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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 9, NOVEMBER 2013 4629

On Exploiting Contact Patterns for Data Forwardingin Duty-Cycle Opportunistic Mobile Networks

Huan Zhou, Jiming Chen, Senior Member, IEEE, Hongyang Zhao,Wei Gao, Member, IEEE, and Peng Cheng, Member, IEEE

Abstract—In this paper, we focus on investigating the impactof duty-cycle operation on data forwarding in duty-cycle oppor-tunistic mobile networks (OppNets) and on designing an efficientdata-forwarding strategy for duty-cycle OppNets. Some recentstudies utilize node contact patterns to aid in the design of a data-forwarding strategy in OppNets. However, when duty-cycle oper-ation is applied in OppNets, several node contacts will be missedwhen nodes are in the sleep state for energy saving, and it becomeschallenging to design an efficient data-forwarding strategy basedon exploitation of node contact patterns. To address this challenge,we first propose a model to investigate the contact process in duty-cycle OppNets and to estimate the probability of contact discovery.We also experimentally validate the correctness of our proposedmodel. Second, based on this model, we propose a novel approachto improve the performance of data forwarding in duty-cycleOppNets. The proposed forwarding strategy takes into accountboth the contact frequency and contact duration and managesto forward data copies along the opportunistic forwarding paths,which maximize the data delivery probability. Finally, extensivereal-trace-driven simulations are conducted to compare the pro-posed data-forwarding strategy with other recently reported data-forwarding strategies in terms of delivery ratio and cost. Thesimulation results show that our proposed data-forwarding strat-egy is close to the Epidemic Routing strategy in terms of deliveryratio but with significantly reduced delivery cost. Additionally,our proposed strategy outperforms the Bubble Rap and Prophetstrategies in terms of delivery ratio with reasonable delivery cost.

Index Terms—Data forwarding, duty-cycle operation, node con-tact pattern, opportunistic mobile networks (OppNets).

I. INTRODUCTION

R ECENTLY, with the rapid proliferation of portable de-vices (e.g., personal digital assistants and smartphones),

a new peer-to-peer application scenario, i.e., opportunistic

Manuscript received December 25, 2012; revised April 19, 2013; acceptedMay 24, 2013. Date of publication June 10, 2013; date of current versionNovember 6, 2013. This work was supported in part by the National NaturalScience Foundation of China under Grant 61061130563, Grant 61004060,Grant 61222305, and Grant 61174177; by the 863 High-Tech Project underGrant 2011AA040101-1; by the National Technology Research and Devel-opment Program under Grant 2013AA10230207; by the Specialized Re-search Fund for the Doctoral Program of Higher Education under Grant20100101110066, Grant 20120101110139, and Grant NCET-11-0445; and bythe Fundamental Research Funds for the Central Universities under Grant2013QNA5013 and Grant 2013FZA5007. The review of this paper was coordi-nated by Prof. G. Mao. (Corresponding author: P. Cheng.)

H. Zhou, J. Chen, H. Zhao, and P. Cheng are with the State Key Laboratory ofIndustrial Control Technology, Zhejiang University, Hangzhou 310027, China(e-mail: [email protected]).

W. Gao is with the Department of Electrical Engineering and ComputerScience, University of Tennessee, Knoxville, TN 37996 USA.

Color versions of one or more of the figures in this paper are available onlineat http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/TVT.2013.2267236

mobile networks (OppNets), has begun to emerge [1]–[7]. InOppNets, it is hard to maintain end-to-end communication linksdue to the time-varying network topology, and only intermit-tent connectivity among portable devices (called nodes below)exist in the network. Nodes have to store their data to betransmitted and opportunistically forward data upon contactswith others. This communication paradigm is referred to as thestore–carry–forward mechanism, standing as a basic strategy ofdata delivery in OppNets.

To enable this data delivery, nodes have to be kept in idlelistening mode to discover if there is any neighbor node in itsvicinity. In OppNets, the intercontact time is generally muchlonger than the contact duration due to node sparsity; hence,nodes will spend most of their energy in idle listening modeduring intercontact times. Experimental studies in [8]–[10]have shown that energy consumption in idle listening mode isalmost as much as that in a receiving mode. Therefore, over95% of the node energy is consumed by the idle listeningmode searching for neighbors [11]. This makes energy savingan important problem with OppNets; it consists of nodes withlimited power supply.

Duty cycle is an effective approach to energy saving andenables mobile nodes to alternatively operate between wake-upand sleep states. The duty-cycle operation can be classified intotwo categories: synchronous and asynchronous [12], [13]. Sincesynchronous duty-cycle operation requires global time syn-chronization, which leads to unacceptable overhead of globalcommunication, the asynchronous operation is more favorablein OppNets. Duty-cycle operation also significantly reduces theperformance of data transmission because nodes miss a largeamount of contact opportunities when they switch to the sleepstate. Therefore, it is pressing to investigate the impact of duty-cycle operation on the performance of data transmission inOppNets.

In this paper, we focus on investigating the impact ofduty-cycle operation on data forwarding in OppNets. Dataforwarding has been well studied in OppNets, and severaldata-forwarding strategies have been proposed. Some data-forwarding strategies rely on comparisons between nodes’probabilities of contacting the destination to make forward-ing decisions [14]–[16]. However, the performance of theseschemes is limited due to the lack of global information atindividual nodes about how to reach the destination. Recently,some studies have exploited the characteristics of node contactpatterns, and data-forwarding decisions are decided based onnodes’ cumulative contact characteristics over a long period oftime [3], [17]–[20]. Since node contact patterns represent the

0018-9545 © 2013 IEEE

4630 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 62, NO. 9, NOVEMBER 2013

long-term relation among nodes with better stability, they makea data-forwarding decision more effective and less susceptibleto the randomness of node mobility.

However, in duty-cycle OppNets, since nodes in the networkoperate at a duty cycle and switch between the sleep andwake-up states, several contacts will be missed when nodesswitch to the sleep state. This leads to distinct characteristicsof the contact process in duty-cycle OppNets and makes itdifficult to utilize node contact patterns to design efficientdata-forwarding strategy. To solve this problem, we propose amodel to investigate the characteristics of the contact process induty-cycle OppNets. For simplicity, we consider periodic dutycycling of individual nodes, such that each node independentlydetermines the start time of itself and works for a constanttime Ton every period T . We quantify the contact discoveryprobability as a function of wake-up time Ton, period T , andcontact duration Td. Here, the contact discovery probabilityrepresents the probability that a contact between two nodescan be discovered by each other in duty-cycle OppNets. Bydoing so, we manage to analytically characterize the relation-ship between energy consumption and the contact discoveryprobability. Based on the proposed model, we then propose anovel approach to data forwarding in duty-cycle OppNets. Theproposed data-forwarding strategy takes into account both thecontact frequency and the contact duration, and manages toforward data copies toward the opportunistic forwarding paths,which maximize the data delivery probability. Our contribu-tions in this paper are fourfold.

