21-The Problem of Medium Access Control in Wireless Sensor Networks

8/3/2019 21-The Problem of Medium Access Control in Wireless Sensor Networks

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R1

A1

A32

A31

W I R E L E S S S E N S O R N E T W O R K S

INTRODUCTIONWireless sensor networks consist of battery-oper-ated sensing devices with computing, data pro-cessing, and communicating components. Such anetwork includes a large number of distributedsensor nodes that organize themselves into mul-tihop wireless networks and collaborate on com-mon tasks such as location sensing, eventdetection, and local actuator control. The prima-ry performance objectives of wireless sensor networks are energy conserv ation, throughputimprovement, scalability, and self-configuration, whereas fairness and temporal delay are oftensecondary issues. Since sensor nodes share a

common wireless medium, an efficient medium

access control (MAC) operation is required.However, the current wireless MAC protocolssuch as IEEE 802.11 and Bluetooth fall short of matching the characteristics of sensor networksand cannot effectively support their applications.

In this article we outline a throughput- and

energy-efficient MAC approach that allows dis-tributed implementation and supports multihopcommunication as required by autonomous andlarge-scale wireless sensor networks with highthroughput needs and energy constraints.

The extent of studies on multiple access hasbeen traditionally limited to simple networks withmultiple transmitters and a single destination.This model is clearly not sufficient to representself-organizing wireless sensor networks with mul-tiple dynamically changing transmitter-receiverpairs. As an extension of MAC operation to mul-tidestination networks, Nguyen et al. [1, 2] lookedat the problem of contention-based access in wireless networks with two fixed receivers and

used conflict resolution algorithms to explore thebounds on the maximum stable throughput. TheGroup time-division multiple access (TDMA)algorithm was proposed in [1] as a time-divisionmechanism in a two-destination network in orderto separate in time interfering groups of nodes with packets addressed to different destinations.The fundamental idea of scheduling transmissionsis not new. However, its use in this context is.Each group is assigned separate fractions of timedepending on traffic needs. The Group TDMAmethod was analyzed in terms of throughputproperties in [2], and the optimal time allocation was determined as function of the offered loadsindependent of the underlying multiple accessprotocol within each group of users. This analysiscan be extended to multidestination networks with arbitrary topology.

In [1, 2], a fixed assignment of transmitter-receiver pairs is assume d in contrast to thedynamic and autonomous nature of sensor networks, where all nodes are both able as well asobligated to transmit and receive packets eitheras parts of source-destination pairs or for relay-ing purposes (as required by multihop operationin large-scale sensor networks). If we furtherassume that only a single transceiver per node isavailable, we need to rule out simultaneouspacket transmission and reception by any node

in the network. Then it is necessary to develop a

YALIN EVREN SAGDUYU AND ANTHONY EPHREMIDES, UNIVERSITY OF MARYLAND

ABSTRACT

In this article we revisit the problem of sched-uled access through a detailed foray into thequestions of energy consumption and throughputfor MAC protocols in wireless sensor networks.

We consider a static network model that rulesout simultaneous transmission and reception byany sensor node and consequently requires parti-tioning of nodes into disjoint sets of transmittersand receivers at any time instant. Under theassumption of circular transmission (reception)ranges with sharp boundaries, a greedy receiveractivation heuristic is developed relying on thenetwork connectivity map to determine distinctreceiver groups to be activated within disjointtime intervals. To conserve limited energyresources in sensor networks, the time allocationto each receiver group is based on the residualbattery energy available at the respective trans-mitters. Upon activating each receiver group sep-

arately, the additional time-division mechanismof Group TDMA is imposed to schedule trans-missions interfering at the non-intended destina-tions within separate fractions of time in order topreserve the reliable feedback information. Thetwo-layered time-division structure of receiveractivation and Group TDMA algorithms offersdistributed and polynomial-time solutions (asrequired by autonomous sensor networks) to theproblems of link scheduling as well as energy andthroughput-efficient resource allocation in wire-less access. The associated synchronization andoverhead issues are not considered in this article.

THE PROBLEM OF MEDIUM ACCESS CONTROL IN

WIRELESS SENSOR NETWORKS

The primary

performance objectives

of wireless sensor

networks are energy

conservation,throughput improve-

ment, scalability, and

self-configuration,

whereas fairness and

temporal delay are

often the secondary

issues. However,

current wireless MAC

protocols fall short

from matching the

characteristics of

sensor networks.


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mechanism that will activate nodes as eithertransmitters or receivers for disjoint time intervals. This requirement is unavoidable.

The problems of deriving optimal channelaccess schedules for multihop networks and network partitioning into activation sets are bothNP-complete [3, 4], and require heuristic subop-timal solutions for practical use. In this article weintroduce a greedy receiver activation methodbased on partial knowledge of the network con-nectivity map to partition nodes into disjoint

transmitter-receiver sets. Rather than ensuringconflict-free schedules as in standard linkscheduling, we allow multiple transmission assign-ments to each receiver and rely on an arbitrarysingle-receiver MAC protocol to resolve theunavoidable packet conflicts. This protocol couldbe contention-based or conflict-free dependingon the application and performance measures,such as throughput, energy efficiency, or com-plexity. To obtain reliable feedback informationfrom each receiver, Group TDMA eliminates thesecondary conflicts in terms of packet collisionsdue to transmissions at nonintended receivers.

The predetermined receiver groups are acti-

vated within disjoint time intervals in a time-divi-sion mechanism. In wireless access, whether incellular, ad hoc, or sensor networks, energy effi-ciency is of paramount importance. Inspired byrecent work on energy-efficient multiple access in wireless networks [5], we can use battery energiesand node lifetimes as decision criteria in temporalallocation for distinct receiver groups in order tomake best use of finite and nonrenewable energyresources. The intuitive idea is to extend nodelifetimes by allocating more time to transmissionsby those nodes that have higher residual energy.

In summary, we outline a resource allocationand link scheduling scheme based on two-layertime-division operation. The outer layer (1) allo-

cates disjoint fractions of time (depending onresidual energy) to activate distinct sets of receivers (predetermined on the basis of network topology). The inner layer (2) creates timeorthogonality (based on throughput properties)between interfering transmitter groups for eachreceiver group.

