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Maximizing Network Topology Lifetime usingMobile Node Rotation

Fatme El-Moukaddem, Eric Torng, Guoliang Xing

Abstract— One of the key challenges facing wireless sensor networks (WSNs) is extending network lifetime due to sensornodes having limited power supplies. Extending WSN lifetime is complicated because nodes often experience differential powerconsumption. For example, nodes closer to the sink in a given routing topology transmit more data and thus consume powermore rapidly than nodes farther from the sink. Inspired by the huddling behavior of emperor penguins where the penguins taketurns on the cold extremities of a penguin “huddle”, we propose mobile node rotation, a new method for using low-cost mobilesensor nodes to address differential power consumption and extend WSN lifetime. Specifically, we propose to rotate the nodesthrough the high power consumption locations. We propose efficient algorithms for single and multiple rounds of rotations. Ourextensive simulations show that mobile node rotation can extend WSN topology lifetime by more than eight times on averagewhich is significantly better than existing alternatives.

Index Terms—Wireless sensor networks, network lifetime, energy optimization, mobile nodes, wireless routing

F

1 INTRODUCTION

In the past decade, wireless sensor networks(WSNs) have been deployed in a wide range of ap-plications such as habitat monitoring [1], environmentmonitoring [2], [3], and surveillance systems [4]. Manyof these applications need to gather and transmit alarge amount of data to a sink for analysis. Moreover,these networks must remain operational for a longperiod of time on limited power supplies (such asbatteries). They are often deployed in remote or in-accessible environments, making it extremely difficultfor any manual maintenance like battery replacement.As a result, one of the main challenges faced by dataintensive WSNs is managing the power consumptionof nodes to maximize the network lifetime.

Recently, the controlled mobility of sensors has beenexploited to improve the energy efficiency of WSNs.For instance, by relocating mobile sensors, the com-munication topology of a network can be dynamicallyconfigured to reduce power consumption. Moreover,mobile sensors can physically carry large chunks ofdata to reduce energy consumption in wireless trans-missions [5]. Such approaches become increasinglyattractive due to the emergence of numerous low-cost mobile sensor prototypes such as Robomote [6],Khepera [7], and FIRA [8].

However, many applications have requirementswhich make existing controlled mobility approachesinfeasible. We identify three key requirements.

1) The location of the nodes and the communica-tion topology are not mutable because of cover-age requirements. For example, in an environ-

• Fatme El-Moukaddem, Eric Torng, and Guoliang Xing are with theDepartment of Computer Science and Engineering, Michigan StateUniversity.

ment monitoring application, the exact place-ment of sensor nodes may not be adjusted with-out compromising the monitoring coverage.

2) Nodes face differential power consumptionwhere some nodes consume significantly morepower than other nodes. For example, nodescloser to the sink in a given routing topologyoften have to transmit more data and thus con-sume more power than nodes farther from thesink in the given topology.

3) All nodes have similar, typically limited, sens-ing/communication/mobility capabilities. Thisrules out approaches that require a few nodeswith extra capabilities and the ability to performcomplex motion planning.

Although individual requirements such as differentialpower consumption may be satisfied using existingcontrolled mobility approaches such as data mules[9], [10], [11] or mobile sinks [5], [12], [13], [14], [15],no existing controlled mobility approach can be usedwhen all three requirements must be satisfied.

To simultaneously address the three requirements,we propose a new approach that we call mobile noderotation which is inspired by the huddling and rotationbehavior of emperor penguins that help them breedin the fierce arctic winter. Penguins on the outside ofthe huddle face temperatures as low as −45 ◦C andstrong winds while those on the inside of the huddleenjoy warm ambient temperatures as high as 37 ◦Cand significant wind protection. Emperor penguinsrotate positions to share the burden of being on theoutside [16]. In mobile node rotation, we propose torotate the physical positions of mobile sensors to sharethe burden of any high power consumption location.Our node rotation approach leverages the low dutycycles of WSNs to minimize the interruptions to the

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network. In many WSN applications, nodes sleep (i.e.,switch off wireless interfaces) for as much as 87% ofthe time [17]. We perform rotations during schedulednode sleep times.

Fig. 1: The nodes at bottleneck locations s1, s2 ands3 can rotate with nodes at locations s8, s7 and s5,respectively after a period of time to balance theenergy consumption between high consumption lo-cations and low consumption locations.

We illustrate the main idea behind node rotationusing the network shown in Figure 1. The three nodesinitially at locations s1, s2, and s3 consume a lot moreenergy than the nodes at other locations; the nodes ats1 and s2 consume lots of energy because they havelots of descendants whose data must be transmittedtowards the sink and the node at s3 consumes lotsof energy because it is far from its parent node ats1. Using mobile node rotation, multiple nodes rotatethrough high energy consumption locations. For ex-ample, the node at s1 rotates with the node at s8, thenode at s2 rotates with the node at s7, and the node ats3 rotates with the node at s5. As a result, the amountof energy required at a high consumption locationis shared by two nodes instead of only one and thelifetime of the network is significantly increased.

We observe that mobile node rotation does not re-quire powerful nodes capable of performing complexmotion planning calculations or developing mobility-aware routing topologies since all movements are toknown positions and the topology does not changeexcept during the transient periods of node rotation.Likewise, we can model mobile sensor platforms withlimited mobility by imposing mobility constraints ofreal mobile sensor platforms. For example, we canmodel NIMS sensors [18] that are only capable ofmoving along fixed cables by restricting such sensorsto rotate with other sensors on the same set of cables.

The main challenges faced in the design of an effec-tive node rotation schedule include deciding when tomove nodes, which nodes should move, and whereeach node should move to. We want to minimize thenumber of interruptions to the network operation;however, regular interruptions are needed or elsenodes at high consumption positions will quickly runout of energy. Ideally we would like to synchronizenode rotations, but rotating each node individuallymay lead to better overall performance. We consider

a variety of approaches including focusing on nodesat high consumption rate positions and focusing onnodes that experience specific energy level drops.

We make the following contributions in this paper.(1) We propose a new controlled mobility approachto extending wireless sensor network lifetime, mobilenode rotation. (2) We present a new problem, Max-lifetime Node Rotation (MaxLife), that models maximiz-ing the lifetime of a WSN using rounds of mobilenode rotation. MaxLife can incorporate any energyconsumption model for both wireless communicationand node movement. (3) We efficiently solve the oneround MaxLife problem by reducing it to the assign-ment problem. (4) We propose a number of algorithmsfor the general multiple round MaxLife problem.We also propose efficient distributed implementationsthat do not require significant synchronization oroverhead. (5) We prove upper bounds on the life-time improvement ratio of mobile node rotation ap-proaches. (6) Our simulations based on energy modelsobtained from existing mobile sensor platforms showthat mobile node rotation can significantly increasethe network lifetime. With just one rotation round,the network lifetime almost doubles. With multiplerounds, it increases by factors exceeding eight.