1) We propose a model to investigate the contact processin duty-cycle OppNets and derive the contact discoveryprobability. Given that contact duration follows the powerlaw distribution, we analytically explore the relation-ship between energy consumption and contact discoveryprobability.

2) We use real mobility traces to validate the correctnessof our proposed model. Via real-trace-driven simulations,our results show that the simulation results are quit closeto the theoretical results, which validate the correctnessof our proposed model.

3) Based on the proposed model, we propose a novel ap-proach to improve the performance of data forwarding induty-cycle OppNets by exploiting node contact patternsin duty-cycle OppNets.

4) Extensive real-trace-driven simulations are conductedto evaluate the performance of our proposed data-forwarding strategy. The simulation results show that ourproposed strategy outperforms other recently reportedstrategies under the considered scenarios.

The remainder of this paper is organized as follows. Wepresent the related work in Section II and give the networkmodel in Section III. Section IV derives the contact discoveryprobability and analyzes the relationship between energyconsumption and the contact discovery probability. Weperform real-trace-driven simulations in Section V to validatethe correctness of our proposed model in Section IV. Basedon the proposed model in Section IV, we present our proposeddata-forwarding strategy in Section VI; then, extensive real-

trace-driven simulations are conducted in Section VII toevaluate the performance of our proposed data-forwardingstrategy. We conclude this paper in Section VIII.

II. RELATED WORK

Here, we first introduce the related work about energy-savingmechanisms in OppNets and then introduce the related workabout data-forwarding strategies in OppNets.

A. Energy-Saving Mechanisms in OppNets

Several energy-saving mechanisms have been proposed inOppNets. Since nodes cost much energy in the contact-probingprocess and a high probing frequency means a large amountof energy consumption, some studies have investigated thecontact-probing process to save energy [21]–[24] in OppNets.The impact of contact probing on the probability of missing acontact and the tradeoff between the missing probability andenergy consumption in Bluetooth devices were investigated in[21]. Real trace-driven simulation results show that their pro-posed adaptive contact-probing mechanism, i.e., STAR, con-sumes three times less energy when compared with a constantcontact-probing interval scheme. The impact of contact probingon link duration and the tradeoff between the energy con-sumption and throughput were investigated in [22]. In addition,this paper provides a framework for computing the optimalcontact-probing frequency under energy limitations and adjuststhe probing frequency according to the node-encountering rate.Two novel adaptive schemes for dynamically selecting theparameters of the contact-probing process were introduced andevaluated in [23]. Nodes in the network switches betweentwo radios: a low-power radio, with slow discovery modefor discovering contacts, and a high-power radio, with fastdiscovery mode for transmitting data, depending on a mobilitycontext. Simulation results show that their adaptive algorithmscan reduce energy consumption by 50% and have up to 8%better performance over a static power-conserving scheme.

However, all aforementioned works only focus on investigat-ing the contact-probing process to save energy; they do not takeinto account the energy consumption in idle listening mode.The idle listening mode consumes much more energy than thecontact-probing process. Therefore, some works have appliedthe duty-cycle operation to save energy in OppNets. Stationarybattery-powered nodes, which are called throw-boxes, wereused in [11] to enhance the capacity of OppNets. This workpresents a duty-cycled controller for long-range radios thatpredicts when and for how long the mobile node will be inthe range of the throw-box, and this paper builds a bus-baseddelay-tolerant network test bed to test their proposal. However,the proposal needs beacon position, speed, and direction to feedthe prediction algorithm, and also needs GPS data to obtaintime synchronization, which is difficult to realize for OppNetsconsisting of portable devices with limited energy supplies.Power saving tradeoffs in duty-cycle OppNets as a functionof the wake-up and sleep intervals and as a function of nodecontact duration were investigated in [25]. This work investi-gates the tradeoff between energy saving and contact discovery

ZHOU et al.: CONTACT PATTERNS FOR DATA FORWARDING IN DUTY-CYCLE OPPORTUNISTIC MOBILE NETWORKS 4631

probability, as well as the tradeoff between delay-tolerant objectdissemination time and energy saving in duty-cycle OppNets.However, this work only gives the tradeoff when the contactduration is a certain value. Another work [26] also proposeda model to investigate the tradeoff between energy saving andcontact discovery probability in duty-cycle OppNets. This workgives the tradeoff when the contact duration follows the powerlaw distribution and uses real mobility trace to validate theirproposed model.

B. Data-Forwarding Strategies in OppNets

In the previous works, several data-forwarding strategieshave been proposed in OppNets. Epidemic routing [27] isa widely used data-forwarding strategy in OppNets, whichsimply floods data to the entire network. This strategy canguarantee a high data delivery ratio but is expensive in terms ofdelivery cost since data in the network are essentially flooded.Attempts to reduce the delivery cost are explored in [28] and[29]. A simple approach to reduce the delivery cost of floodingby only forwarding a copy of data with some probability p(p < 1) was proposed in [28]. The spray-and-wait schemeproposed in [29] reduces the delivery cost by assigning a smallnumber of replica copies to a data item and distributes datacopies to a number of relay nodes by the source node, and thenwaits until a relay node meets the destination. Some other worksintroduce a destination-based approach to reduce the deliverycost and to increase the data delivery performance, whereas themetrics are derived from calculating the probability of deliveryto the destination node. FRESH [14] uses the time elapsed sincethe last contact with the destination node as the data-forwardingmetric. Prophet [15] calculates the probability by using the pastcontact histories to predict the probability of meeting a nodeagain, and data copies are forwarded to nodes that have highercontact probability for the destination node. To reduce deliverycosts even more, delegation forwarding in [16] seeks to forwarddata copies only to nodes whose quality metric is the highestso far.