THE SYSTEM MODEL

We consider a static model of wireless sensornetworks in which simultaneous transmission andreception by any node is not allowed. However,each node needs to act (interchangeably) astransmitter or receiver. We assume circular trans-mission (reception) ranges with sharp boundariessuch that no successful transmission or interfer-ence can be observed beyond that range. This isa simplifying unrealistic assumption; however, weallow these circular regions to overlap significant-ly, and thus the essence of interference is cap-tured. We assume that each node lies within thetransmission (reception) range of at least oneother node. We consider arbitrarily large (orrenewable) energy resources and fixed trafficload distributions among transmitters.

In this article we consider the problem of multiple access for both unlimited transmitterpopulation and a finite number of nodes. Trans-

mitters are equipped with omnidirectional anten-

nas and generate packets at a common rate. Weassume that nodes address their packets to anyreceiver in their transmission ranges with equalprobability. We consider a slotted system whereall transmissions are synchronized into unit timeslots. Any packet transmission is successful onlyif no other packet is simultaneously transmittedto the same receiver in the given time slot. A col-lision occurs if multiple transmitter nodes attemptto transmit (i.e., interfere) simultaneously. Anidle slot is observed if there is no packet trans-

mission attempt in the particular time slot. Eachtransmitter receives immediate and correct infor-mation on the channel output (i.e., whether asuccess, a collision, or an idle slot was observedin the preceding time slot). A separate channelbased on scheduled access is dedicated to feed-back control packets. These are the classicalassumptions of the collision channel model.

TOPOLOGY-BASED RECEIVER ACTIVATION IN

MULTI-DESTINATION NETWORKS

We propose a topology-based greedy heuristic to

sequentially determine distinct receiver groups tobe activated in a time-division mechanism. Wenow describe the logic of the mechanism forselecting receiver nodes. As the first step of receiv-er activation, an arbitrary node is chosen to initi-ate the first receiver group. The decision is eithercompletely random or follows a particular priority-based rule. Then the activated receiver node des-ignates all nodes within a fixed chosen range astransmitter nodes. This can be done in a distribut-ed manner by exchanging control information(about the current transmitter-receiver assign-ments) between the neighboring nodes. Next, anode outside the receiving range of the first activated receiver node is chosen as the second receiv-

er. It also designates all nodes in its range (whichmay overlap with that of the first receiver) astransmitter nodes to itself. We continue withsequential assignments of transmitter-receiverpairs until all nodes are included in either a receiv-er or transmitter activation group at least once.

We repeat the same procedure several timesby selecting next a previously designated trans-mitter node as a receiver and running the samealgorithm. Thus, we create a sequence of differ-ent receiver activation groups, until each node isactivated both as a receiver and a transmitter atleast once in a full cycle of activation periods. Actually, including each node in (at least) onereceiver group is a sufficient condition to termi-nate the process of forming new distinct receivergroups, since all nodes will be consequently des-ignated also as transmitters at least once overthe full cycle of receiver activation periods.

ILLUSTRATIVE EXAMPLE OF RECEIVER ACTIVATIONWe use the simple network shown in Fig. 1 toillustrate the greedy receiver activation heuristic.We pick node 1 as the first activated receiver.Nodes 2, 3, 4, and 5 are designated as transmit-ters, since they are within the receiving range of node 1. If node 6 is the second activated receiv-er, we classify nodes 7 and 8 as transmitters.Similarly, if node 10 is the last activated receiver,

nodes 9, 11, and 12 are classified as transmitters.

Any packet

transmission is

successful only

if no other packet

is simultaneously

transmitted to thesame receiver in the

given time slot.

A collision occurs if

multiple transmitter

nodes attempt

to transmit

simultaneously.


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We exclude nodes 1, 6, and 10 from the futurelist of receiver candidates, and repeat the sameprocedure, until all nodes are activated at leastonce as receivers. The node sets {1, 6, 10}, {2, 4,7, 12}, {5, 3, 8, 12}, and {9, 11, 6, 1} form valid

receiver groups that can be activated insequence. The question is what time fraction of activation to assign to each of these groups. Thisissue is addressed later.

TOPOLOGICAL CONSTRAINTS ON THE

SIZE AND NUMBER OF RECEIVER GROUPS

The number of activated receivers in each receiv-er group is constrained by the total number of nodes n as well as by the topology propertiesincluding the network size and the radius r of the common reception (and transmission) range.We define N i as the number of elements inreceiver group Gi, for 1 ≤ i ≤ N . The cardinality

of any receiver group strongly depends on theeffects of overlapping between the receptionranges of the activated receiver nodes.

The upper bound on N i is imposed by the totalnumber of nodes n and the constraint that theseparation between two activated receivers cannotbe smaller than the radius r of reception range.The lower bound on N i can be achieved if thereception regions of activated receivers arenonoverlapping but still cover the remainingnodes (already designated as transmitters). Forillustrative purposes, we consider a tandem network of length L and a planar network of area A.

For the case of n nodes in the region underconsideration, the number of activated receivers N i in any receiver group Gi has the followingbounds:I. Tandem networks: 1 ≤ N i ≤ min { g( n), L / r +1}II.Planar networks: 1 ≤ N i ≤ min { h( n), 3 A /π r 2}

where the quantities g(1) = 1, g( n) = ϒ 2( n –1)/3 for n > 1 and h(1) = 1, h( n) = 12( n –1)/13 for n >1 are derived from basic geometry.The proposed receiver activation approach

produces a minimum number of distinct receivergroups if the maximum number of receiver nodes(with minimum overlapping between their recep-tion ranges) is included in each receiver groupand each node only appears in a single receivergroup. On the other hand, the maximum number

of receiver groups is achieved if only one new

receiver is activated in each successive receivergroup. For the case of n nodes in the regionunder consideration, the number of distinctreceiver groups N (note this is a different quan-tity than N i) has the following bounds:I. Tandem networks:

II. Planar networks:

STARTING POINT: RANDOM ACCESS FOR

COLLISION CHANNELS

The problem of multiple access for a single acti-

vated receiver has been extensively studied and well-known random access (e.g., stabilized slot-ted Aloha, First-Come-First-Serve [FCFS] algo-rithm) and scheduled access (e.g., time-,frequency-, or code-division multiple access)solutions have been proposed. When we consid-er a large number of transmitters, some form of random access (rather than scheduled access) isunavoidable. The splitting algorithms for colli-sion resolution in random access provide higher values of stable throughput than stabilized slot-ted Aloha. Splitting a group of packets that havecollided in a slot can be implemented based on various criteria, such as coin toss, node or packetID, arrival time, or residual energy [5].