2 RELATED WORK

Several approaches have been proposed for extend-ing the lifetime of a network. In general, they can beclassified into four main groups: duty cycling, datareduction, topology control and controlled mobility.

In duty cycling approaches [19], [20], [21], nodesalternate turning their power on and off and save theirenergy when they are turned off. In data reductionapproaches [22], [23], [24], nodes reduce the amountof data that they generate and/or transmit and con-sequently reduce the energy consumed by the radiocomponent. In topology control approaches, the mainidea is to reduce the energy consumption by reducingthe initial topology of the network. In [25], [26], [27],the authors reduce the transmission power to the min-imum levels needed while keeping connectivity. In[28], [29], [30], cluster based topologies are proposed.In contrast with our approach where nodes performa physical rotation, cluster based approaches performrole rotation where nodes switch between cluster headand cluster member.

The last scheme for extending the lifetime isthrough controlled mobility. These approaches in-clude mobile base stations, data mules, and mobile re-lays. In mobile station approaches, a powerful mobilebase station node moves around the WSN and collectsdata from other nodes through one or multiple hopstransmissions [5], [12], [13], [14], [15]. The goal is tomitigate differential power consumption by rotatingthe set of nodes that are close to the base station.These approaches usually incur high latency because

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of the low speed of the mobile stations. In data muleapproaches [9], [10], [11], one or multiple mobilenodes, called mules, visit all the nodes in the networkto collect the data and then physically carry the datato the sink. Similar to base station approaches, theseapproaches incur high latencies since nodes have towait for a mule to pass by to transmit the data. In mo-bile relay approaches [31], [32], [33], [34], the mobilenodes in the network relocate to different positions toreduce the communication distances between nodes.

Our approach shows several advantages over ex-isting approaches. First, our simulations in Section8 show that our approach significantly outperformsprevious approaches in increasing network lifetime.Second, it can be applied in conjunction with dutycycling approaches to take advantage of the downtime of nodes without significant additional inter-ruption to the network. Third, compared to cluster-ing approaches, our approach introduces significantlyfewer changes to the network. That is, the number ofnode rotations is significantly smaller than the num-ber of cluster rotations, each of which requires newroute computations. Admittedly, it may take longerto perform a node rotation than to compute a clusterrotation, but if this can be performed in node downtime, then our approach introduces fewer disruptionswith no penalty. Finally, none of the mobile relayapproaches can be applied in settings where the exactpositions of the WSN nodes must not change.

3 PROBLEM DEFINITION

3.1 Network, Energy, and Duty Cycle ModelsWe consider WSNs consisting of many wireless mo-

bile sensor nodes and a single static sink. We mainlyexamine applications in which the three requirements(immutable positions, differential power consumptionand limited node capability) apply. The sensor nodesgather data from their surroundings and transmit thedata through one or multiple hops to the sink forminga directed routing tree. We divide time into intervals.In each interval, we assume each sensor node gathersa fixed amount of data and that each node transmitsthe data it gathered as well as the data it receivedfrom its children to its parent along the routing tree.We assume that data gathered from different nodescannot be combined to reduce the transmission loadof nodes in the routing tree; however, our approachcan be easily adjusted to handle cases where data iscombined as long as we can compute the resultingtransmission load. Our goal is to maximize the life-time of the WSN, i.e. the number of time intervalsuntil the first node dies. We use this definition oflifetime due to the immutable position requirementthat nodes are needed in every location or else thesystem is compromised.

Our approach does not depend on any particularenergy consumption models. Since the topology of

the network is fixed, the data flow is known at eachlocation and hence the energy consumption due tocommunication can be computed for every position.Similarly, the energy consumption due to mobility canbe computed based on the distance between everypair of locations. Regardless of the model used, oncethese consumption rates are computed, they are usedas input parameters to our algorithms. Note that ifmobility energy consumption is very high relative totransmission energy consumption, the optimal solu-tion may require no node rotation.

Mobile base station and data mule approachesmitigate differential power consumption by havingpowerful mobile nodes move around the WSN. Wepropose a new solution, mobile node rotation, thatuses multiple low-cost mobile nodes which rotate orswap positions and roles allowing nodes to sharethe burden of high consumption locations and thebenefits of low consumption locations.

Our approach takes advantage of the fact that manywireless sensor networks have a low duty cycle due tothe limited energy availability. Despite the low dutycycle, several power-efficient MAC protocols havebeen proposed to maintain satisfactory communica-tion performance. In [17], nodes sleep for 87% of thetime and still increase the network throughput. In[35], nodes sleep between 60% and 70% of the timewithout compromising the throughput. Our approachbuilds on these duty cycle scheduling approaches:node rotation is performed when nodes are in a sleepmode so the network operation is not interrupted.We show in Section 8 that node rotation requires arelatively short time and can be achieved withoutadditional interruption to the system even for dutycycles as high as 90%.

3.2 Formal Definition

We define two variants of the problem which differin the restrictions imposed on node movement. Wefirst consider a special case, One-Round Max-Lifetime(1-MaxLife), where nodes are allowed to rotate theirpositions once and all relocations occur at the sametime. The reason behind this restriction is to reducethe overhead of the rotation and the duration dur-ing which the network’s activity may be interrupted.Then we consider the more general variant, Multiple-Rounds Max-Lifetime (m-MaxLife), which extendsthe 1-MaxLife problem by allowing nodes to rotatemultiple times in synchronized rounds. This variantincreases the number of times the network is inter-rupted but also increases the total lifetime as eachround of rotation extends the lifetime of the network.

We formally define the problems as follows. Wenote that both problems accept the same input in-stance but differ in the output schedule.Input Instance:• S = (s1, . . . , sn), a list of sensor nodes

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• u, the network sink, and pu, its position• P = (p1, . . . , pn), a list of positions such that nodesi starts at position pi

• E = (e1, . . . , en), a list of initial energies for nodesin S

• T , a directed routing tree represented as a setof non-zero values tij for every arc (pi, pj) inthe tree corresponding to the amount of energyconsumed when transmitting one data unit frompi to pj

• K, a set of values kij for every pair of positionspi and pj , corresponding to the amount of energyconsumed by a node when it moves between piand pj

• Λ = (λ1, . . . , λn), the amount of data gathered ateach position per time interval

Definition 1: Max-Lifetime Node Rotation (1-MaxLife).Output Instance: A permutation π of the positionsof nodes in S, and two durations r1 and r2 suchthat nodes transmit data from their original positionsfor r1 time intervals, relocate to their new positionaccording to π, then generate and transmit data forr2 time intervals such that the total duration r1 + r2is maximized and no node’s energy goes to 0 beforer1 + r2.

