Mobile Relay Configuration in(1)

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Mobile Relay Configuration inData-Intensive Wireless Sensor Networks

Fatme El-Moukaddem, Eric Torng, and Guoliang Xing, Member, IEEE

AbstractWireless Sensor Networks (WSNs) are increasingly used in data-intensive applications such as microclimate monitoring,

precision agriculture, and audio/video surveillance. A key challenge faced by data-intensive WSNs is to transmit all the data generated

within an applications lifetime to thebase station despite thefact that sensor nodes have limited power supplies. We propose using low-

cost disposable mobile relays to reduce the energy consumption of data-intensive WSNs. Our approach differs from previous work in

two main aspects. First, it does not require complex motion planning of mobile nodes, so it can be implemented on a number of low-cost

mobile sensor platforms. Second, we integrate the energy consumption due to both mobility and wireless transmissions into a holistic

optimization framework. Our framework consists of three main algorithms. The first algorithm computes an optimal routing tree

assuming no nodes can move. The second algorithm improves the topology of the routing tree by greedily adding new nodes exploiting

mobility of the newly added nodes. The third algorithm improves the routing tree by relocating its nodes without changing its topology.

This iterative algorithm converges on the optimal position for each node given the constraint that the routing tree topology does not

change. We present efficient distributed implementations for each algorithm that require only limited, localized synchronization.

Because we do not necessarily compute an optimal topology, our final routing tree is not necessarily optimal. However, our simulation

results show that our algorithms significantly outperform the best existing solutions.

Index TermsWireless sensor networks, energy optimization, mobile nodes, wireless routing

1 INTRODUCTION

WSNShave been deployed in a variety ofdata-intensiveapplications including microclimate and habitatmonitoring [1], precision agriculture, and audio/videosurveillance [2]. A moderate-size WSN can gather up to1 Gb/year from a biological habitat [3]. Due to the limited

storage capacity of sensor nodes, most data must betransmitted to the base station for archiving and analysis.However, sensor nodes must operate on limited powersupplies such as batteries or small solar panels. Therefore, akey challenge faced by data-intensive WSNs is to minimizethe energy consumption of sensor nodes so that all the datagenerated within the lifetime of the application can betransmitted to the base station.

Several different approaches have been proposed tosignificantly reduce the energy cost of WSNs by using themobility of nodes. A robotic unit may move around thenetwork and collect data from static nodes through one-hopor multihop transmissions [4], [5], [6], [7], [8]. The mobile

node may serve as the base station or a data mule thattransports data between static nodes and the base station[9], [10], [11]. Mobile nodes may also be used as relays [12]that forward data from source nodes to the base station.Several movement strategies for mobile relays have beenstudied in [12], [13].

Although the effectiveness of mobility in energyconservation is demonstrated by previous studies, the

following key issues have not been collectively addressed.First, the movement cost of mobile nodes is not accountedfor in the total network energy consumption. Instead,mobile nodes are often assumed to have replenishableenergy supplies [7] which is not always feasible due to the

constraints of the physical environment. Second, complexmotion planning of mobile nodes is often assumed inexisting solutions which introduces significant designcomplexity and manufacturing costs. In [7], [8], [14], [15],mobile nodes need to repeatedly compute optimal motionpaths and change their location, their orientation and/orspeed of movement. Such capabilities are usually notsupported by existing low-cost mobile sensor platforms.For instance, Robomote [16] nodes are designed using 8-bitCPUs and small batteries that only last for about25 minutes in full motion.

In this paper, we use low-cost disposable mobile relaysto reduce the total energy consumption of data-intensive

WSNs. Different from mobile base station or data mules,mobile relays do not transport data; instead, they move todifferent locations and then remain stationary to forwarddata along the paths from the sources to the base station.Thus, the communication delays can be significantlyreduced compared with using mobile sinks or data mules.Moreover, each mobile node performs a single relocationunlike other approaches which require repeated relocations.

Our approach is motivated by the current state of mobilesensor platform technology. On the one hand, numerouslow-cost mobile sensor prototypes such as Robomote [16],Khepera [17], and FIRA [18] are now available. Their

manufacturing cost is comparable to that of typical staticsensor platforms. As a result, they can be massivelydeployed in a network and used in a disposable manner.Our approach takes advantage of this capability by

IEEE TRANSACTIONS ON MOBILE COMPUTING, VOL. 12, NO. 2, FEBRUARY 2013 261

. The authors are with the Department of Computer Science, Michigan StateUniversity, 3115 Engineering Building, East Lansing, MI 48824-1226.E-mail: {elmoukad, torng, glxing}@cse.msu.edu.

Manuscript received 27 Dec. 2010; revised 5 Nov. 2011; accepted 23 Nov.2011; published online 13 Dec. 2011.For information on obtaining reprints of this article, please send e-mail to:[email protected], and reference IEEECS Log Number TMC-2010-12-0589.Digital Object Identifier no. 10.1109/TMC.2011.266.

1536-1233/13/$31.00 2013 IEEE Published by the IEEE CS, CASS, ComSoc, IES, & SPS


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assuming that we have a large number of mobile relaynodes. On the other hand, due to low manufacturing cost,existing mobile sensor platforms are typically powered bybatteries and only capable of limited mobility. Consistentwith this constraint, our approach only requires one-shotrelocation to designated positions after deployment. Com-pared with our approach, existing mobility approachestypically assume a small number of powerful mobile nodes,which does not exploit the availability of many low-costmobile nodes.

We make the following contributions in this paper:

1. We formulate the problem ofOptimal Mobile RelayConfiguration(OMRC) in data-intensive WSNs. Ourobjective of energy conservation isholisticin that thetotal energy consumed by both mobility of relaysand wireless transmissions is minimized, which is incontrast to existing mobility approaches that onlyminimize the transmission energy consumption. Thetradeoff in energy consumption between mobility

and transmission is exploited by configuring thepositions of mobile relays.

2. We study the effect of the initial configuration on thefinal result. We compare different initial tree build-ing strategies and propose an optimal tree construc-tion strategy for static nodes with no mobility.