In this article we consider the classical colli-sion channel model and use the FCFS algorithmto resolve packet collisions, although almost anyarbitrary MAC protocol can be assumed. TheFCFS algorithm initiates a new collision resolu-tion period (CRP) whenever a packet collisionoccurs (i.e., multiple packets are simultaneouslytransmitted in a given time slot). All packets thatarrive within a specified time allocation intervalare transmitted in the first period of this CRP. If there is another collision, the time allocation win-dow is further shortened and the same procedureis repeated, until all packets involved in the origi-nal collision are successfully received. Synchro-nization among transmitter-receiver pairs can beachieved as the receiver node sends some form of synchronization information initiating a new com-munication with a control message. Transmitternodes synchronize their clocks with the receiveron receiving this information. The exact methodof synchronization and further implementationissues are out of scope of this article.

GROUP TDMA ALGORITHM FOR

TWO-DESTINATION NETWORKS

In this section we look at the multiple accessproblem in a simple network model with two

activated receivers (i.e., two potential destina-

n

h nA

r

N n

min ( ),3

2π

≤ ≤

n

g nL

r

N n

min ( ),

,

+

≤ ≤1n Figure 1. The simple multihop network model for illustration of the receiver

activation method.

2

5

4 6

8

9

10

11

12

7

3

1



tions) and multiple transmitters, as shown in Fig.2. We assume that transmitters are within thereception range of at least one receiver. Trans-mission ranges are circular with sharp bound-aries, and beyond that range no transmission orinterference is possible. However, these circlesmay overlap significantly. Packets can beaddressed to either of the two receivers withequal probability if the nodes lie in the intersec-tion of these circles. Otherwise, the packets aredestined for the receiver they can reach. Nodes

have immediate access to ternary feedback fromtheir intended destinations: whether a collision,a success, or an idle was observed during thepreceding slot. We assume unlimited popula-tions of unbuffered users in each region. Weassume that these users follow an arbitrary MACprotocol with maximum stable throughput Smax.For example, this could be slotted Aloha withSmax = 1/e = 0.3679 or FCFS with Smax = 0.4878(packets per time slot).

FEEDBACK RELIABILITY PROBLEM IN


We denote receiver nodes R

1 and R

2, as shown inFig. 2. For each time instant (or time slot), weidentify four distinct groups of transmitters. Wedefine A1 and A2 as disjoint transmitter groups inthe reception range of each receiver node R1 and R2, respectively. We define A3 as the group of transmitters that lie in the intersection of the twocircles and hence have both receivers in theirtransmission ranges. We assume that nodes fromgroups A1 and A2 randomly generate packets des-tined only to R1 and R2, respectively, whereasnodes of group A3 transmit to either R1 or R2 with equal probability. At each time the group A3consists of groups A31 and A32, where nodes in A3i, i = 1, 2, are transmitting to receiver Ri.

If the MAC protocol used is stabilized Aloha,there is no problem of propagation of feedbackerror. If, however, we use FCFS with the so-called first improvement [6], there is potentialinstability created by misinterpretation of thefeedback signal from the channel (since colli-sions at Ri can be caused by packets destined foreither receiver); this is equivalent to errors inthe feedback signals. However, if plain FCFS isused, there is no problem of such stability. Thecross-collisions between packets with differentdestinations may reduce the maximum stablethroughput value but will not cause instability atlow traffic rates.

DESCRIPTION OF THE GROUP TDMA ALGORITHM A solution to the feedback reliability problem was proposed in [1, 2] promoting the GroupTDMA algorithm as a time-division mechanismto distinguish four groups of transmitters, A1, A2, A31, and A32, and schedule transmissions of { A1, A2}, A31 , and A32 over three nonoverlappingtime intervals x1, x2, and x3, respectively. Theslots allocated to various groups do not need tobe implemented as contiguous blocks of slotsand can have an arbitrary order as long as theoverall frame length is sufficiently large so thatany given slot apportionment (i.e., fractions x1, x2, and x3) can easily be realized.

For the case of unlimited transmitter popula-

tion, we define f 1, f 2, f 31 and f 32 as the fractionsof the total traffic load λ generated by transmit-

ter groups A

1, A

2, A

31, and A

32, respectively. If we employ Group TDMA with temporal assign-ments of x1, x2, and x3 to transmitter groups { A1, A2}, A31, and A32, the total stable throughput λmust satisfy

λ f 1 ≤ x1 Smax, λ f 2 ≤ x1 Smax,

λ f 31 ≤ x2 Smax, λ f 32 ≤ x3 Smax

(1)

where 0 ≤ x1, x2, x3 ≤ 1, and Σ i=13 xi = 1. Our

objective is to maximize λ over x1, x2, and x3 sub- ject to the stability conditions, which are given byEq. 1 in terms of linear constraints. The first twoconstraints in Eq. 1 can be combined to λmax( f 1, f 2) ≤ x1Smax. Then the stable throughput is maxi-mized if we choose x

1, x

2, x

3to satisfy each of the

constraints λmax( f 1, f 2) ≤ x1Smax, λ f 31 ≤ x2Smax,and λ f 32 ≤ x3Smax with equality. The throughput-optimal temporal allocation is given by

(2)

This is derived in [2] and can be obtained bysolving the simple linear program. The solutionsuggests that separately activated transmittergroups with larger traffic loads should be allocat-ed for longer time intervals. We can interleavethe slots dedicated to different groups as long asthe resulting time allocation satisfies Eq. 2. Weassume sufficiently large frame lengths so that wecan exactly implement the optimal time fractions.

