a new optimization strategy proposal for multi-copy forwarding in energy constrained dtns

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This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. Citation information: DOI10.1109/LCOMM.2014.2346488, IEEE Communications Letters

IEEE COMMUNICATIONS LETTERS, VOL. , NO. , 1

A New Optimization Strategy Proposal forMulti-Copy Forwarding in Energy Constrained

DTNsSergio L. F. Maia, Ederson R. Silva and Paulo R. Guardieiro, Member, IEEE

Abstract—Most routing algorithms in delay tolerant networks(DTNs) have not taken adequately into account the issue ofenergy constraint for communication. In this paper, we propose anew optimization strategy for different DTN routing algorithmsthat use an utility function to select the best nodes to relaymessages, but that were originally proposed without regard tothe issue of energy. Our proposed optimization strategy is basedon the modeling of multi-copy forwarding as a Bayesian signalinggame. A system for belief update concerning the energy of theother DTN nodes based on the accumulated observations of thedestination nodes is considered. Simulation results show that ourproposed optimization strategy can maintain the network nodesoperational for a longer period of time.

Index Terms—DTN, routing, game theory, Bayesian game.

I. INTRODUCTION

DELAY/DISRUPTION Tolerant Networks (DTNs) havebeen envisioned for emerging wireless applications that

do not require the fixed infrastructure associated with tradi-tional communication systems. Most DTN routing algorithmsemploy the technique of store-carry-forward and can use mul-tiple copies of the same message to increase the probability ofat least one being delivered. The typical state-of-the art routingalgorithms combine heuristics and the social network structureto decide for forwarding message copies or replicas fromamong the candidate relays according to an utility function.However, a utility-based replication often leads the routingto direct most of the traffic through a small subset of goodrelays. This unfair load distribution can quickly deplete theconstrained resources utilized in mobile devices, e.g., battery.

In DTN routing literature, the problem of optimal forward-ing for message delivery in an energy constrained environmentis investigated by some works that utilize current energy-state information to make forwarding decisions. For example,there are proposals of energy-aware routing applicable toEpidemic forwarding [1][2][3], and its variations n-Epidemic[4], two-hop [3], where potentially all nodes may receive themessage copy. On the other hand, the work reported in [5],to the best of our knowledge, is the only work publishedwhich combines in a same extended utility function factors

This work was supported in part by the FAPEMIG (Minas Gerais ResearchFoundation, Brazil) under Grant APQ-02117-12.

Sergio L. F. Maia is with the Federal Institute of Triangulo Mineiro,Uberlandia, Minas Gerais, Brazil (e-mail: [email protected]).

Ederson R. Silva and Paulo R. Guardieiro are with the Federal University ofUberlandia, Uberlandia, Minas Gerais, Brazil (e-mail: [email protected];[email protected]).

Manuscript received, 2014.

that reflect socially-aware routing with energy consumptionoptimization. Moreover, these papers consider situations wherenodes are not heterogeneous in terms of friendship, commu-nity, node classes (e.g., static nodes, vehicles and pedestrians),etc. Therefore, there is lack of research on energy-efficientforwarding algorithms to heterogeneous DTNs which use anutility function to decide on the fitness or utility of a givennode as a relay.

For this reason, our goal in this paper is to propose a noveloptimization strategy that is compatible with different utility-based routing algorithms that were originally proposed withoutany regard to the issue of energy constraint. With respect to theexisting energy-efficient approaches, our proposal is supportedby original contributions as follows.

Firstly, we assume a game-theoretic model, the energyconstrained forwarding game, which considers heterogeneousand energy constrained nodes able to learn optimal multi-copyforwarding over time. In our game, nodes are led to potentialselfishness as they may refuse to take on the forwardingtokens of a received message to save energy. A forwardingtoken implies that the node that owns a message can spawnand forward an additional copy of the given message. To thebest of our knowledge, we are the first to relate the decisionmakings in a game model to the number of forwarding tokensallocated to a message in DTN employing an utility-basedrouting algorithm.

In the presented model, the nodes are not motivated todirectly or indirectly report their true energy to be used in for-warding decisions by other nodes. Our assumption is that theforwarding probabilities exchanged between two nodes basedon their current residual energy cannot be sustained over timedue to the dynamics governing the energy consumption. Then,we assume that nodes develop beliefs about the forwardingcompetency of other nodes. This competency can be mappedto match an energy level.

The mechanism employed for belief updating is our secondcontribution of this work. The mechanism uses Bayesian infer-ence based on the accumulated observations of the destinationnodes, concerning the successes and failures of forwardingof messages to them. The assumption is that the greater theparticipation of a particular node for forwarding messages toa destination node, the better the latter node can infer that theformer has sufficient energy to be shared. Thus, we do not usemessage delivery confirmation mechanisms.