3. We develop two algorithms that iteratively refinethe configuration of mobile relays. The first im-proves the tree topology by adding new nodes. It isnot guaranteed to find the optimal topology. Thesecond improves the routing tree by relocatingnodes without changing the tree topology. It con-verges to the optimal node positions for the giventopology. Our algorithms have efficient distributedimplementations that require only limited, localizedsynchronization.

4. We conduct extensive simulations based on realisticenergy models obtained from existing mobile andstatic sensor platforms. Our results show that ouralgorithms can reduce energy consumption by up to45 percent compared to the best existing solutions.

The rest of the paper is organized as follows: Section 2reviews related work. In Section 3, we formally define theproblem of optimal mobile relay configuration. In Section 4,we present our centralized optimization framework, an

optimal solution for the base case with a single mobile relay,an optimal algorithm for constructing a routing tree givenno mobility of nodes, and a greedy algorithm for improvingthe routing tree by adding new nodes. In Section 5, wepresent an optimal relocation algorithm given a fixedrouting topology. In Section 6, we discuss the efficiencyand optimality of our framework. In Section 7, we proposeefficient distributed implementations for our algorithms.Section 8 describes our simulation results and Section 9concludes this paper.

2 RELATEDWORK

We review three different approaches, mobile base stations,data mules, and mobile relays, that use mobility to reduceenergy consumption in wireless sensor networks. A mobile

base station moves around the network and collects datafrom the nodes. In some work, all nodes are alwaysperforming multiple hop transmissions to the base station,and the goal is to rotate which nodes are close to the basestation in order to balance the transmission load [4], [5], [6].In other work, nodes only transmit to the base station whenit is close to them (or a neighbor). The goal is to compute a

mobility path to collect data from visited nodes before thosenodes suffer buffer overflows [7], [8], [14], [15]. In [8], [19],[20], several rendezvous-based data collection algorithmsare proposed, where the mobile base station only visits aselected set of nodes referred to as rendezvous pointswithin a deadline and the rendezvous points buffer the datafrom sources. These approaches incur high latencies due tothe low to moderate speed, e.g., 0.1-1 m/s [14], [16], ofmobile base stations.

Data mules are similar to the second form of mobile basestations [9], [10], [11]. They pick up data from the sensorsand transport it to the sink. In [21], the data mule visits all

the sources to collect data, transports data over somedistance, and then transmits it to the static base stationthrough the network. The goal is to find a movement paththat minimizes both communication and mobility energyconsumption. Similar to mobile base stations, data mulesintroduce large delays since sensors have to wait for a muleto pass by before starting their transmission.

In the third approach, the network consists of mobilerelay nodes along with static base station and data sources.Relay nodes do not transport data; instead, they move todifferent locations to decrease the transmission costs. Weuse the mobile relay approach in this work. Goldenberg

et al. [13] showed that an iterative mobility algorithm whereeach relay node moves to the midpoint of its neighborsconverges on the optimal solution for a single routing path.However, they do not account for the cost of moving therelay nodes. In [22], mobile nodes decide to move onlywhen moving is beneficial, but the only position consideredis the midpoint of neighbors.

Unlike mobile base stations and data mules, our OMRCproblem considers the energy consumption of both mobilityand transmission. Our approach also relocates each mobilerelay only once immediately after deployment. Unlikeprevious mobile relay schemes [13] and [22], we consider

all possible locations as possible target locations for amobile node instead of just the midpoint of its neighbors.

Mobility has been extensively studied in sensor networkand robotics applications which consider only mobilitycosts but not communication costs. For example, in [23], theauthors propose approximation algorithms to minimizemaximum and total movement of the mobile nodes suchthat the network becomes connected. In [24], the authorspropose an optimal algorithm to bridge the gap betweentwo static nodes by moving nearby mobile nodes along theline connecting the static points while also minimizing thetotal/maximum distance moved. In [25], [26], the authors

propose algorithms to find motion paths for robots toexplore the area and perform a certain task while takinginto consideration the energy available at each robot. Theseproblems ignore communication costs which add an

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increased complexity to OMRC, and consequently theirresults are not applicable.

Our OMRC problem is somewhat similar to a number ofgraph theory problems such as the Steiner tree problem[27], [28], [29] and the facility location problem [30], [31].However, because the OMRC cost function is fundamen-tally different from the cost function for these otherproblems, existing solutions to these problems cannot beapplied directly and do not provide good solutions toOMRC. For example, there is no obvious way to include

mobility costs in the Steiner tree problem.

3 PROBLEMDEFINITION

3.1 Energy Consumption Models

Nodes consume energy during communication, computa-tion, and movement, but communication and mobilityenergy consumption are the major cause of batterydrainage. Radios consume considerable energy even in anidle listening state, but the idle listening time of radios canbe significantly reduced by a number of sleep schedulingprotocols [32]. In this work, we focus on reducing the total

energy consumption due to transmissions and mobility.Such a holistic objective of energy conservation is motivatedby the fact that mobile relays act the same as staticforwarding nodes after movement.

For mobility, we consider wheeled sensor nodes withdifferential drives such as Khepera [17], Robomote [16], andFIRA [18]. This type of node usually has two wheels, eachcontrolled by independent engines. We adopt the distanceproportional energy consumption model which is appro-priate for this kind of node [33]. The energy EMdconsumed by moving a distance dis modeled as:

EMd kd:

The value of the parameter k depends on the speed of thenode. In general, there is an optimal speed at which k islowest. In [33], the authors discuss in detail the variation ofthe energy consumption with respect to the speed of themote. When the node is running at optimal speed, k 2 [33].