THROUGHPUT EFFICIENCY OF THE

GROUP TDMA ALGORITHM

We compare Group TDMA to the options of:1 Activating all transmitter-receiver pairs simul-

taneously (i.e., no time division)2 Activating receivers one at a time (i.e., each

group is activated separately)

xf f

f f f f

xf

f f f f

xf

f f f f

11 2

1 2 31 32

231

1 2 31 32

332

1 2 31 32

*

*

*

max( , )

max( , ),

max( , ),

max( , )

=+ +

=+ +

=+ +

n Figure 2. The simple two-destination network model for illustration of theGroup TDMA algorithm.

R1 R2

A1

A32

A31

A2



Then the maximum stable throughput undermethod 1 must satisfy

and under method 2 it must satisfy

where Smax is the maximum stable throughputachievable for the single destination case withoutinterference from the adjoining group and

Smax′ is the maximum stable throughput for thesingle destination with neighboring node inter-ference. Clearly, Smax′ ≤ Smax . By contrast themaximum stable throughput of the GroupTDMA satisfies

Since max( f 1, f 2) ≤ f 1 + f 2 and Smax′ ≤ Smax , we see that Group TDMA achieves higher stablethroughput than method 1 or 2.

GROUP TDMA ALGORITHM UNDER A

MORE REALISTIC CHANNEL MODELSo far, we have assumed that the transmission (orequivalently interference) and reception rangesare both circular areas with common sharp bound-aries, and beyond that range no transmission orinterference can be observed. We can adapt amore realistic criterion for successful packetreception, the protocol model (as introduced in[7]) that extends the interference effects beyondtransmission ranges. According to the protocolmodel, all nodes have a common range r fo rtransmissions, and a transmission is successful if and only if the distance between the intendedtransmitter-receiver pair is smaller than or equal

to a transmission-reception radius r , and the dis-

tance of every other concurrent transmitter to theparticular receiver is greater than or equal to theinterference radius (1 + ∆) r . The quantity ∆ ≥ 0accounts for a guard zone that prevents a neigh-boring node from transmitting over the same sin-gle channel at the same time.

Figure 3 illustrates the two-destination network model, in which the transmission and inter-ference ranges become distinguishable due to theadditional interference effects. We partition thenetwork into five subregions with distinct trans-

mission and interference properties. Regions 1and 2 contain nodes that have only receivers R1and R2 as their destinations, respectively, and can-not cause interference at the other receiver.Nodes in the reception ranges of both receiversare included in region 3. On the other hand,region 4 consists of nodes that are in the recep-tion range of R1 but can also interfere at R2. Simi-larly, region 5 consists of nodes that are in thereception range of R2 but can also interfere at R1.

We denote f i′ the fraction of traffic load gen-erated by transmitter nodes in region i, where 1 ≤i ≤ 5. The set of the nodes in region i is denotedby Ai. We partition A3 into two subgroups, where A

3,1 and A

3,2 denote nodes that attempt to reachreceiver R1 and R2, respectively, with the trafficloads f 3,1′ and f 3,2′ . According to the Group TDMAformulation, we divide the time interval intothree disjoint time fractions, x1′, x2′, and x3′. Thepacket transmissions from A1 and A2 are allocat-ed within x1′ fraction of time. The packet trans-missions from A3,1 and A4 are allocated within x2′fraction of time. The rest of the time, the timefraction of x3′ , is dedicated to transmissions from A3,2 and A5. The optimal temporal allocation andmaximum stable throughput are still given byEqs. 2 and 3, where we need to replace xi

* by xi′*for i = 1, 2, 3, and we let f 1 = f 1′, f 2 = f 2′, f 31 = f 31′+ f 4′, and f 32 = f 32′ + f 5′.

We can easily evaluate the effects of ∆ on λ′*under the assumptions that the traffic load f i′ isdirectly proportional to the area of region i andnodes address their packets with equal probabili-ty to any of the receivers in their transmissionranges. Figure 4 depicts the maximum stablethroughput per destination, λ′*/Smax, as a func-tion of the traffic load fraction f 3′ for different values of ∆. To simplify the analysis, we continuein the rest of the article with the assumption of ∆ = 0. The important thing to note in this sec-tion is that more realistic models (i.e., with ∆ >0) can be tracked in the same fashion as we ana-lyze Group TDMA.

GROUP TDMA IN


We illustrate Group TDMA operation using thesimple network shown in Fig. 1. If nodes 1, 6, and10 are activated in the first receiver group, weinclude nodes 2 and 5 in A1, node 7 in A2, andnodes 9, 11, 12 in A3. Nodes 3 and 4 belong to A1,1or A1,2 depending on whether their packets areaddressed to node 1 or 6, respectively. Node 8belongs to A2,2 or A2,3 if its packets are addressedto node 6 or 10, respectively. The activation periodis divided into fractions of time to be assigned sepa-

rately to each transmitter group. Nodes from A1,

λ *max( , )

.max=+ +

S

f f f f 1 2 31 32

λ 21 2 31 32

* maxmax=

+ + +=

S

f f f f S

λ 11 2 31 32

* max

max( , ),=

′+ +

S

f f f f

n Figure 3. The simple two-destination network operating under the protocol model with more realistic interference effects (solid and dashed circles corre- spond to the transmission and interference ranges, respectively.)

A1 A31

A32

A4

A1A2

R2

r

r: Transmission radius ∆: Guard zone parameter

∆r

R1



A2, A3 are allocated within x1 fraction of time.Nodes from A1,1, A2,3 are allocated within x2 frac-tion of time. The residual fraction of time x3 isassigned to transmissions from A1,2 and A2,2.

