RN. Based on [19], the average network lifetime can be

expressed as follows:

Tnetwork lifetime N;f Einitial Ew

kERTC N;f Ec38

where Ec is the constant continuous energy consumptionper unit of time needed to sustain the network during itslifetime without data collection, Ew is the expected wastedenergy (i.e., the total unused energy in the network whenit dies), k is the average sensor reporting rate defined asthe number of transmitted reports by the WSN per unitof time (i.e., R M) and ERTCN;f is the expected report-ing energy consumed by all the sensors to report an event.In the remainder of this paper, we ignore Ew: Indeed, Ew is

negligible when we achieve balanced energy consumptionacross the network. Hence, to derive the network lifetime,we only need to calculate ERTCN;f and Ec:

5.3.1. Sensor network lifetime in the saturated regime

Hereafter, we first evaluate the average energyERTC satN required by the WSN to successfully transmita report under the saturated regime (i.e., during an RTCcycle) when the number of active reporting nodes equalsto N. To achieve this, we take into account transmitting,listening and idle energies. We denote by Eidle, Etr and Erxthe consumed energy per unit of time during idle, transmit-

ting and listening states, respectively. As shown in Fig. 1, in

our model, each sensor node can listen to all the other sen-sors. In view of this, ERTC satN can be simply written asfollows:

ERTC sat N Etr N Eov N Econt sat N 39

where

EtrN is the amount of energy consumed during thetransmission of a data packet (i.e., during ttr) by the Nactive reporting nodes,

EovN is the amount of energy consumed during theconstant overhead period of time tov by the N activereporting nodes,

and Econt satN is the amount of energy spent in conten-tion procedure under the saturated regime by the Nactive reporting nodes.

Etr N tr Etr N 1Erx Eov N Eidle N DIFS 3 SIFS

Erx N 1tRTS N tCTS N tACK

Etx tRTS

Econt satN 1 PcN N Eidlet1contN

PcN Eidle N t002N DIFS

BcN Slots

PNn2PrfNc njUg

nEtxtRTS N nErxtRTS

8>>>>>>>>>>>>>>>>>>>>>>>>>>>:

40

These quantities are expressed as shown in (40).

Let us now calculate the continuous energy consump-tion Ec considering the desired event reliability R and themean number of events occurring by unit of time M. Weassume 1

MP R TsatN, that is the mean time between

two successive events occurrence i:e:; 1M

is higher thanthe mean time required to report reliably an eventi:e:; Tsat reliablyN. Hence, we get:

Ec N 1 R M Tsat N Eidle 41

The network lifetime in the saturated regime can be there-fore expressed as follows:

Tnetwork lifetime N Einitial

M R ERTC sat N Ec 42

5.3.2. Sensor network lifetime in the unsaturated regime

In the unsaturated regime we deal with successive cyclesof T units of time. During each cycle N reports are trans-mitted (see Fig. 4). Specifically, each time theith i 0; . . . ;N report is successfully transmitted, theremaining N i nodes, which have not yet transmittedtheir packets, compete again to access the data channel.Hence, like in (39), the average energy required to reportan event under the unsaturated regime with N reporting

nodes is given by:



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ERTC unsat N Etr N Eov N Econt unsat N 43

Econt unsat N 1

N

PNi1

1 Pci

N Eidlet1cont i Pci

Eidle N t002 i DIFS

Bc i Slots

Pin2

PrfNc njUg nEtxtRTS

N n ErxtRTS

8>>>>>>>>>>>>>>>>>>>>>>>>>>>>>:

44

where EtrN and EovN are already given in (40), andEcont unsatN can be expressed as shown in (44).

Let us now derive the continuous energy consumptionEc under the unsaturated regime. To do so, we assume that

1M> T bR

Nc R bR

NcN TunsatN

, that is the mean

time between two successive events occurrence 1M

is higher

than the mean time required to report reliably an eventT bRN

c R bRN

cN. So we have,

Ec N 1 R M Tunsat N Eidle 45

Using (38), the network lifetime in the unsaturated regimecan be therefore expressed as follows:

Tnetwork lifetime N Einitial

M R ERTC unsat N Ec46

6. Performance evaluation

In this section, we evaluate the impact of the reporting

nodes on the WSN performances using both analyticaland simulation approaches. The simulations are run onNS-2 simulator [14].

In our simulations, we have not assumed the mobility ofthe sensor nodes. Therefore, the topology does not contin-uously vary with time during simulations. However, wenote that the sensor nodes may die due to energy depletionleading to variation in overall topology. As stated before,the IEEE 802.11 DCF MAC protocol is used. The param-eter settings in our experiments are listed in Table 1.