Recently, some works [3] [18]–[20] utilize node contactpatterns to design efficient data-forwarding strategies forOppNets. For example, cumulative contact probability (CCP)as the centrality metric for multicasting in OppNets is proposedin [3], whereas CCP is calculated based on the cumulative nodecontact frequency and the assumption of exponential distri-bution of pairwise node intercontact time. SimBet [19] uses“betweenness” centrality metrics and social similarity to in-crease the performance of data forwarding, in which data copiesare forwarded toward the node with both higher centrality andsimilarity to increase the possibility of finding the potentialforwarder to the destination node. LABEL [20] uses a smalllabel to indicate affiliation information to help data forwardingin OppNets, in which data copies are forwarded to nodes thatare in the same community with the destination node. Thiswork proves the intuition that simply identifying a communitycan improve data delivery, even during a conference where thepeople from different subcommunities tend to mix together.Bubble Rap [18] considers both the community in LABELand the node centrality information in SimBet to increase the

Fig. 1. Contact between two nodes in duty-cycle OppNets. Each nodeswitches from the sleep state to the wake-up state at the beginning of Ton.(a) Effective contact. (b) Missed contact.

data-forwarding performance. Data copies are first forwardedto nodes that have higher global centrality. When data copiesare forwarded to the same community as the destination, thenlocal centrality will be used instead of global centrality as theforwarding metrics, and data copies are continued to bubbleup until the destination is reached or the data are expired.However, these existing strategies are not suitable to the duty-cycle OppNets; this is because the characteristics of the contactprocess in duty-cycle OppNets are obviously different from thatin OppNets, which makes it difficult to analyze node contactpatterns in duty-cycle OppNets.

This paper differs from the previously stated data-forwardingstrategies because our approach proposes a model to investigatethe characteristics of the contact process in duty-cycle OppNets.Hence, it is more suitable for the duty-cycle OppNets thanother data-forwarding strategies designed in OppNets. Fur-thermore, our proposed data-forwarding strategy utilizes nodecontact patterns to aid the design of an efficient data-forwardingstrategy. Therefore, our proposed data-forwarding strategy ismore efficient and suitable for data forwarding in duty-cycleOppNets.

III. NETWORK MODEL

Without loss of generality, we assume that nodes in thenetwork have enough buffer size to store data and that the sizeof each data is small enough so that nodes can complete the dataexchange process in each contact. Similar to the network modelin [25], each node in the network is duty-cycled with two states,i.e., the wake-up state and the sleep state, as shown in Fig. 1.

1) Wake-up state: A node is in the wake-up state duringan interval of time equal to Ton. Nodes in the wake-upstate can exchange data with other nodes, send beaconmessages periodically to discover contacts with othernodes, or listen to the wireless channel to discover beaconmessages from other nodes.

2) Sleep state: a node is in the sleep state during the remain-ing interval of the period T that is equal to Toff . Nodes in


the sleep state switch their wireless interfaces off to saveenergy; thus, they cannot communicate with other nodes.

Note that T = Ton + Toff ; thus, the duty cycle will be(Ton/T ). Since nodes switch from the sleep state to the wake-up state at the beginning of Ton, after choosing a random timeto start, nodes in the network will schedule themselves to be inthe wake-up state for constant time Ton every period T to saveenergy. A certain node in the wake-up state can periodicallysend beacon messages to discover contacts with other nodes;all nodes in the communication range that hear the beaconmessage respond to this node with some information (e.g.,identity, services available, etc.). Based on this information, thisnode can record the contact history with its neighbor nodes.

In OppNets, two nodes contact each other if they are withinthe communication range of each other, and the interval whennodes are continuously in contact with each other is called thecontact duration. Fig. 1 gives an example about the contactbetween two nodes in duty-cycle OppNets. As shown in Fig. 1,a contact between two nodes A and B happens at the beginningof Td and lasts for Td, which represents the contact duration.Let TB be a random variable indicating the time at which nodeB switches from the sleep state to the wake-up state at a certainperiod, and let TA be a random variable indicating the time atwhich node A switches from the sleep state to the wake-upstate at the same period. To facilitate the modeling, as shownin Fig. 1, we make node B to switch from the sleep state tothe wake-up state at time 0 in this period, and we let Ta bea random variable indicating the offset time between nodes Aand B, which is equal to |TA − TB |. Note that, in duty-cycleOppNets, nodes may miss contacts with other nodes when theyswitch from the wake-up state to the sleep state to save energy.Therefore, we divide the contact in duty-cycle OppNets intotwo kinds: the effective contact and the missed contact. The ef-fective contact contains two cases. The first case happens whentwo nodes are both in the wake-up state at the beginning oftheir contact. The second case happens when two nodes are notboth in the wake-up state at the beginning of their contact, butthey will be both in the wake-up state before the contact ends,as shown in Fig. 1(a). Since this kind of contact between twonodes can be discovered by each other during the contact witheach other, we thus regard this kind of contact as the effectivecontact, which can be used for data exchange. The missed con-tact happens when two nodes are not both in the wake-up stateduring contact with each other, as shown in Fig. 1(b). Sincethis kind of contact between two nodes cannot be discoveredby one another, we thus refer to this kind of contact as missedcontact. Note that the contact in OppNets is infrequent, andthe contact process has a significant effect on data forwardingin OppNets. Therefore, in the following, we will propose amodel to investigate the contact process in duty-cycle OppNetsand to analyze the relationship between energy consumptionand contact discovery probability under different situations.

IV. MODELING THE CONTACT PROCESS

IN DUTY-CYCLE OPPNETS

In OppNets, unlike traditional connected networks (e.g.,peer-to-peer networks and Internet-accessible networks), nodes

are intermittently connected. In the previous studies, authorsin [3], [17], and [18] found that the characteristics of contactprocess in OppNets follow a certain regularity. However, induty-cycle OppNets, since nodes in the network operate at aduty cycle and switch between the sleep and wake-up states,several contacts will be missed when nodes switch to the sleepstate. This leads to distinct characteristics of a contact processin duty-cycle OppNets, and this makes it difficult to utilize nodecontact patterns to design an efficient data-forwarding strategy.Therefore, here, we propose a model to investigate the contactprocess in duty-cycle OppNets and analyze the relationshipbetween energy consumption and contact discovery probability.

A. Contact Discovery Probability

Here, we give the definition and expression of the contactdiscovery probability. Nodes in the network wake up and sleepasynchronously, as introduced in Section III. Nodes A and Bswitch from the sleep state to the wake-up state at time TA andTB at a certain period, respectively. Ta indicates the offset timebetween nodes A and B, which is equal to |TA − TB |. SinceTA and TB are independent of each other and each node in thenetwork works for a constant time Ton at every period T , thenwe can obtain that the offset time Ta is uniformly distributedover the period T , which can be expressed as

fa(t) =1T

for 0 ≤ t ≤ T (1)

where fa(t) is the probability distribution function (pdf) of Ta.Let Tct be a random variable indicating the time when

a contact would begin. As shown in Fig. 1(a), Tct can beexpressed as the beginning of Td. Note that authors in [25] statethat “in sparse networks in which the contact rates are low, theintercontact time is higher than the period T .” Since the contactrates in OppNets are also low, e.g., the average intercontacttime in the Infocom 06 trace [30] is 125.95 min, whereas inthe MIT Reality, trace [31] is 334.2 h (or 13.926 days), we alsoassume that the intercontact time in OppNets is higher than theperiod T . Therefore, when a contact occurs, Tct is uniformlydistributed over T and also independent of random variableTa. Td is the lasting duration of the contact. We assume thatthe contact duration Td is an i.i.d. stationary random variablewith a cumulative distribution function (cdf) of Fd(x). Let usdefine Pc (contact discovery probability) as the probability thata contact between two nodes can be discovered by one anotherin duty-cycle OppNets or the contact is an effective contact.There will be a set of different possibilities for calculating thecontact discovery probability Pc, depending on the lengths ofwake-up time Ton, period T , and contact duration Td.