To model the energy consumed through transmissions,we analyze the empirical results obtained by two radiosCC2420 [34] and CC1000 [35] that are widely used onexisting sensor network platforms. For CC2420, the authorsof [36] studied the transmission power level needed fortransmitting packets reliably (e.g., over 95 percent packetreception ratio) over different distances. Let ETd be the

energy consumed to transmit reliably over distance d. It canbe modeled as

ETd ma bd2;

wherem is the number of bits transmitted and a and b areconstants depending on the environment. We now discussthe instantiation of the above model for both CC2420 andCC1000 radio platforms. In an outdoor environment, forreceived signal strength of80 dbm(which corresponds toa packet reception ratio higher than 95 percent), we obtaina 0:6 107 J=bit and b 4 1010 Jm2=bit from the

measurements on CC2420 in [36]. This model is consistentwith the theoretical analysis discussed in [37]. We alsoconsider the energy needed by CC1000 to output the samelevels. We get lower consumption parameters: a 0:3 107 J=bit and b 2 1010 Jm2=bit. We will see inSection 5 that we maintain this high packet reception ratiothroughout our algorithm. We note that although themobility parameter k is roughly 1010 times larger thanthe transmission parameter b, the relays move only oncewhereas large amounts of data are transmitted. For largeenough data chunk sizes, the savings in energy transmis-sion costs compensates for the energy expended to movethe nodes resulting in a decrease in total energy consumed.

3.2 An Illustrative Example

We now describe the main idea of our approach using asimple example. Suppose we have three nodes s1; s2; s3located at positionsx1; x2; x3, respectively (Fig. 1), such thats2 is a mobile relay node. The objective is to minimize thetotal energy consumption due to both movement andtransmissions. Data storage node s1 needs to transmit adata chunk to sinks3through relay nodes2. One solution isto haves1transmit the data fromx1to nodes2at positionx2and nodes2relays it to sinks3at positionx3; that is, nodes2does not move. Another solution, which takes advantage of

s2s mobility, is to move s2 to the midpoint of the segmentx1x3, which is suggested in [13]. This will reduce thetransmission energy by reducing the distances separatingthe nodes. However, moving relay node s2 also consumesenergy. We assume the following parameters for the energymodels:k 2; a 0:6 107; b 4 1010.

In this example, for a given data chunk mi, the optimalsolution is to moves2to x

i2

(a position that we can computeprecisely). This will minimize the total energy consumptiondue to both transmission and mobility. For small messages,s2moves very little if at all. As the size of the data increases,relay nodes2moves closer to the midpoint. In this example,

it is beneficial to move when the message size exceeds4 MB. We illustrate in Table 1 the energy savings achievedusing our optimal approach and the other two approachesfor the relevant range of data sizes. For large enough data

EL-MOU KADDEM ET AL.: MOBILE RELAY CONFIGURATION IN DATA-INTENSIVE WIRELESS SENSOR NETWORKS 263

Fig. 1. Reduction in energy consumption due to mobile relay. As thedata chunk size increases, the optimal position converges to themidpoint of s1s3.

TABLE 1Energy Consumption Comparison


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chunks (13 MB), one relay node can reduce total energyconsumption by 10 percent compared to the other twoapproaches. As the data chunk size increases further, theenergy savings decrease, and the optimal position con-verges to the midpoint when the data size exceeds 43 MB. Ingeneral, the reduction in energy consumption is higherwhen there are multiple mobile relay nodes.

The above example illustrates two interesting results.The optimal position of a mobile relay is not the midpointbetween the source and sink when both mobility andtransmissions costs are taken into consideration. This is incontrast to the conclusion of several previous studies [12],[13] which only account for transmission costs. Second, theoptimal position of a mobile relay depends on not only thenetwork topology (e.g., the initial positions of nodes) butalso the amount of data to be transmitted. Moreover, asthe data chunk size increases, the optimal positionconverges to the midpoint of s1 and s3. These results areparticularly important for minimizing the energy cost ofdata-intensive WSNs as the traffic load of such networks

varies significantly with the sampling rates of nodes andnetwork density.

3.3 Problem Formulation

In our definitions, we assume that all movements arecompleted before any transmissions begin. We alsoassume there are no obstacles that affect mobility ortransmissions. In this case, as we show in Section 4.2, thedistance moved by a mobile relay is no more than thedistance between its starting position and its correspond-ing position in the evenly spaced configuration whichoften leads to a short delay in mobile relay relocation.Furthermore, we assume that all mobile nodes know their

locations either by GPS units mounted on them or alocalization service in the network. We focus on the casewhere all nodes are in a 2D plane


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nodes. Our tree optimization algorithm improves therouting tree by relocating its nodes without changing its

topology. This iterative algorithm converges on the optimalposition for each node given the constraint that the routingtree topology is fixed. Our node insertion and treeoptimization algorithms use the LocalPos algorithm wepropose in Fig. 3 that optimally solves the simplest case (seeSection 4.2) of the mobile relay configuration problemwhere there is a single source, a single sink, and a singlerelay node. Our approach is not guaranteed to produce anoptimal configuration because we do not necessarily findthe optimal topology, but our simulation results show thatit performs well.

4.2 Base Case

Before presenting our algorithm for OMRC, we revisit theexample of Section 3.2 as it represents the simplest possiblebase case of the problem in which the network consists ofone sourcesi1, one mobile relay nodesi, and one sink si1.

In this section, we calculate the optimal position for therelay node. We use the following notation. In


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The optimal position is then xi 12 xi1 xi1 Yi. If sineeds to move right, then pi is to the left of the midpoint ofnodes si1 an d si1. The optimal position is thenxi

1

2xi1 xi1 Yi. The correspondingyiinboth casesis

xi1 xi1 2pi

yi1 yi1 2qixipi qi:

We note that in some cases it might not be beneficial tomove, so the optimal position for the relay node is its originalposition. The algorithm to compute the optimal position ofa relay node given its neighbors is shown in Fig. 3.