Definition 2: Unlimited Rounds Max-Lifetime NodeRotation (m-MaxLife).Output Instance: A sequence Π = {(rj , πj), j =1, . . . , z} of round length and permutation pairs suchthat nodes operate from their existing positions fora duration rj , then relocate to their new positionsaccording to the permutation πj for 1 ≤ j ≤ z suchthat no node’s energy goes to zero before

∑zj=1 rj and

the total active duration∑zj=1 rj is maximized.

Rotating the nodes over different positions in thenetwork to mitigate differential power consumptionplays a significant role in maximizing the networklifetime. However, finding a practical and efficientrotation schedule has a number of challenges. Movingcan be difficult to perform in rough terrains andis sometimes unreliable. Therefore, it is desirable tolimit movement to relatively close positions so thenetwork activity is not obstructed. Moreover, there arethree main decisions nodes need to make: whetherto move or not, which position to move to and howlong to stay at each position if they decided to move.In the following sections, we propose a number ofalgorithms for node rotations based on several crite-ria such as increase in lifetime, reduction in energyconsumption rate and battery level.

4 ONE ROUND MAX-LIFETIME NODE ROTA-TION ALGORITHM

In this section, we first present our centralizednode rotation algorithm RotateOnce to the 1-MaxLifeproblem. All of our algorithms including RotateOnce

begin by having nodes compute the load lj at eachposition pj in P which is the total energy consumed intransmitting all the data gathered in one time intervalfrom the subtree rooted at pj to its parent. Moreformally, lj = tjq

∑i∈T (pj)

λi where T (pj) is the subtree

rooted at pj and pq is the position of the parent of pjin the tree.

RotateOnce transforms the input instance into aninstance of the assignment problem [36], a combina-torial optimization problem in which we are given npeople and n tasks and an efficiency/cost cij for eachperson performing each task. The goal is to assigneach task to a person in order to optimize some utilitymeasure such as maximizing the bottleneck efficiencyor minimizing the total cost of all tasks.

We first assume we know the optimal length of thefirst time interval r1 for which nodes remain at theirinitial positions. To compute the optimal matchingM of sensor nodes to positions, we transform theinstance I into an instance of the maximum bottleneckassignment problem I ′ for the given r1 as follows.Each mobile node si corresponds to a person and eachlocation pj corresponds to a task. The efficiency cij ofperson si performing task pj corresponds to the totallifetime of si after transmitting for a period r1 fromits original position pi, then moving to pj where ittransmits until its energy is depleted; that is, cij =

r1+e−lir1−kij

lj. The optimal solution for the maximum

bottleneck assignment instance I ′ corresponds to anoptimal matching M for the given r1.

We now need to compute the best duration r1. Weobserve that as r1 increases, r2 decreases since there isless energy for the second round. So we can express r2as a function L2(r1) that decreases as r1 increases. Wethen define the total network lifetime as a functionL(r1) = r1 + L2(r1). We use golden ratio search tofind the best r1. When L(r1) is unimodal, goldenratio search yields an optimal r1 that maximizes L(r1).To start the golden ratio search, we first computeL(I) = minnj=1 ej/lj which is an upper bound onr1. Our algorithm RotateOnce runs in O(logL(I)n2.5)time because golden ratio search has O(logL(I)) timecomplexity and each assignment problem has O(n2.5)time complexity.

Algorithm RotateOnce computes the rotation con-figuration using only consumption rates; it ignores therouting topology except when calculating the load foreach node. It is not clear if regularities in networktopologies such as grids can simplify the computationof node rotations because the most important factoris the traffic loads imposed on each node by therouting topology. Moreover, even when the networkcontains some regularities in traffic loads, after thefirst round of rotations, these regularities disappearsince nodes with similar consumption rates may nowhave different energy levels. It is an interesting openquestion if there are any combinations of routing

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topologies and network topologies that yield simpleoptimal node rotation patterns, particularly when weconsider multiple rounds of rotation.

5 MULTIPLE ROUNDS MAX-LIFETIMEPROBLEM

We present several centralized algorithms for them-MaxLife problem. We first present BL, an extendedversion of RotateOnce that runs in multiple rounds.We use BL for comparison purposes only, as it hasa large overhead and results in unnecessary move-ments. Then we present Swap-Rate, a more efficientalgorithm that maximizes the network lifetime whilereducing the number of rounds. Then we presentSwap-Level, an algorithm with the sole objectiveof maximizing the network lifetime. This algorithmtrades uninterrupted operation for a longer lifetime.Finally, we propose the algorithm Swap-LevelMerge,which blends Swap-Rate and Swap-Level to providea balance between the number of rounds and thelifetime improvement ratio.

5.1 Repeated Optimal Matchings (BL)We propose an extension of RotateOnce, Baseline

(BL), to solve the the m-MaxLife problem. It runsin multiple rounds such that in each round, nodesare matched to positions using an optimal matchingfor that round. First, a node is selected and acts acontroller. The controller gains full knowledge of thenetwork by collecting energy and location informationfrom all the other nodes. Our approach then proceedsin rounds. The duration of each round is fixed toa given duration r. The controller then computesmatchings of nodes to positions for rounds 2 and onusing a fixed duration r as each round length until thefirst node dies. We note that the controller has enoughinformation to estimate each node’s available energyfor each future round. The controller then broadcaststhe number of rounds and all the matchings to theother nodes. Finally, the nodes carry out the roundssynchronizing as needed to initiate each rotation. Wepresent BL solely for benchmarking purposes.

5.2 Observations for Improved AlgorithmsOne of the key flaws of BL is that it generates too

many unnecessary node movements. Specifically, ineach round, many high energy nodes needlessly swappositions. We present several improved algorithms,all of which use different strategies for eliminatingunnecessary movements.

One technique used by all of our improved algo-rithms is to only perform swaps of two nodes. Thisallows us to develop practical distributed implemen-tations of all of our algorithms.

A second technique used by all of our improvedalgorithms is to only perform a swap of two nodes si

and sj if the swap improves the minimum lifetime ofthe two nodes by a sufficient amount. More formally,suppose we are considering a swap of nodes si andsj at time t. Let L1(si, sj , t) be the minimum lifetimeof si and sj if neither node moves after time t, andlet L2(si, sj , t) be the minimum lifetime of si and sjif they swap positions at time t and then never moveagain. We define a swap of nodes si and sj at time t tobe acceptable if and only if L2(si, sj , t)/L1(si, sj , t) ≥f for a given threshold f .

We now present our improved algorithms. We firstgive ideal but impractical centralized algorithms. Inthe next section, we give more practical distributedimplementations of each of these algorithms.

5.3 Consumption Rate Algorithm (Swap-Rate)

Our first algorithm, Swap-Rate, only swaps nodesthat are located at high consumption rate positions.Other nodes only participate in swaps if they can helpcritical nodes located in high consumption positions.The main idea is illustrated in Figure 2.