When Ton < Toff , to facilitate the calculation of the contactdiscovery probability Pc, we use the offset time Ta to dividethe contact discovery probability Pc into three parts. Since Ta isuniformly distributed over the period T , we use Pc1 to representthe contact discovery probability when 0 ≤ Ta ≤ Ton, Pc2 torepresent the contact discovery probability when Ton < Ta <T − Ton, and Pc3 to represent the contact discovery probabilitywhen T − Ton ≤ Ta < T . As shown in Fig. 1(a), nodes A andB have overlapped wake-up time with one another if the offset


time Ta is in the range of [0, Ton]. Under this situation, if Tct

is in the range of (0, Ta) and (Ton, T ), a contact happens whentwo nodes are not both in the wake-up state, and if Tct is inthe range of [Ta, Ton], a contact happens when two nodes areboth in the wake-up state. Since the effective contact containstwo cases, then Pc1 is the sum of three parts, which can becalculated as

Pc1 = Pr{0 ≤ Ta ≤ Ton}× [Pr{0 ≤ Tct < Ta}Pr{Tct + Td ≥ Ta}

+Pr{Ta ≤ Tct ≤ Ton}+Pr{Ton < Tct < T}Pr{Tct + Td ≥ T + Ta}] .

(2)

Note that two nodes do not have overlapped wake-up timewith each other when offset time Ta is in the range of (Ton, T −Ton), which indicates that contacts cannot be discovered byeach other under this situation. Therefore, Pc2 is equal to 0when Ton < Ta < T − Ton.

When T − Ton ≤ Ta < T , two nodes have an overlappedwake-up time with each other in the range of [0, Ton + Ta − T ].Under this situation, when Tct is in the range of [0, Ton + Ta −T ], which indicates that a contact happens when two nodes areboth in the wake-up state. When Tct is in the range of [Ton +Ta − T, T ], which indicates a contact happens when two nodesare not both in the wake-up state. Since the effective contactcontains two cases, similar to the calculating process of Pc1,then Pc3 is the sum of two parts, which can be calculated as

Pc3 = Pr{T − Ton ≤ Ta ≤ T}× [Pr{0 ≤ Tct ≤ Ton + Ta − T}

+Pr{Ton + Ta − T < Tct ≤ T}×Pr{Tct + Td ≥ T}] . (3)

Therefore, the contact discovery probability Pc when Ton <Toff can be calculated as Pc = Pc1 + Pc2 + Pc3.

When Ton ≥ Toff , similar to the calculating process of Pc

when Ton < Toff , we also use the offset time Ta to divide thecontact discovery probability Pc into three parts. We use P ′

c1

to represent the contact discovery probability when 0 ≤ Ta ≤T − Ton, P ′

c2 to represent the contact discovery probabilitywhen T − Ton < Ta < Ton, and P ′

c3 to represent the contactdiscovery probability when Ton ≤ Ta < T . Then, we obtain thefollowing expressions:

P ′c1 = Pr{0 ≤ Ta ≤ T − Ton}

× [Pr{0 ≤ Tct ≤ Ta}Pr{Tct + Td ≥ Ta}+Pr{Ta < Tct ≤ Ton}+ Pr{Ton < Tct ≤ T}×Pr{Tct + Td ≥ T + Ta}] (4)

P ′c2 = Pr{T − Ton < Ta ≤ Ton}

× [Pr{0 ≤ Tct ≤ Ta − T + Ton}+Pr{Ta − T + Ton) < Tct ≤ Ta}×Pr{Tct + Td ≥ Ta}+ Pr{Ta < Tct ≤ Ton}+Pr{Ton < Tct ≤ T}Pr{Tct + Td ≥ T}] (5)

P ′c3 = Pr{Ton < Ta < T}

× [Pr{0 ≤ Tct ≤ Ta − T + Ton}+Pr{Ta − T + Ton < Tct ≤ T}×Pr{Tct + Td ≥ T}] . (6)

Then, the contact discovery probability Pc when Ton ≥ Toff

can be calculated as Pc = P ′c1 + P ′

c2 + P ′c3.

B. Relationship Between Energy Consumption and theContact Discovery Probability

Given the relationship among contact discovery probabilityPc, period T , wake-up interval Ton, and contact duration Td, wenow explore the relationship between energy consumption andthe contact discovery probability Pc under different situations.When contact duration Td is distributed according to a givendistribution, we can analytically obtain the relationship betweenenergy consumption and the contact discovery probability. In[21], it was found that the cumulative contact duration inreal mobility traces follows the power law distribution (Paretodistribution). Therefore, in this paper, we also assume that thecontact duration Td follows the power law distribution and canbe expressed as

Fd(x) =

{0, x < τ1 − (x/τ)−k, x ≥ τ

(7)

where τ is the minimum value of Td, and k is the slope of thedistribution.

Then, we get the expression of Pc under different situationsby substituting (1) and (7) into (2)–(6). When Ton < Toff , Pc1

and Pc3 can be expressed as

Pc1 =1T 2

{τk

[T 2−k − (T − Ton)

2−k]

(1 − k)(2 − k)+ 0.5T 2

on

+ τTon − τTon

1 − k

}(8)

Pc3 =1T 2

{τk

[T 2−k − (T − Ton)

2−k]

(1 − k)(2 − k)+ 0.5T 2

on

+ τTon − τTon

1 − k

}. (9)

The Appendix describes how to obtain the given twoexpressions.

Since Pc2 = 0, then Pc is the sum of the other two parts andcan be expressed as

Pc =2T 2

{τ2k

[T 2−k − (T − Ton)

2−k]

(1 − k)(2 − k)

+ 0.5T 2on + τTon − τTon

1 − k

}. (10)

When Ton ≥ Toff , the expression of Pc is divided into threeparts by τ : 0 < τ ≤ T − Ton, T − Ton < τ < 2(T − Ton), and


Fig. 2. Relationship between energy consumption and contact discovery probability under different situations. (a) Different τ . (b) Different T . (c) Different k.