4.3 Static Tree Construction

Different applications may apply different constraints onthe routing tree. When only optimizing energy consump-tion, a shortest path strategy (as discussed below) yields anoptimal routing tree given no mobility of nodes. However,in some applications, we do not have the freedom ofselecting the routes. Instead, they are predeterminedaccording to some other factors (such as delay, capacity,etc.). In other less stringent cases, we may be able to updatethe given routes provided we keep the main structure ofthe tree. Depending on the route constraints dictated by theapplication, we start our solution at different phases of thealgorithm. In the unrestricted case, we start at the first stepof constructing the tree. When the given tree must beloosely preserved, we start with the relay insertion step.Finally, with fixed routes, we apply directly our treeoptimization algorithm. Our simulations (Section 8) showthat our approach outperforms existing approaches for allthese cases.

We construct the tree for our starting configuration using

a shortest path strategy. We first define a weight functionwspecific to our communication energy model. For each pairof nodessi and sj in the network, we define the weight ofedge sisj as: wsi; sj a bkoi ojk

2 where oi and oj arethe original positions of nodes si and sj and a and b are theenergy parameters discussed in Section 3.1. We observe thatusing this weight function, the optimal tree in a staticenvironment coincides with the shortest path tree rooted atthe sink. So we apply Dijkstra s shortest path algorithmstarting at the sink to all the source nodes to obtain ourinitial topology.

4.4 Node InsertionWe improve the routing tree by greedily adding nodes tothe routing tree exploiting the mobility of the insertednodes. For each nodesoutthat is not in the tree and each treeedge sisj, we compute the reduction (or increase) in thetotal cost along with the optimal position ofsout ifsout joinsthe tree such that data is routed fromsi tosout to sj insteadof directly from si to sj using the LocalPos algorithmdescribed in Fig. 3. We repeatedly insert the outside nodewith the highest reduction value modifying the topology toinclude the selected node at its optimal position, thoughthe node will not actually move until the completion of the

tree optimization phase. After each node insertion occurs,we compute the reduction in total cost and optimal positionfor each remaining outside node for the two newly addededges (and remove this information for the edge that no

longer exists in the tree). At the end of this step, thetopology of the routing tree is fixed and its mobile nodescan start the tree optimization phase to relocate to theiroptimal positions.

5 TREEOPTIMIZATION

In this section, we consider the subproblem of finding the

optimal positions of relay nodes for a routing tree given thatthe topology is fixed. We assume the topology is a directedtree in which the leaves are sources and the root is the sink.We also assume that separate messages cannot be com-pressed or merged; that is, if two distinct messages oflengthsm1andm2use the same link (si; sj) on the path froma source to a sink, the total number of bits that must traverselink (si; sj) ism1m2.

First, we extend the base case solution of Section 4.2 tohandle multiple flows passing through a mobile relay node.Then, we propose an iterative algorithm that uses thesolution for this base case to compute the new positions of

the relay nodes in the routing tree. We also show that thisalgorithm converges to the optimal solution for the giventree given the topology is fixed.

5.1 Extended Base Case

Before we describe our optimal algorithm for this problem,we extend the solution to the base case presented inSection 4.2 to the more general multiple flow traffic pattern.The network now consists of multiple sources, one relaynode, and one sink such that data are transmitted from eachsource to the relay node and then to the sink. We modifyour solution as follows: Let si be the mobile relay node,Ssi the set of source nodes transmitting to si and sd

i

thesink collecting nodes fromsi. The cost incurred by si in thisconfigurationU is

ciU kkui oik ami bmikud uik2;

wheremi is the total amount of data that si transmits to sdi .

Similar to the single source base case, we define

CiU ciU Xsl2Ssi

aml bkui ulk2ml:

This corresponds to the transmission cost of all nodesslthat

send messages to node si plus the total cost of node si. In

this case, this also corresponds to the total cost of

configuration U which we wish to minimize. First, we

computemiasPsl2Ssi

ml. We then follow the same routine

of computing the points at which both partial derivativesCiUxi

and CiUyi become zero. We obtain the following

positions:

xi piBx

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB2x B

2y

q k

AffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB2x B

2y

q

yi qiBy

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB2x B2y

q k

A

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB2x B

2y

q;



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where

A miXsl2Ssi

ml;

Bx mixdXsl2Ssi

mlxl Api;

By miydXsl2Ssi

mlyl Aqi:

We note that these values correspond to two candidatepoints moving in each direction (left/right). The optimalposition is the valid value yielding the minimum cost.

5.2 Optimization Algorithm

We propose a simple iterative approach to compute theoptimal positionuifor each nodesi. We define the following

notations. Letu

j

i x

j

i ; y

j

ibe the position of nodesiafter thejth iteration of our algorithm for j 0 andUj uj1; . . . ; ujn

the computed configuration of nodes s1 through sn after jiterations. We define u0i oi. Note that the mobile relaynodes do not move until the final positions are computed.

Our algorithm starts by an odd/even labeling stepfollowed by a weighting step. To obtain consistent labelsfor nodes, we start the labeling process from the root usinga breadth first traversal of the tree. The root gets labeled aseven. Each of its children gets labeled as odd. Eachsubsequent child is then given the opposite label of itsparent. We definemi, the weight of a nodesi, to be the sumof message lengths over all paths passing through si. This

computation starts from the sources or leaves of our routingtree. Initially, we know mi Mi for each source leaf nodesi. For each intermediate node si, we compute its weight asthe sum of the weights of its children.

Once each node gets a weight and a label, we start ouriterative scheme. In odd iterationsj, the algorithm computesa position uji for each odd-labeled node si that minimizesCiUj assuming that u

ji1 u

j1i1 and u

ji1 u

j1i1 ; that is,

nodesis even numbered neighboring nodes remain in placein configuration Uj. In even-numbered iterations, thecontroller does the same for even-labeled nodes. Thealgorithm behaves this way because the optimization ofujirequires a fixed location for the child nodes and the parent

ofsi. By alternating between optimizing for odd and evenlabeled nodes, the algorithm guarantees that the node si isalways making progress toward the optimal positionui. Ouriterative algorithm is shown in Fig. 4.