More formally, the algorithm works as follows. Asin BL, a node is selected to be the controller. Thecontroller collects energy and location informationfrom all the other nodes once and computes an initiallist of critical nodes Lcr such that si ∈ Lcr if λi > lcrwhere lcr is a given critical consumption rate thresh-old. Then, it proceeds in rounds of fixed length r.At the end of each round, the controller computesa swap partner for each node in Lcr as follows.The nodes in Lcr are considered in descending orderof their current consumption rate. For the currentcritical node c, the controller considers all availablenon-critical nodes s such that a swap of c and s isacceptable. Of these acceptable swap partners, thecontroller selects the one that maximizes the resultingminimum lifetime of nodes s and c. Node s is thenmarked as unavailable for later critical nodes. Afterall the swaps are performed, a new round starts andthe process is repeated until the first node dies.

5.4 Energy Level Algorithm (Swap-Level)

Our second algorithm Swap-Level requires lesscomputation from the controller and also less syn-chronization among nodes as nodes relocate indepen-dently of other nodes. Unlike Swap-Rate, the maincriteria for a swap is the energy level of a node. Aswap is triggered by a node when that node’s energylevel goes below a certain threshold. The controllerstarts by collecting energy and location informationfrom all nodes. For each node si, the controller com-putes si’s swap time t; that is, when si’s energy leveldrops by a given factor ρ. When si reaches its swaptime, the controller finds an acceptable candidate sj toswap with si that maximizes L2(si, sj , t), the expectedlifetime of si and sj assuming no more swaps. Nodes

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(a) Initial configuration (b) After the first round (c) After the second round

Fig. 2: Initially, nodes a, b and c are at high consumption positions (2a). After running for a period r, theyeach find a suitable descendant and swap positions with it (2b). The selected descendants e, j and k are nowat the high consumption positions. After the second round, these nodes find suitable descendants to swapwith; in this example, nodes i, q and m are selected (2c).

(a) Initial configuration (b) After first swap (c) After second swap (d) After third swap

Fig. 3: In this example, node a is the first node whose energy level drops by the factor ρ. This triggers a swapwith descendant e (3b). Next, node b’s energy drops by the factor ρ, and it swaps with descendant j (3c). Thenext node whose energy level drops by the factor ρ is g, and it swaps with i (3d). Unlike algorithm Swap-Rate,any node whose energy level drops by factor ρ gets the chance to swap with a descendant.

si and sj then swap with only node si resetting its crit-ical energy threshold. If no acceptable swap partner sjis available, then si resets its critical energy thresholdand continues to operate at its current position. Whena node’s energy level falls below a given thresholdelow, that node remains at its current position forthe rest of its lifetime. Similar to Swap-Rate, whentwo nodes swap positions, other nodes sleep untilthe swap is complete. We give an example algorithmexecution in Figure 3.

In this solution, the criterion triggering a swapis a node’s energy level. Since most nodes in thenetwork will eventually lose enough energy to triggera swap, almost all nodes will attempt to initiate aswap during the network lifetime. Of course, somenodes will do this more frequently and some nodesmay attempt to swap but are unable to find suitableswap candidates. In contrast, the algorithm Swap-Rateperforms swaps solely based on the consumption rateat node locations; that is, a constant set of locationstriggers swaps throughout the lifetime of the network.In summary, Swap-Level generates swaps at morepositions and thus produces a more thorough rotationof nodes during the network lifetime.

5.5 Merged Swaps Algorithm (Swap-LevelMerge)In our Swap-Level solution, some traffic patterns

include a sequence of node rotations within a shortperiod of time which may cause forced sleep modes,especially if the duty cycle of the network is high.

To mitigate this potential issue, we propose a looselysynchronized variant, Swap-LevelMerge, that mergesclose in time node rotations together. This algorithmprovides a balanced solution between algorithmsSwap-Rate and Swap-Level. Specifically, when thecontroller computes the swap times of nodes in thenetwork, it merges them as follows. Let node s1 havethe first swap time t1. Any nodes that have swaptimes within a period θ of t1 have their swap timesmoved to t1. The controller attempts to find accept-able swap candidates for each of these nodes. Whent1 is reached, nodes with acceptable swap partnersperform their swaps while all the other nodes sleep.Nodes that tried to swap but could not find an accept-able swap partner reset their critical energy thresholdsand sleep until the swapping nodes complete theirswaps. This process continues until the first node’sdeath or a node’s energy level falls below elow atwhich point it no longer triggers swaps.

6 PRACTICAL IMPLEMENTATIONS

In many cases, a centralized solution with a sin-gle controller performing so much work may notbe practical; also, unexpected power consumptionmay invalidate the calculations performed. We pro-pose the following distributed multiple rotation roundalgorithms, which are based on Swap-Rate, Swap-Level and Swap-LevelMerge but require only localinformation. We refer to these distributed implemen-tations by adding the suffice -d to the centralized

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algorithm name, i.e. Swap-Rate-d, Swap-Level-d andSwap-LevelMerge-d. We also propose an uninter-rupted mode of operation in which nodes that are notswitching locations continue their normal operation.

6.1 Distributed Swap-Rate (Swap-Rate-d)As with Swap-Rate, all rounds will have duration

r. In each round, each node s executes the followingalgorithm. It computes its energy consumption ratebased on the amount of data that it needs to transmitand the distance separating it from its parent inthe tree. If s has a consumption rate greater thanthe threshold lcr, it picks one of its descendants toswitch with to improve its own lifetime. Node s onlyconsiders descendants that (1) have not yet committedto switch with another node and (2) are at most hhops away for a given hop distance parameter h.Each of these candidates c sends its local information(its position, its consumption rate and current energylevel) to s. Node s eliminates any candidates thatare not acceptable swap partners. Of the remainingcandidates, node s chooses the candidate c∗ that yieldsthe largest increase in expected lifetime of s and cassuming no more swaps are performed. At this point,c∗ commits to s and is not available to help otherancestors when probed. If there are no acceptablecandidates, s will not swap in this round. All selectednodes then move to their new positions. All the nodesthen run for duration r and start a new round in asimilar manner. We show the algorithm executed byeach node in Figure 1 in the appendix.

This distributed implementation only requires loosesynchronization among nodes. Each node needs toknow its consumption rate, its parent in the routingtree and the threshold lcr. Initially, each node sendsits consumption rate to its parent, which then relaysit along with its own consumption rate to its parent.When the root node receives the set of consumptionrates in the network, it computes the critical energylevel lcr and broadcasts it to the rest of the nodes.We compute the lcr as the weighted average of thelowest and the highest energy consumption rate in thenetwork. In subsequent rounds, critical nodes sendmessages to their descendants and parent only at thebeginning of each round, stating that a new round isabout to start. The overhead of this synchronization ismuch smaller than regular time sync schemes wherenodes have to ping each other all the time to keeptheir clocks in sync. This algorithm results in a smallnumber of rounds since the swap is triggered for allcritical nodes at the same time.