2(T − Ton) ≤ τ ≤ T . The computing process when Ton ≥Toff is similar to the computing process when Ton < Toff ;therefore, here, we omit the computing process. When 0 < τ ≤T − Ton, Pc is the sum of the three parts: P ′

c1, P ′c2, and P ′

c3.Then, we can obtain the following expression:

Pc =1T 2

{2τk

[(2T − 2Ton)

2−k − (T − Ton)2−k

](1 − k)(2 − k)

+T 2on − 2τ(T − Ton)

1 − k+ (4Ton − 2T )

×[(τk(T − Ton)

1−k

1 − k− τ

1 − k

]+ 2τTon

}. (11)

When T − Ton < τ < 2(T − Ton), similar to the approachgiven, we obtain the following expression:

Pc =1T 2

{8TTon − 4T 2

on − 4τTon + 4τT − τ2 − 3T 2

+2τ2

[(2T − 2Ton)

2−k − τ2−k]

(1 − k)(2 − k)

− 2τ(2T − 2Ton − τ)

1 − k

}. (12)

When 2(T − Ton) ≤ τ ≤ T or τ > T , similar to the ap-proach above, we can obtain Pc = 1.

After obtaining the expression of Pc under different situ-ations, here, we represent Pc graphically and show the rela-tionship between energy consumption and contact discoveryprobability when the contact duration follows the power lawdistribution. Energy consumption is described as the duty cycleTon/T , whereas a larger duty cycle to achieve a certain Pc

means more energy consumption. Fig. 2 shows the relationshipbetween energy consumption and contact discovery probabilitywhen the contact duration follows the power law distribution.It can be found that the contact discovery probability Pc isincreasing along with the duty cycle, which means that nodes inthe network have to consume more energy to increase the net-work performance. Moreover, when Ton ≥ Toff and τ ≥ 2(T −Ton), contact discovery probability Pc is always 100%, whichmeans that Pc is always 100% when the duty cycle is no lessthan max{0.5, 1 − (τ/2T )}. In Fig. 2(a), it can be found thatthe contact discovery probability Pc is increasing along withτ , which means that larger τ needs less energy to achieve

a certain Pc. In Fig. 2(b), it can be found that the contactdiscovery probability Pc increases when T decreases, and Pc

reaches 100% more quickly when T is smaller; thus, smaller Tneeds less energy to achieve a certain Pc. However, T cannotbe too small because small T means that the nodes have toswitch between the wake-up state and the sleep state more oftenand that the switching process also consumes a lot of energy.Fig. 2(c) shows that contact discovery probability Pc increaseswhen k decreases; thus, smaller k needs less energy to achieve acertain Pc.

This can be summarized with the following conclusions.Given that the contact duration Td follows the power lawdistribution, we analytically obtain the relationship betweenenergy consumption and contact discovery probability. It canbe found that the contact discovery probability Pc increaseswhen the duty cycle increases, and Pc is always 100% whenthe duty cycle is no less than max{0.5, 1 − (τ/2T )}. Fig. 2(b)shows the situation when T = τ = 40 s. It can be found thatPc is always 100% when the duty cycle is no less than 50%.Moreover, the contact discovery probability Pc increases whenτ increases, and decreases when k increases. From here, it canbe found that the contact duration has a significant impact on thecontact discovery probability. It is worth noting that the modelproposed in [25] only gives the contact discovery probabilitywhen the contact duration Td is a certain value; thus, results in[25] only analyze the relationship between energy consumptionand the contact discovery probability when the contact durationTd is a certain value.

V. MODEL VALIDATION

Here, we use the real mobility trace Infocom 06 collectedfrom realistic environment to validate our proposed model. TheInfocom 06 trace was collected by 78 volunteers using iMoteswith Bluetooth. Each device detects the vicinity every 120 s.When a device discovers other devices, it records the contacttime and the ID of other devices. By using the informationrecorded by these mobile devices, we can obtain knowledgeof the contact duration between two nodes. If a device isdiscovered in m contiguous scans, then the duration of thecontact is the difference between the discovery time in the mthscan and the first scan. If a device is only detected in one scan,similar to the approach in [21], we treat the duration of contactas 120 s. Then, we look at the cumulative contact duration


Fig. 3. Cumulative contact duration distribution.

distribution in the Infocom 06 trace. Fig. 3 plots the 1 − Fd(x)curve in log–log scale. It can be found that the cumulativecontact duration follows the power law distribution. By curvefitting, we can estimate Fd(x) = 1 − (x/τ)−k with τ = 120 sand k = 1.523. The fact that the cumulative contact durationfollows the power law distribution has been also validated byother studies [21], [32].

After introducing the real mobility trace, we then use it tovalidate the correctness of our proposed model. Fig. 4 showsthe comparison between the real-trace-driven simulation resultsand the theoretical results. Fig. 4(a) shows the comparisonbetween the real-trace-driven simulation results and the the-oretical results obtained in this paper. It can be found thatthe theoretical results are quite close to the real-trace-drivensimulation results when the duty cycle is increasing, which con-firms the correctness of our proposed model. Fig. 4(b) showsthe comparison between the real-trace-driven simulation resultsand the theoretical results obtained in [25]. It can be foundthat the real-trace-driven simulation results and the theoreticalresults have large errors when the contact duration Td = 50,200, and 400 s, respectively. From here, it can be found that ourproposed model is more suitable to the real environment thanthe model proposed in [25].

VI. DATA FORWARDING STRATEGY

IN DUTY-CYCLE OPPNETS

Here, we propose a data-forwarding strategy for duty-cycle OppNets. The proposed data-forwarding strategy aims toforward data copies toward the opportunistic forwarding paths,which maximize data delivery probability. To obtain the datadelivery probability of each opportunistic forwarding path induty-cycle OppNets, we start off by analyzing the pairwisecontact duration distribution in real mobility traces.

A. Pairwise Contact Duration Distribution in RealMobility Traces

In Section IV, we have given the expression of the contactdiscovery probability Pc when the contact duration follows the

Fig. 4. Comparison between real-trace-driven simulation results and theoret-ical results. (a) Validation of our proposed model. (b) Validation of the modelproposed in [25].

power law distribution. Note that the previous studies [21],[32] only show that the cumulative contact duration followsthe power law distribution, and they do not take into accountthe distribution of the pairwise contact duration. Althoughsome studies [33], [34] have the assumption that the pairwisecontact duration follows the power law distribution, they didnot validate it experimentally. Therefore, in this paper, we firstuse two real mobility traces, i.e., Infocom 06 and MIT Reality,to validate the hypothesis that the pairwise contact duration alsofollows the power law distribution.