The remainder of the paper is organized as follows: inthe next section, our game model is briefly described. The




behavior strategies of the nodes are presented in Section III.Our simulation scenario and certain results are presented inSection IV. Finally, Section V concludes this paper.

II. THE ENERGY CONSTRAINED FORWARDING GAME

A. Related Work

An adaptive learning framework that allows nodes to learnthe optimal strategies over time can be seen in [6], where theauthors apply the evolutionary game theory to non-cooperativeforwarding control of relay nodes in DTNs. The paper presentsa general framework for competitive forwarding in DTNsunder two-hop routing, without considering the candidate nodeselection. In contrast, our model presents forwarding in DTNunder multi-hop and replications based on an utility functionU(·).

The repeated traditional Bayesian game-theoretic modelwith an adaptive learning process reported in [7] for an adhoc network composed of selfish nodes is the closest one toour game model. However, we use an appropriate repeatedBayesian signaling game formulation for copy forwarding, ina heterogeneous and energy constrained DTN. Moreover, weassume that the message to be transferred needs to be split intoK smaller units called chunks, and L copies or forwardingtokens for each chunk are initially defined. Our belief systemis based on the successful forwarding of chunk sequences.Table I lists the main variables commonly used in this paper.

B. Game Specification

We define that a new stage of the game begins whenever anode i, which has a chunk and c > 1 forwarding tokens forthis chunk, encounters a node j with no copy of the chunk.The variable m is used to denote this chunk to be disseminatedto a destination d. If Uj(d) > Ui(d), then node i should makedecisions based on our game model. We focus on the decisionmaking process regarding how many li(c) tokens for copy ofm node i hands over to node j, and how many lj(c) tokensnode j accepts.

In our game model, the energy class θ of a node correspondsto the concept of type in Bayesian games [8]. The set Θincludes all possible energy values. At each stage, we considera two-player Bayesian signaling game, where node i and j arethe players. A node i cannot observe the type of node j is,however, i can observe the value Uj(d) as a signal of node j’sability to replicate its copies. Node i can use the observablevalue of the utility function of node j to form a judgment aboutthe real energy class of node j. At the encounter moment, theupdated belief that node i has about the energy class of nodej just by observing the value of the utility function is denotedby µ(θj |Uj(d)).

Furthermore, node i has a prior belief given by a probabilityp(θ) that the type of node j is θ; the probability distributionp(·) over Θ is common knowledge among the players. Theaction space of node i is the set Ai

m = {li(c) | 0 ≤ li(c) ≤c − 1}, i.e., the possible amounts of forwarding tokens thatnode i can grant a node j the right to further forward copiesof m. Note that li(c) = 0 means that node i makes the finaldecision not to send copies of m. The action space of a relay

TABLE ILIST OF COMMONLY USED VARIABLES

Variable DescriptionUi(d) [Uj(d)] Reflects the fitness or utility that node i [j] will be

able to make a delivery to destination node dθ Energy class of a nodep(θ) Prior probabilityK Total chunks of a messageL Total forwarding tokens for each chunks and f Successes and failures of delivery of K chunksθj Belief of node i about the energy class of node jψ(θ) Probability to accept messages according to θα and β Parameters of a beta distributionli(c) [lj(c)] Forwarding tokens sent [accepted] by node i [j]

node j is the set Ajm = {lj(c) | 0 ≤ lj(c) ≤ li(c)}, i.e., the

action space of node j consists of alternatives between zero(that do not accept copy of m) and li(c) forwarding tokens.

C. Belief System

In this paper, we assume that the successes s and failuresf = K − s of the forwarding of a sequence of K chunks areused by the destination node to estimate the willingness ofintermediate nodes to participate in the multi-hop forwardingprocess. Based on accumulated observations of s and f for acandidate relay, we use Bayesian inference to reason the beliefof nodes about the reputation of the candidates forwardingcompetency, which is mapped to match an energy class θ.

We assume that the parameter θ is a random variable andthat its prior probability p(θ) is given by a beta distributionBeta(α, β), where α and β are non-negative shape parametersthat are initialized to some values α0 and β0. According toBayesian inference, when a new observation about s successesand f failures for a node j is collected at new encounter, theprior distribution is updated by α ← α + s and β ← β + f .Then, a belief θj of node i about the energy class θ of nodej can be quantified by θj = (α/(α+ β)) · (1− u), where theuncertainty u is given by (12 ·α ·β)/((α+β)2 · (α+β+1)).