6.2 Distributed Swap-Level and Swap-LevelMergeAlgorithms

The distributed implementation of Swap-Level-ddoes not require any synchronization between nodes.The main idea is that each node computes its own

energy drop level. When a node si reaches that energylevel, it probes its descendants that are at most h hopsaway to find candidates that can perform acceptableswaps and swaps with the candidate c that maximizesthe expected lifetime. Node si then sets its next criticalenergy level to ei(1−ρ) and runs from its new positionuntil it reaches this critical level. We note that immedi-ately after the swap, node c’s energy may go below itscritical level. In this case, it immediately starts a swapprocess of it own from its new position. This processis repeated until energy levels drops below elow or thefirst node in the network dies. In Swap-LevelMerge-d,nodes perform the same algorithm as in Swap-Level-d with one additional step. When a node is ready toswitch, it broadcasts this information to the rest of thenetwork so that other nodes that will need to swapsoon can start the swapping process early.

Swap-Level results in better lifetimes than Swap-Rate. Thus, in most applications, Swap-Level is pre-ferred. However, Swap-Level generates more asyn-chronous swaps than Swap-Rate rounds. If the dutycycle is too high such that the relatively large numberof asynchronous swaps cannot be performed duringnode sleep times, Swap-Rate may be a better choice.

6.3 Uninterrupted Operation

In general, performing node rotations is not ex-pected to have any effect on the network operationas it takes place during the sleep time of the nodes.However, this may not be possible for some appli-cations. For example, there may be networks wherethe duty cycle is too high so that node rotationscannot all be performed during node sleep times.We now discuss an uninterrupted implementation ofour algorithms to accommodate this scenario. We firstobserve that Swap-Rate-d requires no modificationsince all nodes rotate at the same time. For Swap-Level-d and Swap-LevelMerge-d, if one part of thenetwork is interrupted due to one or more swaps,the rest of the network, mainly where paths from thenodes to the sink remain connected, does not need tointerrupt its activity and hence continues its normaloperation.

In this solution, when a node si is swapping witha node sj , only nodes si, sj and their immediatechildren are affected by the swap; the rest of the nodesin the network continue their normal operation ofsensing and generating data, receiving data from theirchildren and relaying the data to their parent withoutinterruption. The operation of immediate children ofsi and sj is partially interrupted. They keep on gener-ating and receiving data from their children. However,instead of immediately transmitting this data, theyhold on to it until the new parent arrives and is readyto receive the data. This may create the possibilityof buffer overflow if the child node suspending itstransmission has a high data generation rate. In this

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case, we use existing congestion control techniques[37] to prevent or mitigate loss of data.

7 UPPER BOUNDS ON LIFETIME IMPROVE-MENT RATIO

Our algorithms are primarily based on finding suit-able pairs of nodes and having each pair of nodesswap positions. In this section, we first give conditionsfor which a swap is both feasible and beneficial.We then prove some upper bounds on the lifetimeimprovement ratio. We present the proofs for all thetheorems in the appendix.

Theorem 1: Consider two nodes s1 and s2 with ini-tial energies e1 and e2, respectively, at two locationswith consumption rates λ1 and λ2, respectively, suchthat λ1 > λ2, and the energy consumed by movingfrom one location to the other is k. It is beneficial toswap s1 and s2 if and only if

(a)λ1e1 − λ2e2λ1 − λ2

< k <e1λ1

(λ1 − λ2) or

(b) k <λ1e2 − λ2e1λ1 − λ2

and

{k ≤ λ1e2−λ2e1

2λ1if e1

λ1≤ e2

λ2

k ≤ λ2e1−λ1e22λ2

otherwise

We note that if the two consumption rates are thesame, it is never beneficial to swap.

We now derive some upper bounds on lifetimeimprovement ratios for any node rotation algorithms.We first consider the 1-MaxLife problem. We thenconsider the general MaxLife problem. We use thefollowing notation in our analysis. For any noderotation algorithm A and input instance I , let L(A, I)denote the lifetime achieved using algorithm A onI , L(I) the lifetime without node rotation, andRA(I) = minI L(A, I)/L(I) the lifetime improve-ment ratio (LIR) of A on I . Finally, let EV (I) =maxni=1 ei/minnj=1 ej be the initial energy variance ofI .

Theorem 2: For any one round node rotation algo-rithm A and any input instance I RA(I) ≤ 1 +EV (I).

This leads to two corollaries, one for the special casewhere all nodes have the same initial energy and onefor multiple round rotation algorithms.

Corollary 1: For any one round node rotation algo-rithm A and any input instance I with EV (I) = 1,RA(I) ≤ 2.

Corollary 2: For any j round node rotation algo-rithm A and any input instance I , RA(I) ≤ 1 + (j −1)EV (I).

We note that although our one round solutionRotateOnce is optimal for 1-MaxLife only when L(r1)is unimodular, our simulations (Section 8) show thatRotateOnce’s LIR is usually very close to the upperbound of 2 for input instances I with EV (I) = 1.Moreover, for input instances I where EV (I) > 1,RotateOnce’s LIR is often better than 2.

We now derive upper bounds on the RA(I) forinputs I corresponding to balanced trees of degreed+ 1 using a multiple rotation round algorithm.

Theorem 3: For any node rotation algorithm A andany input I where T represents a balanced tree ofdegree d + 1 and tij = t for all non-zero tij , h is thelowest level of the tree where the root is at level 0,and for 1 ≤ i ≤ n, ei = e and λi = 1, then

RA(I) ≤ (dh+1 − 1)2

(h(d− 1) + d− 2)dh+1 + 1

Table 1 displays some of the upper bounds fordifferent values of d and h. The L starts at a factorof 1.8 for a tree with 3 nodes and rapidly increaseswith both the degree and the level. These bounds givesome insight into the potential of node rotation, butthe realizable improvement will be diminished as thecost of mobility energy consumption increases relativeto transmission energy consumption.

TABLE 1: Upper Bounds on Lifetime ImprovementRatios in Balanced Trees

d / h 1 2 3 4 52 1.80 2.88 4.59 7.45 12.363 2.29 4.97 11.27 26.77 66.084 2.78 7.74 23.08 72.99 240.825 3.27 11.17 41.53 164.37 679.26

8 SIMULATION RESULTS

In this section, we evaluate the performance ofour algorithms through simulations. For comparisonpurposes, we also evaluate the performance of thebaseline algorithm BL. We generated 100 networkseach consisting of 100 nodes placed uniformly atrandom in a 150m by 150m area with the sink nodechosen uniformly at random. We set the maximumcommunication distance to 35m, which was shown in[38] to lead to a high packet reception ratio for TelosBmotes in outdoor environments; our algorithms workwith a general communication model in which thecommunication ranges of nodes can be different. Foreach network, we constructed the routing tree fromthe sources to the sink using greedy geographic rout-ing in which each node forwards its data to theneighbor that is closest to the sink. We set the tij andthe kij values based on the energy models in [34], [38]because they are based on realistic platforms; We notethat any other network topology and energy modelfor communication or mobility could could be usedwithout any algorithmic change. We set each node’sei to the same value typically ranging from half full tofull. We refer to our distributed algorithms by addingthe suffix -d to the centralized algorithm’s name.