Fig. 5 shows an example of an optimal configuration fora simple tree with one source node. Nodes start atconfiguration U0. In the first iteration, odd nodes (s3 ands5) moved to their new positions (u

13; u1

5) computed based on

the current location of their (even) neighbors (u02; u0

4; u0

6). In

the second iteration, only even nodes (s2 ands4) moved totheir new positions (u2

2; u2

4) computed based on the current

location of their (odd) neighbors (u11; u1

3; u1

5). Sinces3 ands5

did not move, their position at the end of this iterationremains the same, so u1

3 u2

3andu1

5 u2

5. In this example,

nodes did two more sets of iterations, and finally convergedto the optimal solution shown by configurationU6.

Even though configurations change with every iteration,nodes only move after the final positions have beencomputed. So each node follows a straight line to its finaldestination. As the data size increases, nodes in the optimalconfiguration get more evenly spaced. In fact, in any givenconfiguration, the maximum distance traveled by a node isbounded by the distance between its starting position andits final position in the evenly spaced configuration.

The above example shows another property of ouralgorithm. When a node si moves and its neighbors (si1and si1) remain in place, it moves in the direction of themidpoint ofsi1si1. This results in a reduction in the lengthof one of the transmission links. The other may increase inlength but will never exceed the new length of the first link.This remains valid for multiple children case. So in anyconfigurationUi1, the length of the largest link is at mostthe length of the largest link in the previous configurationUi. So if we start with a route along good quality links, thisquality will be preserved in the optimal configuration (andthroughout intermediate configurations).

6 EFFICIENCY AND OPTIMALITY

We first consider efficiency. Our initial tree constructionalgorithm is essentially a single source shortest pathalgorithm. Using Dijkstra s algorithm, the time complexityis On2 where n is the number of nodes. Our secondalgorithm needs to compute the reduction in cost for eachpair of node and tree edge, so the time complexity is On2.Our tree optimization algorithm runs until the change inposition for each node falls below a predefined threshold.The value of this threshold represents a tradeoff betweenprecision and cost. As the threshold decreases, more

iterations are needed for convergence. Upon termination,no node can move by itself to improve the overall cost(within the threshold bound). We have not completed a rateof convergence analysis for this algorithm. However, in our


Fig. 4. Centralized algorithm to compute the optimal positions in a giventree.

Fig. 5. Convergence of iterative approach to the optimal solution. Eachline shows the configuration obtained after two iterations. The optimalconfiguration is reached after six iterations.


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simulations, we reach our error threshold within 8 to 10iterations. Since each iteration involves only half the nodesand each computation ofuji can be performed in constanttime, the time complexity of our algorithm is On, where is the number of iterations to reach convergence. Giventhat 10 in our simulations, our observed time complex-ity is On. The resulting time complexity for the fullapproach is On2.

With respect to optimality, our resulting configurationis not necessarily optimal because we do not necessarilyfind the optimal topology. However, two of our algo-rithms, the initial tree construction algorithm and the treeoptimization algorithm, are optimal for their respectivesubproblems. That is, our initial tree construction algo-rithm is optimal in a static environment where nodescannot move so that only the original positions of thenodes are considered. Likewise, for our tree optimizationalgorithm, we prove that the final configuration where nonode can move by itself to improve the overall cost(within the threshold bound) is globally optimal; that is,

no simultaneous relocation of multiple nodes can improvethe overall cost. We present the proof of optimality in theappendix, which can be found on the Computer SocietyDigital Library at http://doi.ieeecomputersociety.org/10.1109/TMC.2011.266.

7 DISTRIBUTEDALGORITHMS

Our solutions to the three subproblems assume a centra-lized scheme in which one node has full knowledge of thenetwork including which nodes are on the transmissionpaths to each source, the original physical position oi ofeach nodesi, and the total message lengthmto be sent from

each source. Whereas the centralized algorithm computesthe optimal static tree and the optimal position of each nodein the restructured tree, it incurs prohibitively high over-head in large-scale networks. We now present a distributedand decentralized version of each of our algorithms.

We modify the first phase, the tree construction phase, touse a fully distributed routing algorithm. We pick greedygeographic routing since it does not require global knowl-edge of the network although any algorithm with suchproperty can be used.

After a routing tree is constructed, the tree restructuringphase begins. Network nodes outside the tree broadcasttheir availability (as NODE_IN_RANGE message) to tree

nodes within their communication range and wait forresponses for a period of timeTw. Similarly, tree nodes entera listening phaseTu. During that period, tree nodes receivemessages of different types (NODE_IN_RANGE, OFFER,. . . ). Each tree node that receives one or more NODE_IN_RANGE message responds to the sender by giving it itslocation information and its parent s location information.Each nontree node so that receives location informationfrom a tree node si during Tw computes the reduction incost if it joins the tree as parent ofsi and addssi to a list ofcandidates. At the end ofTw, the nontree node selects fromthe candidate list the node that results in the largest

reduction and sends it an offer. It also sends the tree nodewith the second largest reduction a POTENTIAL_OFFERmessage. At the end ofTu, each tree node vt that collectedone or more offers and potential offers operates as follows:

Ifvts best potential offer exceeds its best offer by a certainthreshold B and vt has not already waited R rounds, vtwaits rather than accepting its best offer in the hopes that itsbest potential offer will become an actual offer in anotherround. By waiting, it sends everyone a REJECT_OFFER,restarts the listening phase, and records that it has waitedanother round. Otherwise, vt accepts its best offer byresponding to its sender p with an ACCEPT_OFFERmessage and to the remaining nodes with a REJECT_OFFERmessage. It then updates its parent in the tree to p, resetsTuand starts the listening phase again.

A nontree node p that receives an ACCEPT_OFFERmessage moves to the corresponding local optimal locationand joins the tree. It becomes a tree node and enters thelistening phase. On the other hand, ifp does not receive anACCEPT_OFFER, p repeats the process by broadcasting itsavailability again and resetting Tw. We note that values inps candidate list cannot be reused to extend offers to oldtree nodes since those tree nodes could have a new parent atthis point in time. When the second phase ends, anyremaining nontree nodes stop processing whereas treenodes enter the tree optimization phase. Fig. 6 shows thealgorithm executed by each tree node.