III. STRATEGIES

A. Behavior of Node j

Firstly, node j observes its type θj and sends the signalUj(d). The model assumes that a same signal Uj(d) maybe sent by nodes from different energy classes (poolingequilibrium). Then node i observes Uj(d) and acts decidingon the value of li(c) forwarding tokens for a chunk copy tobe forwarded to node j. In a second period of the game, nodej decides how many of the li(c) forwarding tokens that havebeen granted it must accept.

In this second period, the behavior strategy of node j isgiven by probability ψ(θj) = exp(−(1.0 − θj)/1.15) whichindicates the willingness to accept messages according to theenergy class θj . The function ψ(·) maintains ordering of theenergy class, i.e., if θj1 < θj2, thus ψ(θj1) < ψ(θj2). Hence,given the action of node i to grant li(c) tokens for eachchunk copy, node j will take on average ψ(θj) ·

∑n li(cn)

forwarding tokens for all the n copies of chunks at the time




of the encounter. Therefore, the greater the energy, the largerthe number of tokens node j can take on.

B. Behavior of Node i

Once the pooling equilibrium is admitted in which allpossible types of node j can send the same type of signalUj(d), a perfect Bayesian equilibrium with this behaviorstrategy of node j is only consistent with a belief of nodei such that, according to Bayes’ rule, µ(θj | Uj(d)) = p(θj).This means that the node cannot form any other expectationabout node j besides the prior distribution that exists for thenode types, so the signal is inefficient in revealing the type ofnode j.

For this, our model assumes that node i makes decisionsabout the value of li(c) based on its own energy level andbeliefs formed from observations about the behavior of nodej. These beliefs are about the type of node j given by θj(after the update of p(θj), as shown in Section II-C) and aboutits behavior strategy defined as ψ(θj). This latter probabilityindicates the belief of node i in relation to the ability of nodej to accept and hold on to the li(c) tokens for a forwardedchunk copy. It is assumed that this probability offers a degreeof confidence about the value Uj(d) in the sense that it iscorrected to a new value given by U ′

j(d) = Uj(d) · ψ(θj).Regarding its own utility function, it is assumed that node i

performs a balance on its utility function based on its currentenergy class θi, such that the new value for Ui(d) is givenby U ′

i(d) = Ui(d) · ψ(θi). Thus, the model assumes that theactions of node i must balance the dispersion of copies ofchunks it carries and the use of energy. For this purpose, weassume that a node i of energy class θi and U ′

i(d) decideshow many tokens for a chunk it should grant to a node jmaximizing the payoff composed of two components (gainand cost) given by

Uθi,U ′i(d)(li(c), U

′j(d), θj) =

[c1 · (1− ψ(θi)) + c2 · U ′j(d)/(U

′i(d) + U ′

j(d))] · li(c)−(1− ψ(θj)) · exp(c3 · li(c)), (1)

where c1, c2 and c3 are parameters whose values are setempirically so that the payoff function reflects the sensibilityof node i for making the decision regarding an action li(c).

The gain component of the payoff equation considers thatnode i has more to gain by granting a greater number offorwarding tokens when its energy is low. In addition, thegreater the ratio of the corrected values of utility given byU ′j(d)/(U

′i(d) + U ′

j(d)), the greater the gain. On the otherhand, for an action li(c) it is assumed that if the probabilityestimation of node j to reject the granted tokens, given by1−ψ(θj), is greater, also then the cost component is greater.

Furthermore, the model guarantees the experimental condi-tions of the adaptive learning framework. According to thistheory, node i selects the action li(c) that maximizes (1) witha probability of 1 − εk, where εk is a sequence of smallerrors that decreases in relation to the number of contacts.The equilibrium and optimality proofs of the game-theoreticmodel with the learning process can be seen in [7].

IV. SIMULATION AND RESULTS

We conducted simulation experiments to evaluate our opti-mization strategy applied in PRoPHETv2 [9] and SimBetTS[10]. These algorithms were chosen as they are quite popularwithin the DTN research community. PRoPHETv2 is the oldPRoPHET updated with a new transitive update equation anddirect encounter update equation; and SimBetTS is basedon social analysis of past interactions of a node. For theexperiments carried out of this paper, we developed the DTNsimulator presented in [11] from the OMNeT++ SimulationEnvironment, which provides the basic machinery and toolsto write network simulations.