We assess the performance of algorithms using sev-eral criteria. The main criteria is lifetime improvementratio. We also assess the number of rounds requiredand the number of nodes that move per round.

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Fig. 4: Average lifetime improvement ratios of Swap-Rate and Swap-Rate-d (with h = 2) as a function ofr plotted as a fraction of L(I)

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Fig. 5: Average lifetime improvement ratios of Swap-Rate and Swap-Rate-d with h = 1, 2, 4 as a functionof r plotted as a fraction of L(I)

8.1 Threshold SelectionFor all of our distributed algorithms, we want a

value for the local improvement factor f that is nottoo low to allow unnecessary movement and not toohigh to deny beneficial swaps. Our simulations showthat setting f between 1 and 1.5 for Swap-Rate and be-tween 1 and 2 for Swap-Level satisfies these require-ments. In the rest of our simulations, we set f to 1.25as it results in slightly better performance. Similarly,we analyze the effect of the energy reduction factor ρon the improvement ratio. We observe that for valuesof ρ between 10% and 50%, the improvement ratiosattained are comparable and for values of ρ greaterthan 50%, the performance decreases sharply. We set ρto 33% as it provides a balance between switching toooften and too infrequently and results in the highestlifetime improvement. Choosing a larger value of ρleads to too much energy drain with 2/3 of the energyremaining. Likewise, the number of swaps initiated byany node will be no more than log3/2 emax/elow whereemax is the largest initial energy for any node.

We compute the critical consumption rate thresh-old λcr as the weighted average of the highest andthe lowest consumption rates in the network: lcr =ωλhi + (1 − ω)λlo. Again, our simulations show thatour results are not very sensitive to the value of ω.Choosing ω between 1% and 10% ensures that enoughnodes are considered critical without generating un-necessary swaps. The highest improvement rate wasreached when ω = 6%. In the next set of simulations,we describe our choices for parameters r and h.

8.2 One Round Max-LifetimeWe first evaluate the performance of RotateOnce for

the 1-MaxLife problem in trees. For all 100 inputs,1.91 ≤ RRotateOnce(I) ≤ 1.99, and the average value ofRRotateOnce(I) = 1.95. We observe that the results arevery close to the theoretical upper bound of 2 from

Corollary 1. When we varied the starting energy levelof the nodes between half full and completely full,the average lifetime improvement ratio of RotateOnceincreased to 2.3. We also observe that most of thenodes change their positions; on average 86 nodesrelocate to new positions and 14 nodes remain at theiroriginal location. This is not too costly since only asingle rotation is performed.

8.3 Consumption Rate Based RotationsWe now evaluate the performance of algorithms

Swap-Rate and Swap-Rate-d.

8.3.1 Round DurationWe first study the effect of varying r on the perfor-

mance of Swap-Rate and Swap-Rate-d with h = 2 forthe m-MaxLife problem using our BL algorithm as abaseline. Figure 4 shows the average lifetime improve-ment ratios for all three algorithms as we increase rdenoted as a fraction of the static lifetime L(I). Wesee that both Swap-Rate and Swap-Rate-d outperformBL for all values of r but especially smaller r. Forr ≤ 7L(I)/10, RSwap−Rate(I) ≥ 2.5 + RBL(I). Forr ≤ 3L(I)/5, RSwap−Rate−d(I) ≥ 2.5 + RBL(I). Atr = L(I)/5, the difference in lifetime improvementratio reaches 6.4 and 5.1 for Swap-Rate and Swap-Rate-d respectively. One notable feature of Swap-Rate and Swap-Rate-d’s performance is that the LIRdecreases slowly for 3L(I)/10 ≤ r ≤ 7L(I)/10; Swap-Rate takes on a maximum value of 10.1 and Swap-Rate-d a maximum value of 8.7. Both are reached forL(I)/5 ≤ r ≤ 3L(I)/10. When r is too large, the LIRof both algorithms drops because nodes stay at highconsumption positions for too long.

For most of the remaining simulations, we set r =L(I)/2. This value is chosen as a tradeoff betweenmaximizing the LIR and minimizing the number ofdisruptions to the network.

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8.3.2 Lifetime Improvement Ratio Increase perRound

We now assess how much effect each round hason the LIR. Specifically, if we stop node rotationsafter round n, what will the lifetime be? All threealgorithms, BL, Swap-Rate and Swap-Rate-d, result ina LIR that is essentially linear in the number of roundswith each round increasing the lifetime improvementratio by between 40 and 50%. This analysis shows thatthese algorithms are effective in increasing the LIR butthat Swap-Rate and Swap-Rate-d are more effectivethan BL in minimizing distance moved and maintain-ing a reserve of energy rich nodes for later rounds.This is why Swap-Rate and Swap-Rate-d outperformBL which moves 93% of the nodes in each round.

8.3.3 Effect of Hop Distance Parameter on Swap-Rate-d

We now analyze the effect of the hop distanceparameter h on the performance of Swap-Rate-d.We plot the complementary cumulative distributionfunction (CCDF) of the LIR for Swap-Rate-d with hset to 1, 2, and 4 in Figure 5. The CCDF gives usthe probability that the lifetime improvement ratioexceeds a given threshold. For comparison, we alsoplot the CCDF of Swap-Rate and BL. From this data,we see that setting h = 2 is sufficient to achieveexcellent performance as the CCDF for h = 2 is almostidentical to that of h = 4. In both cases, 95% of thetopologies have lifetime improvement ratios of at least465% and more than 50% of topologies have lifetimeimprovement ratios over 750%. With h = 1, Swap-Rate-d is much less effective; this is due to the numberof nodes taking turns transmitting from the highconsumption position being too low. We also notethat we varied the critical rate parameter between 5%and 15% but it did not result in significant differencesin the lifetime of the networks. This shows that theperformance of the algorithm is not very sensitive tosmall changes in that parameter.

8.3.4 Swap-Rate vs Swap-Rate-d

We now compare the performances of Swap-Rateand Swap-Rate-d. We observe that when h ≥ 2, Swap-Rate-d remains close to Swap-Rate despite the avail-ability of only local information in the case of Swap-Rate-d. When h = 2, Swap-Rate-d achieves an averagelifetime ratio RSwap−Rate−d ≥ 0.9 + RSwap−Rate, andwhen h = 4, the difference becomes smaller withRSwap−Rate−d ≥ 0.5+RSwap−Rate. In general, limitingthe candidates set to the descendants of a node isenough to achieve good performance as these nodeshave smaller traffic loads while being close to thecritical node. So aside from a few distant nodes withreally low energy consumption, most relevant nodesare considered for a switch in the distributed setting.