Fig. 5a and b represent the probability of collision in thesaturated and unsaturated regimes, respectively, for a vary-

ing number of reporting nodes. We can see that this prob-ability increases, in both cases, with the increase of thereporting nodes. Indeed, collisions become more frequent

when the number of competing access nodes increases,which leads to increasingly extra energy expenditure andincreases the average time to report an event (RTC). Toalleviate these shortcomings, we have to reduce the numberof reporting nodes. We note that Fig. 5 shows a goodmatch between analytical and simulation results, whichconfirms the accuracy of our models. This also holds forthe remaining simulations described in this section. More-over, Fig. 5a shows that our analytical results match betterthe simulation results than those given in [20].

Fig. 6 plots the average backoff time (i.e., t1contN)required by a host to access the medium in order to success-fully report an event to the sink node from the first attemptin the saturated regime. We can observe that this waitingtime decreases when the number of reporting nodes Nincreases. Doing so, the overall time required to reportan event (i.e., RTC cycle) may be reduced.

According to Figs. 5a and 6, we can see that we have

two opposite requirements to minimize the time required

Table 1Simulation parameters

Communication range 40 mSensing range 30 mPacket length 30 bytesIFQ length 65 packetsTransmit power 0.660 WReceive power 0.395 WIdle power 0.035 W

Initial network energy 100 J

Fig. 5. Probability of collision.



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to report an event in the saturated regime. On one hand,increasing the number of reporting nodes enables a fasteraccess to the medium during each RTC cycle and hence,the average RTC time decreases. On the other hand, risingthe number of reporting nodes, increases the probability ofcollision which amplifies the time lost in contention proce-dure during each RTC cycle. Hence, the optimal RTC is atradeoff between these two opposite requirements. Recon-ciling these requirements, the minimum RTC time isobtained for Nopt latency 8. In fact, Fig. 7a shows thatthe RTC cycle in the saturated regime is a convex functionof N where the minimum is obtained for Nopt latency 8.

Accordingly, the fastest way to report reliably an event inthe saturated regime is to devise a network where the num-ber of active reporting nodes is set equal to Nopt latency.

Similar behavior is also observed in the unsaturatedregime (Fig. 7b) where the minimum RTC time is obtainedin this case for Nopt latency 9. In other words, considering aparticular reporting node frequency f belonging to theunsaturated range, the fastest way to report reliably anevent is to let only Nopt latency nodes among the N potentialones to report a detected event. In this case, the remainingN Nopt latency reporting nodes undergo a sleep mode.

So far, we have presented the impact of N on the RTC

time for each regime (saturated, unsaturated). In what fol-lows, we are interested rather in understanding the impactof the reporting frequency f on the RTC time. Fig. 8reports the average RTC time as a function of the networkreporting frequency f. In this case, when f exceeds approx-imately 900 reports=s we deal with the saturated regime,otherwise we get the unsaturated regime. Fig. 8 shows thatthe RTC time decreases significantly in the case of the sat-urated regime. Indeed, the saturated regime enables a fasteraccess to the medium in order to report an event (i.e.,min

ih1;NiBi) compared to the unsaturated regime. According

to this result, we can see that considering a reporting fre-

quency in the saturated range allows faster event reporting

Fig. 6. Average backoff time for a successful transmission in the saturatedregime (i.e. t1cont).

Fig. 7. Average time to report an event (i.e. RTC).

Fig. 8. Average time to report an event (i.e., RTC).



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compared with the unsaturated case. Combining, theresults of Figs. 7 and 8, we can conclude that the fastestway to report reliably an event (i.e., transmit R reports tothe sink) is to plan a network where the number of activereporting nodes is set equal to Nopt latency 8, and to adoptthe saturated reporting mode as depicted in Fig. 9. As

shown in Fig. 9 the saturated regime is more efficient fromthe latency point of view than the unsaturated regime.Fig. 10a and b show the average amount of energy con-

sumed during each RTC cycle (i.e., to report an event) for avarying number of reporting nodes N in the saturated andunsaturated regimes, respectively. Unlike, the RTC curves(i.e., Fig. 7), these figures show that the amounts of energy

ERTC satN and ERTC unsatN are monotonically rising withN. This monotonous increase is mainly due to two factors.First, increasing N amplifies the wasted energy due to col-lisions. Moreover, increasing N means waking up moresensor nodes within the event radius Rc. Doing so, the totalamount of energy consumed by the network in the recep-

tion of the signaling messages (RTS, ACK) increases con-siderably (see the hatched zones of Fig. 10). Finally, weunderline that the impact of these two factors is dominantwith respect to the slight idle energy reduction when Nincreases due to the faster access to the medium. Accordingto these results, we can see that the optimal number ofreporting nodes enabling the minimal energy consumptionis Nopt energy 1 for both saturated and unsaturatedregimes. Hence, we can state that the fastest way to reportan event does not correspond to the optimal manner toconsume the network energy. In this regard, the choice ofthe number of active reporting nodes depends mainly on