THROUGHPUT-OPTIMAL

TIME ALLOCATION BY GROUP TDMAWe assume systems with either unlimited energyresources or an unlimited number of nodes toeliminate changes in the traffic load characteris-

tics of any transmitter group. We consider thereceiver activation period in which a particularreceiver group Gi is activated. The transmitternodes in that group are divided into ci number of disjoint transmitter groups Gi, k, 1 ≤ k ≤ ci. Trans-mitter group Gi, k is activated within xi, k fraction of time in the given receiver activation period suchthat Σ k=1

ci xi, k = 1. We define Ri, k as the set of receivers that can be reached by transmittergroup Gi, k and define the jth receiver in group Ri, k R

i, k( j) . We define A

i, k( j) as the subset of nodes

that belong to the kth transmitter group Gi, k andhave packets destined to the receiver R

i, k( j) . The

fraction of the traffic load generated by node

group A

i, k

( j)

is given by f

i, k

( j)

. We assume that eachtransmitter node generates one-hop packet trans-missions with equal rate (either as a source or forrelaying purposes). Provided that receiver groupGi is activated, the quantity λi stands for the totalrate of packet arrival to the rest of the nodes thatare classified as transmitters in this period. Allnodes in transmitter group Gi, k, k ∈ {λ, …, ci},must jointly satisfy the stability condition of

λi f i, k( j) ≤ xi, k Smax, ∀ j: R

i, k( j) ∈ Ri, k (4)

The optimal temporal allocation and maxi-mum achievable throughput can be obtainedaccording to a linear programming solution(similar to the one previously obtained for the

two-destination case), and are given by

(5)

Note that the quantity λi* does not representthe end-to-end throughput but denotes the maxi-mum number of successful one-hop transmis-sions per time slot.

ILLUSTRATIVE EXAMPLE OF TANDEM NETWORKS

As an extension to networks with an unlimitednumber of destinations, we consider the tandemnetwork model with at most two-neighbor con-nectivity where nodes are placed in tandem on asingle line. Provided that the receiver group Gi isactivated, we enumerate the activated receiversfrom left to right. Transmitters that are in thereception range of one receiver only belong to thetransmitter group Gi,1. The rest of the transmit-ters (i.e., transmitters in the reception ranges of two receivers) are divided into two subgroups Gi,2and Gi,3 such that Gi,2 consists of nodes transmit-ting to the odd-numbered receivers and Gi,3 con-sists of nodes transmitting to the even-numbered

receivers. Simultaneous transmissions of nodes

from different groups can cause secondary inter-ference effects. Therefore, transmitter groupsGi,1, Gi,2, and Gi,2 (i.e., the packet transmissionsoriginating from the three distinct transmittergroups) need to be activated separately withindisjoint fractions of time x1,i, xi,2, and xi,3, respec-tively. The special nature of the tandem topologyreduces the number of distinct transmitter groupsto three for each activated receiver group.

TOPOLOGY-INDEPENDENT BOUNDS ON THE

MAXIMUM STABLE THROUGHPUT

Consider a tandem network deployed over length L and a two-dimensional planar network of area A both with common transmission radius r . Wedenote λ i* the maximum stable throughputachievable by an unlimited population of nodesoperating according to the Group TDMAmethod during the ith receiver activation period.For any tandem and planar topology, we have

(6)

where Smax is the maximum stable throughputachievable by an arbitrary MAC protocol for thesingle destination case.

GROUP TDMA ALGORITHM FOR THE

FINITE POPULATION OF TRANSMITTERS

Instead of revisiting the stability problem of mul-tiple access systems with finite numbers of trans-mitters [8], we assume that the maximumachievable (stable) throughput of MAC protocolSmax(T i) is known as a function of the number of transmitters T i. We use the following simple

example to illustrate the temporal allocation

S L

r

S L

r

S A

r

S A

r

i

i

max * max

max * max

( )

4 2

3 32 2

≤ ≤

+

≤ ≤

λ

π

λ

π

and

x f

f k c

S

f

i k

j R R i k j

k c

j R R i k j i

i

k c

j R R i k j

i k j

i k

i

i k j

i k

i

i k j

i k

,* : ,

( )

: ,( )

* max

: ,( )

max

max, { , }

max

,( )

,

,( )

,

,( )

,

= ∈ …

=

∈

= ∈

= ∈

∑

∑

1

1

1 and

λ

n Figure 4. Effects of the receiver range overlapping (i.e., the value of f 3′ ) andinterference level (i.e., the value of ∆ in the protocol model) on the maximum value of the normalized stable throughput (i.e., λ′*/ Smax ).

Fraction of traffic f ’3

0.9 10

0.4

0.5

λ ‘

1 *

/ S m a x

0.6

0.7

0.8

0.9

1

0.80.70.60.50.40.30.20.1

∆= 0

∆= 1 / 4∆= 1 / 2∆= 1

∆ ≥ 2



solutions of the Group TDMA algorithm in thecase of finite number of transmitters. We assumethat the ith receiver group Gi is activated withtwo receivers and three transmitters. The recep-tion region of each receiver contains two trans-

mitters, whereas the overlapping area of tworeception ranges includes only one transmitter.Transmitters are divided into four groups eachof cardinality one. Nodes in Ai,1

(1) and Ai,1(2) are

activated within a fraction of time equal to xi,1, whereas transmissions of nodes in Ai,2

(1) and Ai,3(2)

are assigned within xi,2 and xi,3 fractions of time,respectively. If we assume that the overall trafficload is homogeneously distributed among trans-mitters (i.e., each transmitter has the same pack-et arrival rate), the load fractions are given by f i,1

(1) = f i,1(2) = 1/3, f i,2

(1) = f i,3(2) = 1/6. Under the sta-

bility condition given byEq. 4 with Sma x =Smax(1), the optimal temporal allocation is xi,1* =1/2, xi,2* = xi,3* = 1/4. The maximum achievable

throughput can be expressed as λi* = 3/2Smax(1), where Smax(1) = 1 is the obvious solution due tothe absence of primary or secondary interferenceeffects for this simple example. Hence, 3/4 pack-ets per slot can be transmitted to each receiveron the average in this example.

ENERGY-EFFICIENT TEMPORAL ALLOCATION

FOR RECEIVER ACTIVATION

We now depart from the discussion of GroupTDMA for a given receiver group and addressthe issue of scheduling the activation of the dif-ferent receiver groups. If these receiver activa-tion groups have been predetermined based onthe network topology according to the heuristicoutlined earlier, it remains to determine the activation order and duration of each receiver groupGi. We propose to use node lifetimes and energyconsumption rates as measures for time alloca-tion to the different receiver groups. This is asensible criterion for sensor networks. We define RG m as the receiver group activated in the mthactivation period with an allocated time fractionof t m. We assume that the energy of each node isequally dedicated to transmissions for eachreceiver in its transmission range. We denote E m(Gi) the total energy available for transmis-

sions to Gi before the mth receiver activation

period and ∆ E m(Gi) the change in the amount of energy E m(Gi) during the mth period.