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Fig. 6: Average lifetime improvement ratios of Swap-Level and Swap-Level-d with h = 1, 2, 4 as a functionof r plotted as a fraction of L(I)

8.4 Energy Level Based RotationsWe now assess the performance of algorithms

Swap-Level and Swap-Level-d.

8.4.1 Improvement RatioWe first consider the lifetime improvement ratio.

Figure 6 shows the complementary cumulative distri-bution function (CCDF) of the lifetime improvementratios for Swap-Level and Swap-Level-d with differ-ent values of h. We observe that Swap-Level resultsin a significant increase in the lifetime starting at496% and exceeding 2000% with an average of 1210%.Moreover, more than two thirds of the topologiestested showed an improvement ratio greater than1000%. In the distributed implementation, the lifetimeimprovement ratio is still substantially higher than thelifetime improvement ratio for Swap-Rate-d with anaverage improvement of 998% and exceeding 1850%in some cases. These solutions perform particularlywell because each node behaves in its best interest.A node reaching a critical energy level does not haveto stay at its high consumption position for longerthan it needs to (i.e. to finish the round); instead, itfinds a swapping candidate and lowers its energyconsumption rate as soon as its energy level dropsto the predefined target.

8.4.2 Effect of Hop Distance Parameter on Swap-Level-d

We now study the effect of the hop distance pa-rameter on the performance of Swap-Level-d. Similarto Swap-Rate-d, it is enough to set h = 2 to getessentially similar performance as when the full de-scendants subtree is considered. When h = 1, the setof nodes rotating to fill a high consumption positionis small so the lifetime improvement ratio suffers.However, even with h = 1, the average lifetime im-provement ratio is still a respectable 591%. Similar toour analysis for Swap-Rate-d, limiting the candidateset of swap partners to the descendant nodes does

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Fig. 7: Average lifetime improvement ratios of Swap-Rate-d with h = 2 and nodes speed of 0.1, 0.5, 1 and10 m/s.

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Fig. 8: Average lifetime improvement ratios for all al-gorithms in both centralized and distributed settings.

not exclude most of the good candidates. In general,for topologies that are not too sparse, setting h = 2provides a large enough set of nodes to take turnsrotating and filling the high consumption positions.

8.4.3 Interrupted vs. Continuous OperationWe now examine the performance of Swap-Level-d

under two modes of operation: (i) interrupted trans-missions during node relocations and (ii) continuoustransmissions at the unaffected nodes. For the contin-uous mode, we additionally studied the effect of thespeed of the node on the performance. We varied thespeed between 0.1 m/s and 10 m/s. Figure 7 showsthe CCDF of the average lifetime improvement ratiofor both modes, considering a number of differentspeeds for the continuous operation mode. We firstnote that the speed of the node does not have asignificant effect on the lifetime improvement ratioin the continuous operation mode. For the lowestspeed of 0.1 m/s, the average improvement ratiois 950%. When the speed increases to 0.5m/s, theLIR increases to 956%, and for any speed of 1 m/sor above, the LIR becomes 958%. This is becausenodes spend very little time moving even given veryslow speeds; most of their time and energy is spenton transmissions. Second, we note that the lifetimeimprovement ratios are essentially identical for bothmodes with the interrupted mode outperforming thecontinuous operation mode by less than 2%. Thisimplies that we can design for the interrupted modebut deploy in the continuous transmission mode withlittle change in expected performance.

8.5 Overall ComparisonIn this section, we compare all algorithms including

Swap-LevelMerge and Swap-LevelMerge-d using anumber of performance metrics such as the averagelifetime improvement ratio, the total number of relo-cations and interruptions to the network operation,and the number of relocations for individual nodes.

8.5.1 Lifetime Improvement RatioWe first compare our algorithms with respect to

their average lifetime improvement ratio. Figure 8shows the LIR of all our node rotation algorithms.For the centralized implementations, we observethat Swap-Level has the highest average improve-ment ratio, 1208%. The Swap-LevelMerge algorithmis slightly below with an average improvement ra-tio of 1154%. Finally, the Swap-Rate algorithm hasa smaller improvement ratio of 893%. We observesimilar behavior in the distributed implementations;Swap-Level-d results in the highest improvement ra-tio (981%), Swap-LevelMerge-d comes slightly behindwith an LIR of 935% and lastly Swap-Rate-d with anLIR of 802%. In both cases, we see that the averageimprovement ratios of our algorithms increase as thetotal number of rounds and relocations in the networkincrease. When the application tolerates a high num-ber of interruptions, Swap-Level and Swap-Level-dachieve the best performance. When this overhead isnot acceptable, it can be reduced by combining swapsusing Swap-LevelMerge and Swap-LevelMerge-d al-gorithms while achieving almost the same lifetime im-provement ratio. Finally, if many fewer interruptionsare required, Swap-Rate and Swap-Rate-d are the bestchoice.

8.5.2 Node MovementWe now compare our algorithms based on how

much node movement each one requires. Table 2summarizes the average number of rounds required,the average number of nodes relocating per round,and the total number of relocating nodes for all ofour algorithms.

As we observed earlier, BL does not perform wellbecause it makes too many unnecessary moves. Ineach round, it moves almost every node. As a result,it has the shortest lifetime improvement ratio whichleads to the smallest number of rounds comparedwith all of our other algorithms.

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TABLE 2: Average number of rounds and relocationsfor all node rotation algorithms

Rounds Total Re-locations

Relocations/ Round

BL 7.7 726.1 94.1Swap-Rate 13.1 189.9 15.9Swap-Rate-d 12.5 137.1 12.6Swap-Level 200.8 401.6 2.0Swap-Level-d 124.7 249.4 2.0Swap-LevelMerge 68.0 434.9 6.7Swap-LevelMerge-d 48.6 263.4 5.9

For our other more effective algorithms, Swap-Rateand Swap-Rate-d require the fewest number of roundsand hence the fewest interruptions to the networkactivity. On average, they both need between 12 and13 rounds, and only 12 to 16 nodes move in eachround. This is in contrast to Swap-Level and Swap-Level-d where nodes do not rotate at the same time, soevery swapping pair of nodes causes an interruptionto the system and can be viewed as one round consist-ing of a single swap. The centralized implementationSwap-Level requires an average of 200 rounds i.e.200 interruptions to the network’s activity which ismuch higher than Swap-Rate. The distributed settingSwap-Level-d requires an average of 124.7 relocationswhich, although lower than Swap-Level, remainssignificantly higher than Swap-Rate-d. As expected,Swap-LevelMerge and Swap-LevelMerge-d, in whichnodes synchronize their swaps in groups of 3, reducethe number of rounds from Swap-Level and Swap-Level-d by roughly a factor of 3 to an average of 68rounds and 48.6 rounds.