the specific QoS requirements of the WSN application.In the previous paragraph, we showed the impact of N

on the energy consumption. Hereafter, we want to under-stand the impact of the reporting frequency fon the energyconsumption. Fig. 11 plots the analytical results of the

amount of energy required to report reliably an event(i.e., transmit R reports to the sink) as function of the net-work reporting frequency f. We note that the simulationresults practically overlap analytical ones, thus we repre-sent only the analytical results. We can observe that theenergy reduces with f and becomes constant once the satu-rated regime is reached. Indeed, increasing f in the unsatu-rated range, reduces the idle period that experience thereporting nodes each time they finish the transmission oftheir N reports and before generating the N new ones(see Fig. 4). Hence, increasing f reduces the time requiredto report reliably an event (Fig. 9) as well as the associatedconsumed energy. Doing so, we reduce the idle energyspent by the network to report reliably an event. Thisamount of energy is null when we reach the saturatedregime. Combining the results of Figs. 10 and 11, we canconclude that the optimal way to consume energy is to acti-vate only one reporting node that works in the saturated

regime.

Fig. 9. Average time needed to report reliably an event

Tsat reliablyN; Tunsat reliablyN;f: case R 20.

Fig. 10. The amount of energy consumed to report an event.



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Fig. 12a and b plot the network lifetime evolution, inboth saturated and unsaturated regimes, respectively, as afunction of the number of reporting nodes N for a varyingvalues of the desired event reliability R. In our simulations,we consider the rate of event occurrence M 5. In otherwords, 5 events occur per unit of time. Fig. 12 shows thatthe smaller N is, the longer the network lifetime becomeswhatsoever the value ofR. Thus, the maximal network life-time is reached when N is equal to 1. Indeed, when Nincreases the probability of collision rises causing impor-tant energy depletion. In contrast, when N is set equal to

1, the probability of collision is null, avoiding thus extraenergy expenditure due to collisions.

7. Tradeoff between energy and latency

Energy-efficiency is a critical issue in wireless sensor net-works. However, minimizing the energy consumption insuch networks must be achieved while respecting the max-imum tolerable time to report an event. The optimal solu-tion must therefore take into account these two metrics.

In this section, we propose a simple function fchoice todetermine the optimal number of reporting nodes Nopt thatachieves the above-mentioned tradeoff. For illustrationpurposes, we give hereafter the expression of fchoice in thesaturated regime. Similar results can be easily obtained inthe unsaturated regime. fchoice can be expressed as follows:

fchoice N; a a ERTC sat N

Esat average 1 a

Tsat N

Tsat average47

where a is a weight that ranges between 0; 1. It is fixed bythe network administrator depending on the particularneeds of the sensor application (i.e., whether more empha-sis is given to energy conservation or to reporting latencyminimization), Esat average and Tsat average are, respectively,the mean value of ERTC satN and TsatN for the different

number of reporting nodes N:

Fig. 13 plots the evolution of fchoice as a function of thenumber of reporting nodes N: We consider two values ofthe weight a 1=8 and a 1=4: Two main observationscan be identified through Fig. 13. First, fchoice is a convexfunction of N where the minimum is obtained for Nopt. Inthis regard, Nopt minimizes the weighted function fchoiceand achieves therefore the desired tradeoff between theenergy conservation and reporting latency minimization.Moreover, we can observe through Fig. 13 that the valueofNopt depends of the weight a. Specifically, if more empha-sis is given to the energy conservation aspects (i.e., a is setclose to 1), the value of Nopt will be close to Nopt energy(i.e., Nopt 1). In contrast, if more priority is given to thelatency minimization aspects (i.e., a is set close to 0), thevalue ofNopt will be close to Nopt latency (i.e., Nopt 8). Thisresult is shown in Fig. 14, where Nopt decreases with a from

Nopt latency to Nopt energy. It is worth noting that for theextreme cases where a 0 and a 1 we get, respectively,

the same curves as Figs. 7a and 10a.

Fig. 11. The amount of energy needed to report reliably an event: caseR 20.

Fig. 12. Sensor network lifetime.



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8. Conclusion

In this paper, we explored the relationship between thewireless sensor network performance and the number ofreporting nodes. To the best of our knowledge, we arethe first to investigate the energy optimization problemfrom this perspective. Accordingly, we demonstrated thatthe optimal number of reporting nodes that minimizesthe energy expenditure in the sensor network does not cor-respond to the fastest way to report an event. Based on thisresult, we propose a simple methodology to achieve thistradeoff, which depends on the specific requirements ofeach WSN application.

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Fig. 13. Tradeoff between energy conservation and latency minimization.

Fig. 14. The optimal number of reporting nodes for a varying value of theweight a.

http://www.isi.edu/nsnam/nshttp://www.isi.edu/nsnam/nshttp://www.isi.edu/nsnam/nshttp://www.isi.edu/nsnam/ns

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