The intuitive energy-efficient solution forreceiver group activation is that group RG m

should be the one (from all possible receiver

groupsG

i, 1≤ i ≤ N

) that maximizes E

m(G

i). Inother words, we activate (at any time instant)only the receiver group for which the respectivetransmitters have the highest amount of residualcumulative energy.

We denote LT the function to be maximized,namely the residual system lifetime, which isdefined as LT = min1≤i≤ N LT i, where LT i denotesthe lifetime of energy supplies dedicated topacket transmissions to receiver group Gi.

The approach to the given optimization prob-lem is based on load balancing, that is, equalizingthe cumulative residual energies of different nodegroups. The idea is to keep the quantity E m(Gi)of all Gi close to each other over successive acti-

vation periods m so that no node group (transmit-ting to a particular receiver group) runs out of energy earlier than other node groups. As a result,the minimum of node lifetimes, LT , is maximized.

The underlying theoretical solution for thegiven receiver activation policy is that the mthactivated receiver group RG m maximizes E m(Gi),as lim t m → 0 for all values of m. A new receiveractivation period m + 1 is initiated only if theresidual energy of transmitters for RG( m) fallsbelow the residual energy of transmitters foranother receiver group. The optimal solutionsuggests switching between receiver groups withinfinitesimal activation durations. A suboptimalbut practical solution is to activate first the receiv-er group with the highest total energy of corre-sponding transmitters and to replace RG m withanother receiver group for receiver activationperiod m + 1 if E m+1( RG m) falls belowminGi≠ RG m E m+1(Gi) – c. We introduce the con-stant c to prevent rapid changes in the activationprocess. An intuitive solution for selecting thelength of activation period with RG m = Gi is c /µ(Gi), where µ(Gi) denotes the rate of change(measured in unit energy per unit time) in thecumulative residual energies of the nodes whenev-er receiver group Gi is activated. A sample solu-tion is illustrated in Fig. 5 for four receiver groups.

Next, we explore the optimal time allocation

with c = 0. According to the energy-efficient

nnnn Figure 5. Illustration of temporal allocation among four receiver groups over successive activation periods.

∆E0(G2)

E0(G1) E0(G2) E0(G3) E0(G4)

∆E1(G4)

E1(G1) E1(G2) E1(G3) E1(G4)

∆E2(G1)

E2(G1) E2(G2) E2(G3) E2(G4)

We propose to use

node lifetimes and

energy consumption

rates as measures

for the time

allocation to thedifferent receiver

groups. This is a

sensible criterion for

sensor networks.



receiver activation, we select ∆ E m(Gi) for all Gi’s with the objective of making the node lifetimesapproach each other. In other words, the lengthof temporal allocation to Gi, namely τi, shouldbe selected inversely proportional to µ(Gi). The value of τi is simply given by

(7)

The energy consumption rates µ(Gi), i ∈ {1,…, N } strongly depend on the underlying MACprotocol and the transmitter-receiver activationby the Group TDMA algorithm. We can expressµ(Gi) for any i ∈ {1, …, N } as follows:

(8)

where ε( y) is the energy consumption rate of anarbitrary single-receiver MAC protocol (e.g.,FCFS) operating with rate y packets per timeslot. The time fractions xi, k, load fractions f i, k( j),

number of transmitter groups c

i and stablethroughput λi can be obtained from the previ-ously outlined analysis of Group TDMA. Theenergy consumption rates ε( y) are depicted inFig. 6 as function of the achievable stablethroughput y under MAC protocols such as thestabilized slotted Aloha and FCFS algorithms with and without improvement.

Although in this section we omit the detailsof the analysis and the notation is s omewhatcumbersome, we intend to show that the energy-based criterion results in a concrete solution tothe optimal receiver group activation schedule.

JOINT RECEIVER ACTIVATION ANDGROUP TDMA AS SOLUTIONS TO

MODIFIED LINK SCHEDULING PROBLEM

STANDARD AND

MODIFIED LINK SCHEDULING PROBLEMS

The standard form of general link scheduling [3,4, 9] involves the assignment of channels (i.e.time slots, frequencies or codes) to connectinglinks between nodes so that all links assigned tothe same channel may transmit in a conflict-freefashion. The network topology is described by adirected graph where directional links betweennodes are only possible if nodes are within eachother’s transmission-reception ranges. For con-flict-free packet transmission, the following con-ditions should be satisfied:I Nodes cannot simultaneously transmit and

receive packets.IINodes cannot transmit packets to multiple

destinations in the same time slot.III Primary packet conflicts — multiple number

of simultaneous transmissions to the samereceiver — are not allowed.

IV Secondary packet conflicts — interferenceeffects at nonintended receivers — are nottolerated.

Standard link scheduling allocates conflict-free

links without violating any of conditions I–IV forthe same fraction of time. This can be formulatedas a link coloring problem [9]. The problems of determining the edge chromatic number of graphs(i.e., the fewest number of colors necessary tocolor each graph edge so that no two graph edgesincident on any graph vertex have the same color)and optimal link scheduling are both NP-com-plete [3, 4, 10]. Instead of solving the standardscheduling problem, we rely on a receiver activa-tion heuristic to determine disjoint subsets of transmitters and receivers at each time instant (sothat condition I is satisfied and possible violationsof other conditions are reduced, but not eliminat-

ed, for all links) and on the Group TDMAmethod to create time orthogonality betweenlinks violating conditions II and IV.