Giving tree nodes the ability to wait before accepting anoffer increases the chances of using mobile relay nodes totheir full potential. For example, consider a scenariowhere several mobile relay nodes can greatly improvethe capacities of several tree links but are all closest to onespecific link. They will all send offers to the same tree nodewhile the rest of the tree nodes in their proximity willreceive modest offers from more distant mobile nodes. If thetree nodes cannot wait, they will be forced to accept a

modest offer and the mobile nodes will either remainunused or they will help more distant tree nodes wheretheir impact is reduced since they use up more energy to getto their new location.

The centralized tree optimization algorithm can betransformed into a distributed algorithm in a natural way.The key observation is that computing each uji for node sionly depends on the current position ofsis neighbors in thetree (children and parent), nodes that si normally commu-nicates with for data transfers. Thus, si can perform thiscomputation. The distributed implementation proceeds asfollows: First, there is a setup process where the sender s1

sends a discover message that ends with the receiver sn; thetwo purposes of this message are 1) to assign a label of oddor even to each node si and 2) for each node si to learn thecurrent positions of its neighbors. A node si sends itscurrent position to node sj when acknowledging receipt ofthe discover message. Second, there is a distributed processby which the nodes compute their transmission positions.We make each iteration of the basic algorithm a round,though there does not need to be explicit synchronization.In odd rounds, each odd node computes its locally optimalposition and transmits this new position to its neighbors. Ineven rounds, each even node does the same. A node begins

its next round when it receives updated positions from allits neighbors. The final step is to have the nodes move totheir computed transmission positions, send messages totheir neighbors saying they are in position, and finally



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perform the transmission. To ensure the second process

does not take too long, we limit the number of rounds to 8;that is, each node computes an updated position four times.Simulation results show that this is enough to obtain costsclose to optimal (see Section 8).

8 SIMULATIONS

We carried out simulations on 100 randomly generatedinitial topologies, each of which has 100 nodes placeduniformly at random within a 150 m by 150 m area. We

used these initial topologies to generate two subsequentsets of complete topologies with established sources and

sink. We used the first set to study the effectiveness of ouralgorithms as the amount of data transferred to the sinkvaries and the second set to study the effectiveness of ouralgorithms for different numbers of sources. In the first set,

we selected sources and sinks uniformly at random fromthese 100 nodes. We varied the number of sources from 4 to12, by increments of two, and used each number of sourcesfor 20 initial topologies. For each resulting topology, wecreated many separate input instances by varying the datachunk size from 1 to 150 MB where the data chunk size foran input instance is the common amount of data to betransferred from each source to the sink. In the second set,for each initial topology, we generated 10 differentcomplete topologies by starting with two randomly selectedsources, and adding two new sources to the previous set ateach step.

We used the following settings to model the transmis-sion and mobility costs of our nodes. For transmission, weusea 0:6 107 andb 4 1010 as the standard settingwhich is consistent with the empirical measurements onCC2420 motes [36]. For mobility, we used different settingsin each of our two sets. In the first set, we used k 2 as thestandard setting because it models several platforms suchas Robomote [16], [17]. In the second set, we set k to be 1, 2,and 4 since we additionally use that set to study the effectof different mobility costs on the energy reduction.Furthermore, we set the maximum communication distanceof a node to be 30 m, which was shown to result in a highpacket reception ratio for the CC2420 radio [36]. We ransimulations using different values for the convergencethreshold. We obtained similar gains for values less than orequal to 0.01. In the following simulations, we set thethreshold to 0.01.

Our algorithmic framework starts with an initial routingtree. In the centralized setting, we construct this initialrouting tree using the following three widely used routing

algorithms: power-based routing, hop-based routing, andgreedy geographic routing. Power-based routing computesa shortest path from the sink to each source with each edgeweight being the square of the distance between the twocorresponding nodes plus some constant value to representthe energy consumeda bd2 to transmit each byte of dataover that edge. Hop-based routing minimizes the numberof hops between each source and the sink and is the baseof several widely used algorithms in wireless networks(e.g., AODV [39]). Given our maximum communicationrange of 30 m, we do not have any links with poor qualitywhich is a common concern with hop-based routing.

Greedy geographic routing is a greedy strategy in whicheach node forwards messages to the reachable node(within the communication range of the node) that isclosest to the sink. The first two tree constructionapproaches require global knowledge of the networkwhereas the last one is fully localized. For the distributedsetting, we construct the initial routing tree using greedygeographic routing because it is fully localized. Of the 100initial topologies, the distributed routing algorithm re-sulted in a disconnected path between the sources and thesink in only four networks given our maximum commu-nication distance of 30 m.

We study variants of our strategy where we use onlyone optimization, inserting nodes or optimizing a giventree, to determine the benefit of both optimizations.Specifically, we use TREE to represent the variant where


Fig. 6. Local algorithm executed by tree nodes.


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we only construct an initial tree and do no optimizations,TREE FOto represent the variant where we optimize theinitial tree, TREE INSto represent the variant where weinsert nodes into the initial tree, and TREE INS FO torepresent the variant where we insert nodes into the initial

tree and then optimize the final tree. The three possibilitiesfor TREE are PB, HB, and GG which represent the PowerBased, Hop Based, and Greedy Geographic tree construc-tion algorithms, respectively. For each input instance I, weletTREEIdenote the energy consumed by the initial treeconstructed by our three tree construction algorithms PB,HB, and GG, and we let TREEOPTI denote theenergy consumed by the final optimized tree where TREEcan be PB, HB, or GG and OPT can be INS, FO orINS FO. The reduction ratio achieved by optimizationOPT on input I for tree construction algorithm TREE isTREEI TREEOPTI=TREEI. We measure the

performance of optimization OPT on initial tree strategyTREE by computing the average reduction ratio achievedby OPT over all input instances I of set 1 that have thesame data chunk size. Moreover, for each input instance Iand each algorithm TREE+OPT, we define the static energyratio TREEOPTI=PBI where PBI is the cost ofthe power-based tree which is the optimal cost for the staticversion of this problem where no nodes can move. Thestatic energy ratio measures the benefit of our algorithmswhich exploit mobility of nodes versus the static optimalconfiguration. We measure the overall performance ofalgorithm TREE OPT by computing the average staticenergy ratio achieved by TREE OPT over all inputinstances I of set 1 that have the same data chunk size.Finally, we measure the performance of optimization INS FOon initial tree strategy TREE by computing the averagereduction ratio achieved by INS FO over all inputinstancesIof set 2 that have the same number of sources.