To validate this hypothesis, we conduct chi-square hypothe-sis test [35] on each contacted node pair in the given traces, totest whether the hypothesis “the pairwise contact duration alsofollows the power law distribution.” Similar to the approach inSection V, we first use curve fitting to estimate the pairwisecontact duration distribution parameters k and τ of each con-tacted node pair, where k is the slope of the distribution, and τis the minimum value of the contact duration. Then, we conducta chi-square hypothesis test on each contacted node pair inthe given traces by comparing the contact duration sample fre-quencies with the theoretical probabilities. Since the power lawdistribution is continuous, in the chi-square tests, we divide the


TABLE IACCEPTANCE RATIO OF CHI-SQUARE TESTS FOR THE Infocom 06 TRACE

TABLE IIACCEPTANCE RATIO OF CHI-SQUARE TESTS FOR THE MIT Reality TRACE

range of the sample values into several test intervals and com-pare the sample frequencies with theoretical probabilities oneach interval. The results of the acceptance ratio for the giventraces under different significance levels α are listed in Tables Iand II. The results show that more than 80% of the contactednode pairs in the given traces pass the test when the test intervalis 5, and more than 90% of the contacted node pairs in thegiven traces pass the test when the test interval increases to 15.

Based on the given experimental results, we validate thehypothesis that the pairwise contact duration follows the powerlaw distribution. Therefore, the pairwise contact discoveryprobability Pc(ij) between nodes i and j can be expressed asequations in Section IV when the contact duration follows thepower law distribution. Then, we can use this pairwise contactdiscovery probability to investigate node contact patterns induty-cycle OppNets.

B. Opportunistic Forwarding Path in Duty-Cycle OppNets

In OppNets, nodes’ contact can be described as network-connected graph G(V,E). The random contact process betweennodes i and j can be modeled as eij ∈ E, where i, j ∈ V .Some recent studies [3], [36], [37] have found that the pairwiseintercontact time in real mobility traces follows the exponentialdistribution. Specifically, in [3], a chi-square hypothesis testis conducted on each contacted node pair in the Infocom 06and MIT Reality traces to test whether “the pairwise nodeintercontact time follows the exponential distribution.” Theirresults demonstrate that, when enough number of test intervals(≥ 10) is used, over 85% of the contacted node pairs in thegiven traces pass the test. Therefore, in this paper, we alsoassume that the pairwise intercontact time in OppNets followsthe exponential distribution. Then, the contact frequency λij

between nodes i and j is indicated by the contact rate and canbe computed by the following time average method:

λij =n

Σnl=1T

lij

. (13)

Thus, the pdf of the intercontact time Xij between nodes iand j can be expressed as

fXij(t) = λije

−λijt. (14)

Note that, in duty-cycle OppNets, each contact between twonodes has a pairwise contact discovery probability, which is

Fig. 5. Opportunistic forwarding path in OppNets.

Fig. 6. Edge weights of a certain opportunistic forwarding path between Sand D (a) Path edge weights in OppNets. (b) Path edge weights in duty-cycleOppNets.

relevant to the contact duration between two nodes. Therefore,according to the thinning property of the Poisson process [38],the pairwise intercontact time X ′

ij between nodes i and j induty-cycle OppNets also follows the exponential distribution,and the contact frequency λ′

ij between nodes i and j in duty-cycle OppNets can be calculated as Pc(ij)λij , where Pc(ij)is the pairwise contact discovery probability between nodes iand j.

Thus, the pdf of the pairwise intercontact time X ′ij between

nodes i and j in duty-cycle OppNets can be expressed as

fX′ij(t) = Pc(ij)λije

−Pc(ij)λijt. (15)

After obtaining the distribution of the pairwise intercontacttime in duty-cycle OppNets, we then introduce the concept ofthe opportunistic forwarding path [39]. As shown in Fig. 5,we assume that there is a certain data item that is transferredfrom the source node S to the destination node D, and thereare L opportunistic forwarding paths from S to D. As shownin Fig. 6, the definition of the opportunistic forwarding path isgiven as follows.

Definition 1: In OppNets, a certain m-hop opportunisticforwarding path between S and D, which is denoted as l,consists of node set {S,R1, R2, . . . , Rm−1, D} and edge set{e1, e2, . . . , em} with edge weights {λ1, λ2, . . . , λm}, where{λ1, λ2, . . . , λm} are the contact rates (or contact frequen-cies) of each adjacent node pair along the opportunistic for-warding path in OppNets. In duty-cycle OppNets, since eachcontact between two nodes has a pairwise contact discov-ery probability, the corresponding edge weights change to{Pc(1)λ1, Pc(2)λ2, . . . , Pc(m)λm}.

It is worth noticing that, when m is equal to 1, which meansthat there exists a direct edge between S and D, the node setwill be changed to {S,D}, and the corresponding edge weight


is λSD. Note that the intercontact time X ′i between two nodes

Ri−1 and Ri in duty-cycle OppNets follows the exponentialdistribution with a pdf of fX′

i(t) = Pc(i)λie

−Pc(i)λit. As aresult, the total time to transfer a data item from S to Dalong opportunistic forwarding path l in duty-cycle OppNetsis Yl =

∑mi=1 X

′i, and the pdf fYl

(t) can be calculated as

fYl(t) = fX′

1(t)⊗ fX′

2(t), . . . ,⊗fX′

m(t) (16)

where ⊗ is the convolution operator.Then, by referring to the theoretical results in [3], we have

the following theorem.Theorem 1: For a certain m-hop opportunistic forwarding

path l with edge weights {Pc(1)λ1, Pc(2)λ2, . . . , Pc(m)λm},when m is larger than 1, pYl

(t) is expressed as

fYl(t) =

m∑i=1

Cmi fXi

′(t) (17)

where the coefficients are given as follows:

Cmi =

m∏j=1,j �=i

Pc(j)λj

Pc(j)λj − Pc(i)λi. (18)

From fYl(t), the probability that a certain data item is

successfully delivered from S to D within time T0 alongan opportunistic forwarding path l in duty-cycle OppNets isexpressed as

PrYl(T0) =P (Yl < T0) =

∫ T0

0

fYl(t)dt

=

m∑i=1

Cmi (1 − e−Pc(i)λiT0). (19)

Note that if there exists an edge directly between nodes Sand D, which means that m is equal to 1, then the probabilitythat a certain data item is successfully delivered from S to Dwithin time T0 in duty-cycle OppNets is

PrYl(T0) =P (Yl < T0) =

∫ T0

0

Pc(SD)λSDe−Pc(SD)λSDtdt

= 1 − e−Pc(SD)λSDT0 (20)

where Pc(SD) is the pairwise contact discovery probabilitybetween nodes S and D.