In the considered scenarios, the nodes are heterogeneous andmove according to the “Community-based Mobility Model”(CBM) as in [12]. Forty nodes are uniformly and sparselydistributed in four communities (e.g., the user’s departmentbuilding on a campus) in a square of size 200 m × 200 m.The transmission range (25 m) is sufficiently small so that itcan be expected that the network will be highly partitioned andnot clustered. We set the scenario so that in every communitythere are special nodes or “better” relays (roaming nodes)with high mobility and that quite often roam outside theircommunity around four points of interest (POIs) (e.g., libraryand restaurant).

In the experiments, at the beginning of each simulation run,600 messages (K =10; L =16) are generated. The pair sourceand destination nodes are chosen randomly and belong todifferent communities. With this, the most requested nodes toforward chunks between communities are the roaming nodesand these chunk exchanges occur at POIs or on the way to thecommunities. Consequently, the chunks are largely deliveredin more than one hop.

The proposed evaluation is performed assuming that theenergy reserves of the nodes are not replenished. Thus, whena node runs out of energy, it dies and does not forward anychunks nor does it generate new traffic to the network. A priorprobability distribution Beta(45, 15) of the energy level forthe nodes is used. We defined a nominal charge for a batteryas being able to perform 2400 transmissions.

Under the same energy constrained scenario, we comparethe performance of PRoPHETv2 and SimBetTS with regardto three different settings: default mode, energy-aware modeand our optimization strategy. The former mode makes routingdecisions based on the original utility function. The secondintroduces energy awareness in the routing decision. In thismode, there is a resultant utility function that is the sum ofthe original utility function defined by the routing algorithmand an energy-aware utility function as used in [5]. In bothmodes, the amount of copies is split between two nodes inproportion to their utility function. In this paper, the resultsare the average from five simulation runs, and the error barsin the graphs represent the 95% confidence intervals.

Fig. 1 shows that under the proposed strategy, the amountof offline nodes is lower when compared to the default andenergy-aware modes at the same observed simulated time.Our proposal of optimization allows in particular the roamingnodes to remain operational for a longer period of time, which




Fig. 1. Result of PRoPHETv2 with energy constraint to average percentageof offline nodes.

Fig. 2. Result of PRoPHETv2 for average delivery ratio between the deliveredchunks at destination nodes and 6000 chunks sent to network.

results in delayed shutdown. Consequently, as shown in Fig.2, the use of our strategy over the default mode results inapproximately a 13% increase of the average delivery ratio atdestination nodes by the end of the simulated time (48h).

Note that the energy-aware mode makes a poor capture ofthe dynamic structure of forwarding decisions in the consid-ered scenario with multiple communities and heterogeneousnode populations. This result is due to the fact that some copiesend up with nodes that have high remaining energy level, butwhich are less likely to be good forwarders to nodes of othercommunities. However, unlike the energy-aware mode, ourstrategy uses the belief about energy level as the reliabilityfactor for delivery probability based only on parameters asencounter information and social relations.

Moreover, we observe that the improvement in the averagedelivery ratio obtained by our strategy results in increasedaverage delivery delay. This result is in agreement with themost of the research on routing algorithms for DTN, whichfocuses on reducing the total energy consumed for forwardingat the expense of increased delivery delay [2].

SimBetTS’s results exhibit the same trends seen in the re-sults of PRoPHETv2. However, when our proposal is used, theperformance of delivery ratio and delivery delay in SimBetTSis slightly better than in PRoPHETv2, as shown in Table II.This observed behavior can be explained by the fact that, inSimBetTS, the number of total transmissions performed bynodes is higher when compared to PRoPHETv2. The largerthe number of transmission events, the larger the number ofsuccesses and failures in delivery of chunks, which reduces the

TABLE IIPERFORMANCE COMPARISON FOR PROPOSED OPTIMIZATION STRATEGY a

Metric PRoPHETv2 SimBetTSIncrease for the average delivery ratio (%) b 13 20Increase for the average delivery delay (%) b 34 25Average transmissions 40458 45193a Averages at 48h of simulated time.b Percentage of proposed strategy over default mode.

degree of uncertainty in Bayesian inference. This allows for abetter approximation of the estimates compared to the actualvalues of the energy levels of the nodes as seen in Section II.

V. CONCLUSION

In this paper, the authors presented a new strategy tooptimize DTN routing algorithms which does not considerthe energy constraint and uses an utility function to selectthe best nodes to relay. Our strategy is based on a Bayesiansignaling game theoretical model for the modeling of multi-copy forwarding in heterogeneous and energy constrainedDTN. In this scenario, our model promotes a greater balancingof the spent energy and the network remains operational fora longer period of time, mainly the nodes more required torelay. In addition, no neighborhood watch or acknowledgmentmechanism is used.

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a new optimization strategy proposal for multi-copy forwarding in energy constrained dtns

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