DISTRIBUTED IMPLEMENTATION FOR

GROUP TDMA ALGORITHM

We can set up the transmitter group classifica-tion as a link coloring problem. We assume thattransmitters can discover receivers up to a two-hop distance. Two receivers are called neighborsif there is at least one transmitter in the intersec-tion of their reception ranges. Interfering trans-mitter groups are assigned to distinct fractions of time (i.e., different colors are assigned to linksfrom different transmitter groups). Transmitters with only one receiver in their transmissionranges acquire membership in group A1, and alllinks from A1 are given color C1. Next, an arbi-trary receiver R1 is selected such that any trans-mitter that has multiple receivers in itstransmission range including R1 as the intendeddestination initiates a transmitter group A2 (i.e.,links from A2 to R1 are given a new color, C2).Next, we consider all neighbors of R1 for linkcoloring purposes. If R2 is a neighboring receiverof R1, we assign different colors to all links fromtransmitters that lie in the intersection of R1 and R2 to the particular receiver R2. We continue

with coloring links to receivers one by one.

µ ε λ ( ) ( / ), ,( )

,

: ,( )

,

G x f xi i k k

c

i i k j

i k j R R

i

i k j

i k

== ∈∑ ∑

1

τ µ

µ

i

i

i

i N i

i

E G

G

E G

G

i N = ≤ ≤=∑

0

10

1

( )

( )

( )

( )

,

n Figure 6. The energy consumption rate ε( y ) as function of the achievable stablethroughput y (with unit energy for packet transmissions).

y: arrival rate

FCFS with improvement

FCFS without improvement

Stabilized slotted aloha

0.45 0.50

0

0.2

ε ( y ) : e n e r g y c o n s u m p t i o n r a t e

0.4

0.6

0.8

1

1.2

1.4

0.40.350.30.250.20.150.10.05

Stabilized slotted alohaFCFS without improvementFCFS with improvement



Transmitters that originate links with new colorsinitiate new transmitter groups.

For receiver activation group Gi, we denote r ithe maximum number of intersections of receptionranges (i.e., the maximum number of neighbors)for each receiver and we denote ei the modifiededge chromatic number, which is the minimumnumber of colors necessary to color graph edges sothat no two graph edges violating condition IVhave the same color (i.e., links to neighborreceivers are assigned different colors). Note that r i+ 1 ≤ ei, which follows from plain geometry.

Since the separation between receiver nodesis greater than the reception radius r (as a conse-quence of receiver activation), there exists afixed upper bound on the number of intersec-tions of reception ranges for each receiver. Atmost 13 different colors are needed for planarnetworks (with r i = 12), and at most three differ-ent colors are needed for tandem networks (with r i = 2). As a result, transmitters with any intend-ed destination R choose one of the finite num-ber of available group memberships differentthan those previously acquired by other trans-mitter groups with intended destinations that areneighbors to R. Packets are addressed randomlyto any of the receivers in the transmission rangeso that condition II is also satisfied.

If the receiver activation has already parti-tioned nodes to subsets of transmitters andreceivers (so condition I is satisfied for all links),the remaining problem of creating time orthogo-nality among transmitter groups (so conditionsII and IV are satisfied for all possible links) canbe solved in polynomial time by the distributedGroup TDMA method.

So we see that the entire problem of schedul-ing transmitters and receivers in a sensor network, a problem that needs to be solved one wayor another, reduces to a combination of stan-dard graph coloring techniques and Group

TDMA with arbitrary MAC protocol. This is the

main contribution in this article and the princi-pal point we want to get across.

NUMERICAL RESULTS

For numerical evaluations, we consider both stat-ic tandem and planar network models with 1000unbuffered nodes as approximate models forinfinitely dense wireless sensor networks. Weconsider systems with first unlimited energy sup-ply and then with hard finite energy constraints.

For the latter case, we assume that each nodehas an amount of initial battery energy Emax =106 (unit energy). Each packet transmission con-sumes π r 2 units of battery energy. We assumethat nodes generate packet transmissions withthe same rate according to a common Poissonprocess and employ the FCFS collision resolutionalgorithm to resolve primary packet conflicts.

In the single destination case, the maximum sta-ble throughput achievable by the unlimited nodepopulation employing the FCFS algorithm (withthe first improvement) is Smax = 0.4878 (packetsper unit time or time slot), which represents only alower bound on the maximum stable throughput

achievable by a finite number of transmitters.The value of the common transmission (recep-tion) radius characterizes the distribution of theactivated transmitter-receiver pairs on the network as well as specifies the overlapping betweenthe reception regions, on which the operation of receiver activation and Group TDMA stronglydepends. To illustrate the topology effects, weintroduce the quantities 2 r / L and π r 2 / A, whichdenote the ratios of the transmission range to thenetwork length and network area in tandem andplanar networks, respectively.

We first apply the topology-based receiveractivation heuristic (without energy-efficientsolutions) to unlimited energy systems and com-

pare the Group TDMA algorithm with simulta-neous operation of the activated receivers. Forboth cases, equal fractions of time are allocatedto each receiver group.

The network approaches a single-destinationsystem for large values of transmission ranges, whereas the number of one-destination systemsincreases with smaller transmission ranges. Fig-ure 7 depicts the maximum achievable through-put per destination (over a single hop) asfunctions of the quantities 2 r / L and π r 2 / A fortandem and planar networks.

Simulation results indicate the superior per-formance of the Group TDMA algorithm oversimultaneous operation of the transmitter-receiv-er pairs (for the entire range of transmissionradius r ). Lower values of the maximum stablethroughput are achieved in planar networks thanin tandem networks. This is expected because of the increased overlapping effects between thereception ranges in planar topologies.

We also consider systems with hard energyconstraints and evaluate the performanceimprovement by incorporating energy-efficientsolutions into the topology-based receiver activa-tion. We run both receiver activation heuristicsover the layer of the Group TDMA algorithmoperating with the maximum stable throughput.The energy-efficient receiver activation has the

objective of maximizing the system lifetime,

n Figure 7. Comparison of Group TDMA and simultaneous operation of transmitter-receiver pairs for different reception ranges in tandem networks.

2r/L or πr2 / A = ratio of transmission range to network length or area

0.9 10

0.1

0.15 M a x i m u m t h

r o u g h p u t p e r d e s t i n a t i o n ( p a c k e t s / s l o t )

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.80.70.60.50.40.30.20.1

Tandem networks

Planar networks

Simultaneous operationGroup TDMA


http://slidepdf.com/reader/full/21-the-problem-of-medium-access-control-in-wireless-sensor-networks 10/10IEEE Wir l ss Comm nic tions • D c mb r 2004 53

which is defined as the length of time intervalfrom the start of network operation until thefirst time the energy supplies dedicated to any of the activated receiver groups are completelydepleted. The corresponding time allocation fol-lows the solution outlined earlier. On the otherhand, the topology-based receiver activation(without energy-efficient solutions) allocatesequal fractions of time to each receiver group.