C. Maximum Data Delivery Probability Forwarding Strategy

After obtaining the data delivery probability along a certainopportunistic forwarding path in duty-cycle OppNets, here,we introduce our proposed data-forwarding strategy for duty-cycle OppNets. Take two nodes A and B as an example.When node A encounters node B, we assume that node Ahas a copy of the data item that is delivered from S to D,and the remaining time-to-live (TTL) is Tr; then, it has todecide whether or not to forward a data copy to node B. Notethat there are LA opportunistic forwarding paths between Aand D, LB opportunistic forwarding paths between B and D,

and each opportunistic forwarding path has a data deliveryprobability. Therefore, we use PrAD

max(Tr) and PrBDmax(Tr) to

indicate the maximum data delivery probability of these LA

and LB opportunistic forwarding paths in duty-cycle OppNets,respectively, which are calculated as

PrADmax(Tr) = max

{PrAD

Y1(Tr),Pr

ADY2

(Tr), . . . ,PrADYLA

(Tr)}

(21)

PrBDmax(Tr) = max

{PrBD

Y1(Tr),Pr

BDY2

(Tr), . . . ,PrBDYLB

(Tr)}.

(22)

Then, we use the maximum data delivery probability asthe data-forwarding metrics and introduce our proposed data-forwarding strategy. The pseudocode in Algorithm 1 depicts thebasic operations of our proposed data-forwarding strategy froma node’s perspective. When node A encounters node B, theyfirst compare each data’s maximum data delivery probabilityin their buffer with each other. Then, the node with a lowermaximum data delivery probability forwards a copy of thecorresponding data to the node with a higher maximum datadelivery probability.

Algorithm 1 Maximum data delivery probability forwardingstrategy

1: When node A encounters node B and the remaining TTLis Tr

2: for all data(i) stored at the buffer of node A3: if node B does not have data(i) in its buffer4: if data(i) · destination = B or data(i) ·

PrBDmax(Tr) > data(i) · PrAD

max(Tr) then5: A forwards a copy of data(i) to B6: end if7: end if8: end for9: node B do the same loop as node A

D. Overhead Reduction

As introduced earlier, to conduct the Algorithm 1, nodes Aand B need to calculate the maximum data delivery probabilityamong LA opportunistic forwarding paths between A and D,as well as LB opportunistic forwarding paths between B andD using (21) and (22), respectively. If the length of theseopportunistic forwarding paths is long or the value of LA andLB is large, the calculation overhead for nodes A and B will behuge. Moreover, the overhead for nodes A and B to collect nodecontact patterns (including the pairwise intercontact time andthe pairwise contact duration) of these LA and LB opportunisticforwarding paths will be also huge.

To reduce the calculation and collection overhead, in thispaper, we exclude those opportunistic forwarding paths, whichare larger than three hops. This is because most node pairs inthe Infocom 06 and MIT Reality traces only need less than threehops to connect each other. As shown in Fig. 7, when the num-ber of minimum hops to connect node pairs in the Infocom 06trace is less than three, the cumulative percentage is more than


Fig. 7. Percentage of the number of minimum hops to connect nodes pairs inthe Infocom 06 and MIT Reality traces.

95%, whereas the corresponding value in the MIT Reality traceis more than 97%. Since a larger number of hops means lessdata delivery probability of the opportunistic forwarding path,we can exclude those opportunistic forwarding paths, which arelarger than three hops. Furthermore, in the calculation processof the maximum data delivery probability, we also excludethose opportunistic forwarding paths, which are subtrees of acertain opportunistic forwarding path. For example, we assumethat there are three opportunistic forwarding paths from S toD, i.e., path 1 S−A−D, path 2 S−A−B−D and path 3S−A−B−C−D. We can exclude paths 2 and 3. This isbecause Pr1(Tr) is absolutely larger than Pr2(Tr) and Pr3(Tr).

VII. PERFORMANCE EVALUATION

Here, we mainly focus on evaluating the performance of ourproposed data-forwarding strategy, and investigating the impactof some parameters on the performance of our proposed data-forwarding strategy. Here, we use Maximum to indicate ourproposed data-forwarding strategy.

A. Simulation Setup

We evaluate the performance of our proposed data-forwarding strategy Maximum in terms of delivery ratio anddelivery cost. The delivery ratio is the ratio of data successfullydelivered by nodes, and the delivery cost is the average numberof data copies forwarded in the network. The delivery delay isnot taken into consideration, as long as the data can be deliveredon time. In our simulation studies, we compare our proposeddata-forwarding strategy Maximum with the following threedata-forwarding strategies.

1) Epidemic Routing: Data copies are simply flooded tonodes in network.

2) Bubble Rap: Data copies are first forwarded to nodesthat have higher global centrality. When data copies areforwarded to the same community as the destinationnode, then local centrality will be used instead of globalcentrality as the forwarding metrics, and data copies

TABLE IIIBASIC STATISTICS OF THE TRACES

continue to bubble up until the destination is reached orthe data expire.

3) Prophet: Nodes in the network use the past contacthistory to predict the probability of meeting a node again,and data copies are forwarded to nodes that have highercontact probability for the destination node.

We use two real mobility traces Infocom 06 [30] and MITReality [31] collected from real environments to evaluate theperformance of the selected data-forwarding strategies. Usersin these two traces are all carrying Bluetooth-enabled portabledevices, which record contacts by periodically detecting theirpeers nearby. The traces cover various types of corporate envi-ronments and have various experiment periods. The details ofthe traces are summarized in Table III.

We use a part of the traces (the first day of Infocom 06,and the September and October of MIT Reality) to model andcharacterize node contact patterns (i.e., calculate the contactfrequency λij and distribution parameters of the pairwise con-tact duration for our proposed data-forwarding strategy, andcalculate the betweenness centrality and form a community forBubble Rap, respectively). We use another part of the traces (thesecond day of Infocom 06 and the November of MIT Reality)to evaluate the performance of the selected data-forwardingstrategies.

B. Performance Comparison

Here, we compare the performance of our proposed data-forwarding strategy with other existing data-forwarding strate-gies in the Infocom 06 and MIT Reality traces, respectively.Here, Epidemic Routing represents the baseline for the bestdelivery ratio performance and the baseline for the worst de-livery cost performance. This is because Epidemic Routingalways finds the best possible opportunistic forwarding path tothe destination but is expensive in terms of delivery cost sincedata copies in Epidemic Routing are simply flooded to nodesin the network. As a result, the ultimate goal of our proposeddata-forwarding strategy Maximum is to achieve delivery ratioas close to Epidemic Routing as possible and achieve deliverycost as small as possible.

Fig. 8 shows the performance comparison of our proposeddata-forwarding strategy Maximum with other existing data-forwarding strategies when T is 10 min and TTL is 1 h in theInfocom 06 trace. It can be found that the delivery ratio and costare both tightly related to the duty cycle (Ton/T ). As the dutycycle increases from 10% to 90%, the delivery ratio and costboth increase, particularly when the duty cycle is less than 50%.This is because fewer contacts will be missed when the duty


Fig. 8. Performance comparison of Maximum with other existing data-forwarding strategies when T is 10 min and TTL is 1 h in the Infocom 06 trace.(a) Delivery ratio. (b) Delivery cost.