8.1 Centralized Algorithm

We first show the benefit of exploiting the mobility of relaynodes by computing the average static energy consump-tion ratio of TREE INS FO for all data chunk sizes foreach of our three tree building strategies PB, HB, and GGas shown in Fig. 7. For all three initial tree strategies, we

see that the average static energy consumption ratio dropsquickly as the data chunk size increases. For HB and GG,the average static energy consumption ratio starts outhigher than 100 percent because PBI, the optimal tree for

the static case, is roughly 37 percent lower than HBIandGGI for any of our input instances. Even given thisinitial disadvantage of a poor starting tree from an energyconsumption perspective, we see that the average staticenergy consumption ratios of HB INS FO and GG

INS FO drop below 100 percent for data chunk sizes of12 and 15 MB, respectively. As the data chunk sizeincreases further, both HB INS FO and GG INS FO achieve average static energy consumption ratios of 75and 60 percent for data chunk sizes of 60 and 150 MB,respectively. The results for PB INS FOare even betterbecause we start with the optimal tree for the static case.Thus, the average static energy consumption ratio for PB INS FO is always below 100 percent and reaches55 percent for 150 MB.

We now evaluate the benefit achieved by our optimiza-tions FO, INS, and INS FO for each of our tree building

strategies PB, HB, and GG. We note that in this set ofsimulations, we used our centralized improvement schemeswith the distributed tree building approach GG. Thepurpose is to test the limits of our optimizations given anonoptimal starting tree. A fully distributed setup isstudied later in this section.

We start with optimization INS FO. Fig. 8 plots theaverage reduction ratio for optimization INS FO for PB,HB, and GG. In all three cases, we see the same basic trend;the average reduction ratio increases as data chunk sizeincreases. For both HB and GG, the average reduction ratiostarts at roughly 25 percent for small data chunk sizes andexceeds 60 percent for large data chunk sizes; for PB the

average reduction ratio starts near 0 percent and exceeds43 percent for large data chunk sizes. The difference inaverage reduction ratio, in particular for small data chunksizes, is due to the quality of the initial tree. For PB, theinitial tree is good so there is little that our optimizationINS FOcan do to improve energy consumption for smalldata chunk sizes. For HB and GG, the initial tree can be verypoor, so INS FOcan provide immediate improvement tothe tree to significantly reduce energy consumption by anaverage of 25 percent for data chunk sizes of only 1 MB. Wenote that although INS FO achieves higher reductionratios for HB and GG than for PB, the total energy

consumed by PB INS FOis lower than the total energyconsumed by HB INS FO or GG INS FO.

We next consider optimization FO alone. Fig. 9 plots theaverage reduction ratio for optimization FO for PB, HB,


Fig. 7. Graph of the average static energy consumption ratio of TREE INS FOas a function of data chunk size for our three tree constructionstrategies PB, HB, and GG.

Fig. 8. Graph of the average reduction ratio of optimization INS FOasa function of data chunk size for our three tree construction strategiesPB, HB, and GG.


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and GG. In all three cases, the average reduction ratio startsat 0 percent for small data chunk sizes and increases toroughly 18 percent for HB and GG and 33 percent for PBfor large data chunk sizes. It is interesting to note that FO ismost effective for PB whereas INS FO achieved signifi-

cantly greater reduction ratios for GG and HB for all datachunk sizes.

Finally, we consider optimization INS alone. Fig. 10plots the average reduction ratio for optimization INS forPB, HB, and GG. In all three cases, we see the averagereduction ratio of INS alone is comparable to that of INS FO (within 5-8 percent for data chunk sizes of at least15 MB). For very small data chunk sizes, the averagereduction ratio is constant until a certain threshold isexceeded and then rises significantly.

We now evaluate our approach as we vary the number ofsources. We used the greedy geographic tree GG as our

initial tree and INS FO as our optimization algorithm.Fig. 11 shows the average reduction ratio as a function ofthe number of sources. We observe that this ratio remainsalmost constant for different values ofk as the difference inratios for different number of sources does not exceed3.5 percent. Fig. 11 also shows the effect of mobility costs onthe reduction in energy consumption costs in general. Asmobility costs decrease, it becomes more effective formobile nodes to move over longer distances and reducethe communication consumption further so the reduction intotal costs increases ask decreases.

Given our simulation results, we draw the following five

conclusions. First, we achieve the best results when we use

the power-based tree PB as our initial tree. Second, if we usethe power-based tree, either optimization alone is veryeffective and both optimizations together achieve the bestresults. Third, if we start with either the hop-based tree HBor the greedy geographic tree GG, the most effective

optimization is the node insertion optimization INS whichachieves nearly as good an average reduction ratio asINS+FO. Fourth, if we start with the hop-based or greedygeographic tree, we can achieve a static energy ratio that isclose to that achieved by starting with the power-based treeif we apply both optimizations. In particular, the nodeinsertion optimization INS helps alleviate the initial dis-advantage by adding a lot of new nodes into the tree. Webriefly explain the reason for all of these conclusions. Thekey observation is that the hop-based and greedy geo-graphic trees HB and GG tend to create initial trees withrelatively long edges and relatively few nodes whereas the

power-based tree PB tends to create trees with lots of nodesand relatively short edges because of the quadratic costmetric. As a result, for HB and GG, optimization FO alonewhich rearranges nodes is relatively ineffective as it canonly balance the relatively long edges. On the other hand,optimization INS alone can insert new nodes into the treeand thus create a new tree with significantly shorter edgeson average given HB or GG as the initial tree. Because PBstarts with many more nodes and shorter edges, PB doesnot benefit as much from node insertion INS as HB and GGdo, and PB benefits a lot more from node rearrangement FOthan HB and GG do. Fifth, the improvement ratios that weobtain are almost independent of the number of sources inthe network.