Figure 8 depicts the system lifetimes for bothreceiver activation heuristics. Simulation results

verify that the solutions based only on the con-nectivity map are outperformed by the energy-aware receiver activation heuristic for alltransmission ranges. The gap between the twoheuristics increases for intermediate values of r , where there are several potentially interferingmultidestination systems. The performance of both methods becomes identical as r increases,so in the end we have a single activated receiverin each receiver activation group.

CONCLUSIONS

In this article we rediscover the value of scheduled

access in wireless sensor networks from the per-spectives of throughput and energy efficiency. Wepropose a two-layered time-division mechanismbased on receiver activation and Group TDMA asa form of link scheduling and resource allocation with suboptimal but polynomial time solutions.

We develop a topology-based greedy heuristicto determine distinct receiver groups to be activated within disjoint fractions of time, and deter-mine temporal allocations based on cumulativebattery energies left at transmitter groups toextend the node lifetimes. We use the GroupTDMA method to formulate a linear program-ming solution to the problem of throughput-optimal temporal allocation for transmissions to

activated receivers, and derive bounds on themaximum stable throughput for tandem and pla-nar networks. We also evaluate via numericalexamples the performance improvement byenergy-efficient receiver activation and through-put-efficient Group TDMA.

Far from constituting a complete solution tothe MAC issue in s ensor networks, this workidentifies a fruitful approach to handle the coor-dination of transmissions and receptions in sucha network. It is only a first step in the process of examining the operation of sensor networks, butit focuses on the problem at a fundamental level,rather than at a level of immediate deployment.

REFERENCES[1] G. D. Nguyen, J. E. Wieselthier, and A. Ephremides,

“Multiple-Access for Multiple Destinations in Ad-hocNetworks,” Proc. WiOpt ’03, Sophia-Antipolis, France,Mar. 2003.

[2] G. D. Nguyen, J. E. Wieselthier, and A. Ephremides,“Collision-resolution Algorithms for Multiple Destina-tions in Wireless Networks,“ Proc. Conf. Info. Sci. and

Sys., Baltimore, MD, Mar. 2003.[3] E. Arikan “Some Complexity Results about Packet Radio

Networks,“ IEEE Trans. Info. Theory , vol. IT-30, July1984, pp. 681–85.

[4] A. Ephremides and T. Truong, “Scheduling Broadcastsin Multihop Radio Networks,“ IEEE Trans. Commun.,vol. 38, no. 4, Apr. 1990, pp. 456–60.

[5] Y.E. Sagduyu and A. Ephremides, “Energy-Efficient Colli-sion Resolution in Wireless Ad Hoc Networks,“ Proc.IEEE INFOCOM, San Francisco, CA, Apr. 2003.

[6] D. Bertsekas and R. Gallager, Data Networks, 2nd Ed.,Prentice Hall, 1992.

[7] P. Gupta and P. R. Kumar, “The Capacity of WirelessNetworks,“ IEEE Trans. Info. Theory , vol. 46, no. 2,Mar. 2000, pp. 388–404.

[8] W. Szpankowski, “A Multiqueue Problem: Bounds andApproximations,“ Adv. Appl. Probab., vol. 26, 1994,pp. 498–515.

[9] S. Ramanathan and E.L. Lloyd “Scheduling Algorithmsfor Multihop Radio Networks,“ IEEE/ACM Trans. Net.,vol. 1, no. 2, Apr. 1993, pp. 166–77.

[10] I. Holyer, “The NP-Completeness of Edge Colorings, “ SIAM J. Comp., vol. 10, 1981, pp. 718–20.

BIOGRAPHIESANTHONY EPHREMIDES ([email protected]) received his B.S.degree from the National Technical University of Athens(1967), and M.S. (1969) and Ph.D. (1971) degrees fromPrinceton University, all in electrical engineering. He hasbeen at the University of Maryland since 1971, and cur-rently holds a joint appointment as professor in the Electri-cal Engineering Department and the Institute of SystemsResearch (ISR). He is co-founder of the NASA Center forCommercial Development of Space on Hybrid and SatelliteCommunications Networks established in 1991 at Marylandas an offshoot of the ISR. He was a visiting professor in1978 at the National Technical University of Athens,Greece, and in 1979 at the Electical Engineering and Com-puter Science Department of the University of California atBerkeley and INRIA, France. During 1985–1986 he was onleave at Massachusetts Institute of Technology and theSwiss Federal Institute of Technology, Zurich. He has alsobeen director of the Fairchild Scholars and Doctoral FellowsProgram, an academic and research partnership program insatellite communications between Fairchild Industries andthe University of Maryland. He has been President of theInformation Theory Society of the IEEE (1987), and servedon the Board of the IEEE (1989 and 1990). His interests arein the areas of communication theory, communication sys-tems and networks, queuing systems, signal processing,and satellite communications.

YALIN EVREN SAGDUYU ([email protected]) received hisB.S. degree from Bogazici University, Turkey, and M.S.degree from the University of Maryland at College Park in2000 and 2002, respectively, all in electrical engineering.He is currently working toward his Ph.D. degree at the Uni-versity of Maryland, where he has been a graduate researchassistant with ISR since 2000. His research interests includewireless communication, ad hoc and sensor networkdesign, stochastic games, and optimization.

n Figure 8. Comparison of energy-efficient and topology-based receiver activa-

tions for different reception ranges in tandem and planar networks.

2r/L or πr2 / A = ratio of transmission range to network length or area

0.9 10

0.5

1

S y s t e m

l i f e t i m e ( n u

m b e r o f s l o t s )

1.5

2

2.5

3

3.5

0.80.70.60.50.4

Planar networks

Tandem networks

0.30.20.1

x 109

Energy-efficient receiver actionPurely topology-based receiver action

21-The Problem of Medium Access Control in Wireless Sensor Networks

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