We now show that all of our algorithms do notrequire any one node to move too many times. Inparticular, we measure the maximum number of relo-cations required by any node and the average numberof relocations made by all nodes. Figure 9 plots theaverage value for both of these measures for all ofour algorithms. For all of our algorithms, the maxi-

mum number of relocations done by a single node isrelatively small, varying on average between 4 and 8during the network lifetime. Furthermore, for our ef-fective algorithms, the average number of relocationsper node is much smaller; generally 40%-60% of themaximum number of relocations. We do observe thatnodes move slightly more for each centralized algo-rithm compared to its distributed counterpart. Thereare two explanations for this. First, the centralizedalgorithms have a slightly longer lifetime. Second, thecentralized algorithms consider all the positions in thenetwork as target positions for a given node whereasthe distributed algorithms only consider nodes thatare within a certain number of hops of the given node.

We next examine the largest total distance movedby a node during its lifetime. Figure 10 shows thesedistances with respect to the average distances movedover all the nodes in the network. The largest totaldistances moved are on average 804m, 271m, 362mand 391m for algorithms BL, Swap-Rate, Swap-Leveland Swap-LevelMerge, respectively. These distancescorrespond to 2 to 3 times the average distance movedby all nodes in the network. We note that for the mo-bility energy consumption model that we adopt, withthe exception of BL, this corresponds to consumingat most 20% to 30% of the available battery energyon mobility and 70% to 80% on communications, forthe nodes that moves the most. On average, nodesconsume as little as 6% to 16% of their energy onmobility. We also observe that the difference in thetotal movement for individual nodes is insignificantbetween the centralized and distributed implementa-tions with nodes in the distributed implementationsmoving slightly less.

Finally, we note that for all our algorithms, the totalmoving time for all the nodes is very small with re-spect to the lifetime of the network. With low speeds,such as 0.5-1 m/s, the movement time corresponds to15%-30% of the network’s lifetime. When the nodes

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Fig. 11: CCDF of the lifetime improvement ratio ofEnergy Aware Leach and Multihop Leach with respectto the lifetime improvement ratio of Swap-Level-d

move with a speed at least 5 m/s, they move for atmost 3% of the network lifetime. This is assuming thatnodes are either operating (receiving/transmitting) ormoving. When nodes operate with sleep/wake upcycles, most movement may be scheduled during thesleep time so the network activity is not interrupted.Even with low moving speeds where movement maytake up to 30% percent of the time, nodes can performall their movement during the networks sleep timewith duty cycles as high as 70%.

8.6 Comparison with Rotation-based TopologyControl

In this section, we compare our node rotation ap-proach to existing approaches. For a fair comparison,we consider only approaches that do not changethe positions where nodes are placed. This rules outexisting mobile relay approaches and leaves us withnon-mobility approaches that rotate the roles of dif-ferent nodes by periodically changing the topology ofthe network but not modifying any node positions.Specifically, we compare our distributed algorithmswith two improved variations of the LEACH pro-tocol: (1) Energy Aware LEACH [28] which takesinto account the energy available at the nodes whenforming the clusters and (2) Multihop LEACH [39],a variation that uses multihop transmissions betweencluster heads. These two protocols are representativeof a class of rotation-based topology control schemeswhere the roles of nodes rotate based on their energyconsumption. Despite the lack of mobility, the designof role rotation in these schemes is close to ourapproach in spirit. The comparison thus demonstratesthe key advantages of exploiting mobility in topologycontrol. Both LEACH approaches assume that data iscompressed before being transmitted while our algo-rithms do not. To compare all approaches in a similarsetting, we run them all without data compression.

We now compare the performance of our algo-rithms to both LEACH variations. Figure 11 shows the

complementary cumulative distribution function ofthe lifetime improvement ratio for all five algorithms:Swap-Rate-d, Swap-Level-d, Swap-LevelMerge-d, en-ergy aware LEACH and multihop LEACH. First,we note that all our algorithms outperform bothLEACH variations for every topology: Swap-Level-d and Swap-LevelMerge-d attain lifetimes between2.7 and 6.3 times better than Energy Aware LEACHand between 1.4 and 3.2 times better than multihopLEACH, whereas Swap-Rate-d attains lifetimes be-tween 2.7 and 6.3 times better than Energy AwareLEACH and between 2 and 5.7 times better thanmultihop LEACH. Additionally, we observe that allour algorithms need many fewer rounds than bothLEACH variations. On average, as shown in table 2,Swap-Level-d needs around 125 rounds of rotations,Swap-Rate-d 15 rounds and Swap-LevelMerge-d 48rounds whereas energy aware LEACH needs 1880rounds and multihop LEACH needs 2100 rounds. Wealso note that the round duration used for the LEACHapproaches was 20% of the round duration r used bySwap-Rate-d as using the same r resulted in muchlower lifetime improvements ratios for LEACH.

9 CONCLUSION

In this paper, we present a new node rotationparadigm for maximizing the lifetime of mobileWSNs. Our approach exploits the mobility of nodesto mitigate differential power consumption by havingnodes take turns in high power consumption posi-tions without modifying the existing topology. Ournode rotation approach is very different than otherschemes such as data mules in that all nodes expendrelatively little energy on movement and move onlya few times during the network lifetime. Our sim-ulations show that our node rotation approach canimprove average lifetime by more than a factor ofeight and that our algorithms outperform existingnon-mobility approaches for mitigating differentialpower consumption to prolong network lifetime.

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Fatme El-Moukaddem received the B.S. and M.S. degrees inComputer Science from the American University of Beirut in 2000and 2002, respectively, and the Ph.D. degree from Michigan StateUniversity in 2012. Her research interests include algorithms andwireless sensor networks.

Eric Torng received the Ph.D. degree in computer science fromStanford University in 1994. He is currently an Associate Professorand Graduate Director with the Department of Computer Scienceand Engineering at Michigan State University. His research interestsinclude algorithms, scheduling, and networking. Dr. Torng received aNational Science Foundation CAREER Award in 1997.

Guoliang Xing is an Associate Professor in the Department ofComputer Science and Engineering at Michigan State University. Hereceived the B.S. degree in Electrical Engineering from Xi’an JiaoTong University, China, in 1998, and the M.S. and D.Sc. degrees inComputer Science and Engineering from Washington University inSt. Louis, in 2003 and 2006, respectively. He is an Associate Editorof ACM Transactions on Sensor Networks and IEEE Transactionson Wireless Communications. Dr. Xing is an NSF CAREER Awardrecipient in 2010. He received the Best Paper Awards at the 18thIEEE International Conference on Network Protocols (ICNP) in 2010and the 12th ACM/IEEE Conference on Information Processing inSensor Networks (IPSN) SPOTS track in 2012. His research inter-ests include Cyber-Physical Systems for sustainability, smartphonesystems, and wireless networking.