In all our simulation results, the standard deviationvaried between 4 and 6.5 percent. We identified six outliertopologies which deviated from the mean by more than10 percent. In these topologies, the sources were either veryclose to the sink so there was little room for improvement orvery far from the sink so the improvement was muchgreater than the average case.

8.2 Distributed Algorithm

We now evaluate how well our distributed implementa-tion works. Our initial tree is the greedy geographic tree

GG. We consider four optimizations: the centralizedimplementation of INS FO, the distributed implementa-tion of just FO, the distributed implementation of just INS,and the distributed implementation of INS followed by the


Fig. 10. Graph of the average reduction ratio of optimization INS as afunction of data chunk size for our three tree construction strategies PB,HB, and GG.

Fig. 11. Graph of the average reduction ratio of the centralized anddistributed GG INS FOoptimizations as a function of the number ofsources, a data chunk of 75 MB and different values of k.

Fig. 9. Graph of the average reduction ratio of optimization FO as afunction of data chunk size for our three tree construction strategies PB,HB, and GG.


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distributed implementation of FO. For the distributedimplementation of INS, we set parameter B to 10 percent(a potential offer must be 10 percent better than the bestactual offer to cause a node to wait). Fig. 12 shows the

average reduction ratio of each of these optimizations. Theaverage reduction ratio for distributed INS FO starts at20 percent for small data chunk sizes, reaches 30 percentfor data chunk sizes around 20 MB, and exceeds 40 percentfor data chunk sizes larger than 75 MB. The gap betweenthe average reduction ratio for centralized INS FO anddistributed INS FO starts at roughly 5 percent for smalldata chunk sizes and increases to roughly 15 percent forlarge data chunk sizes. This gap is due to the lack of globalinformation when performing the insertion step. Expensivelinks in the tree that do not have nearby relay nodes arenot able to communicate with further but available relay

nodes whose help is only offered to cheaper but nearbylinks. This problem is exacerbated as the data chunk sizeincreases. We varied values for B between 10 and50 percent and for R between 1 and 3. For all combinationsofBand R that we tested, we obtained similar results tothose of Fig. 12. As in the centralized case, distributed INSis more effective than distributed FO. However, doing bothdistributed optimizations does result in roughly a 10 per-cent improvement compared to only doing the distributedINS optimization for most data chunk sizes.

Similar to the centralized implementation, we observe aslow reduction in the improvement ratio as the number ofsources increases for k 2 and 4 (Fig. 11). For cheapermobility cost (k 1), the difference in improvement ratiosincreases at a faster rate and reaches 9 percent as thenumber of sources increases from 2 to 20. This is becausewhen mobility is cheaper, in an optimal setting, nodes canmove over longer distances to help expensive links.However, as we mentioned earlier, in a distributed setting,mobile nodes are not aware of those distant expensiveedges. Moreover, as the number of sources increases, thenumber of mobile nodes available to help decreases. Bothfactors combined make the distributed implementationslightly less effective for a high number of sources.

9 CONCLUSION

In this paper, we proposed a holistic approach to minimizethe total energy consumed by both mobility of relays and

wireless transmissions. Most previous work ignored theenergy consumed by moving mobile relays. When wemodel both sources of energy consumption, the optimalposition of a node that receives data from one or multipleneighbors and transmits it to a single parent is not themidpoint of its neighbors; instead, it converges to thisposition as the amount of data transmitted goes to infinity.Ideally, we start with the optimal initial routing tree in a

static environment where no nodes can move. However,our approach can work with less optimal initial configura-tions including one generated using only local informationsuch as greedy geographic routing. Our approach im-proves the initial configuration using two iterativeschemes. The first inserts new nodes into the tree. Thesecond computes the optimal positions of relay nodes inthe tree given a fixed topology. This algorithm is appro-priate for a variety of data-intensive wireless sensornetworks. It allows some nodes to move while others donot because any local improvement for a given mobilerelay is a global improvement. This allows us to potentiallyextend our approach to handle additional constraints on

individual nodes such as low energy levels or mobilityrestrictions due to application requirements. Our approachcan be implemented in a centralized or distributed fashion.Our simulations show it substantially reduces the energyconsumption by up to 45 percent.

ACKNOWLEDGMENTS

The authors thank Philip McKinley, Chiping Tang, andSandeep Kulkarni for their help.

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Fatme El-Moukaddemreceived the BS and MSdegrees in computer science from the AmericanUniversity of Beirut in 2000 and 2002, respec-tively. She is working toward the PhD degree atMichigan State University. Her research inter-ests include algorithms and wireless sensornetworks.

Eric Torngreceived the PhD degree in compu-ter science from Stanford University, California,in 1994. He is currently an associate professorand graduate director with the Department ofComputer Science and Engineering, MichiganState University, East Lansing. His researchinterests include algorithms, scheduling, andnetworking. He received a US National ScienceFoundation CAREER Award in 1997.

Guoliang Xing received the BS degree inelectrical engineering and the MS degree incomputer science from Xian Jiao Tong Uni-versity, China, in 1998 and 2001, respectively,and the MS and DSc degrees in computerscience and engineering from Washington Uni-versity in St. Louis in 2003 and 2006, respec-tively. He is an assistant professor in theDepartment of Computer Science and Engineer-ing at Michigan State University. From 2006 to

2008, he was an assistant professor of computer science at the CityUniversity of Hong Kong. He received the US National ScienceFoundation CAREER Award in 2010. His research interests includewireless sensor networks, mobile systems, and cyberphysical systems.

He received the Best Paper Award from the 18th IEEE InternationalConference on Network Protocols (ICNP) in 2010. He is a member ofthe IEEE.

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