Fig. 9. Performance comparison of Maximum with other existing data-forwarding strategies when T is 20 min and TTL is five days in the MIT Reality trace.(a) Delivery ratio. (b) Delivery cost.

cycle increases, or more contacts can be used for data exchangeswhen the duty cycle increases, resulting in the increase in thedelivery ratio and cost. Moreover, as the duty-cycle increases,Epidemic Routing performs best in terms of delivery ratio andperforms worst in terms of delivery cost, as expected. AlthoughEpidemic Routing outperforms Maximum in terms of deliveryratio, however, the delivery cost of Epidemic Routing is almostthree to five times of Maximum, whereas the delivery ratio ofEpidemic Routing is only 10%–15% larger than Maximum.Maximum outperforms Bubble Rap and Prophet in terms ofdelivery ratio, and the delivery cost is only slightly larger thanthat of Bubble Rap. The main reason is that Maximum takesnode contact patterns in duty-cycle OppNets into considerationand manages to forward data copies toward a better path tothe destination in duty-cycle OppNets. Therefore, Maximumcan achieve a high delivery ratio with a low delivery cost.It is worth noting that Bubble Rap performs worst in termsof delivery ratio in duty-cycle OppNets, although the deliverycost of Bubble is the least. The main reason is that BubbleRap is a node contact pattern-based data-forwarding strategythat is designed in OppNets; however, the node contact pat-tern in duty-cycle OppNets is obviously different from that inOppNets. Therefore, the social relationship between nodes andthe centrality of nodes in OppNets is not suitable for those induty-cycle OppNets, which makes it difficult to forward datacopies toward a better path to the destination in duty-cycleOppNets.

Fig. 9 shows the performance comparison of our proposeddata-forwarding strategy Maximum with other existing data-

forwarding strategies when T is 20 min and TTL is five daysin the MIT Reality trace. It can be found that, similar to theresults in Fig. 8, the delivery ratio and cost are also both tightlyrelated to the duty cycle. Moreover, as the duty cycle increases,Epidemic Routing also performs best in terms of delivery ratioand performs worst in terms of delivery cost as expected. Inaddition, our proposed data-forwarding strategy outperformsBubble Rap and Prophet in terms of delivery ratio, and thedelivery cost is only slightly larger than that of Bubble Rap.It is worth noting that the delivery cost of Prophet severelydecreases in Fig. 9, compared with the results in Fig. 8. Themain reason is that the contacts in the MIT Reality trace aremuch sparser than that in the Infocom 06 trace, particularlywhen the duty-cycle operation is applied to the network. There-fore, it is difficult to compare nodes’ probabilities of contactingthe destination to make forwarding decisions, resulting in thedecrease in delivery cost in Prophet.

To summarize, the delivery ratio and cost are both tightlyrelated to the duty cycle in the Infocom 06 and MIT Realitytraces. Moreover, Maximum outperforms Bubble Rap andProphet in terms of delivery ratio with reasonable delivery cost.Therefore, compared with other existing data-forwarding strate-gies, Maximum is more efficient and suitable for duty-cycleOppNets.

C. Impact of T and TTL

Here, we carry out experiments when T is different inthe Infocom 06 trace, and when TTL is different in the MIT


Fig. 10. Performance of Maximum when T is different in the Infocom 06 trace. (a) Delivery ratio. (b) Delivery cost.

Fig. 11. Performance of Maximum when TTL is different in the MIT Reality trace. (a) Delivery ratio. (b) Delivery cost.

Reality trace, aiming to check the impact of the changing pa-rameters on the performance of our proposed data-forwardingstrategy.

Fig. 10 shows the impact of T on the performance of ourproposed data-forwarding strategy in the Infocom 06 trace.As T increases from 2 to 30 min, the delivery ratio andcost of our proposed data-forwarding strategy both decrease.The main reason is that the contact discovery probabilitydecreases as T increases. Therefore, more contacts will bemissed when T increases, or fewer contacts can be used fordata exchanging, which causes the decrease in delivery ratioand cost.

Fig. 11 shows the impact of TTL on the performance of ourproposed data-forwarding strategy in the MIT Reality trace. Itcan be found that the delivery ratio and cost of our proposeddata-forwarding strategy both increase as TTL increases fromone to three days. A reasonable explanation is that, when TTLincreases, nodes have more time to deliver the data to thedestination. Therefore, more nodes are involved in the data-forwarding process, resulting in the increase in the deliveryratio and cost.

In summary, T and TTL both have a significant impacton the performance of our proposed data-forwarding strategy.Although increasing the value of T can decrease the deliverycost, it also decreases the delivery ratio of our proposed data-forwarding strategy. Similarly, increasing the value of TTLcan increase the delivery ratio, but it also obviously increasesthe delivery cost of our proposed data-forwarding strategy.Therefore, we should choose an appropriate value of T and TTLaccording to different applications.

VIII. CONCLUSION

In this paper, we have proposed a model to investigatethe contact process in duty-cycle OppNets and analyzed therelationship between energy consumption and the contact dis-covery probability under different situations. Moreover, weused real-trace-driven simulations to validate the correctnessof our proposed model. Then, based on the proposed model,we have proposed a novel data-forwarding strategy for duty-cycle OppNets. The proposed data-forwarding strategy usesnode contact patterns to aid the design of the data-forwardingstrategy for duty-cycle OppNets and manages to forward datacopies toward the opportunistic forwarding paths that maximizedata delivery probability. Extensive real-trace-driven simulationresults show that our proposed data-forwarding strategy isclose to Epidemic Routing in terms of delivery ratio but withsignificantly reduced delivery cost. Additionally, our proposeddata-forwarding strategy outperforms Bubble Rap and Prophetin terms of delivery ratio with reasonable delivery cost.

APPENDIX

When Ton < Toff , since the contact duration Td follows thepower law distribution, as shown (7), then the expression of Pc

is divided into three parts by τ : 0 < τ ≤ Ton, Ton < τ ≤ T −Ton, and T − Ton < τ ≤ T . When 0 < τ ≤ Ton, according to(2), Pc1 can be calculated as

Pc1 =1T 2

Ton∫0

dTa

⎛⎝ Ta∫

0

Pr{Tct + Td ≥ Ta}dTct +

Ton∫Ta

dTct


+

T∫Ton

Pr{Tct + Td ≥ T + Ta}dTct

⎞⎠

=1T 2

⎧⎨⎩

τ∫0

dTa

⎡⎣ Ta∫

0

dt+ Ton − Ta +

τ∫Ta

dt

+

T+Ta−Ton∫τ

(t

τ

)−k

dt

⎤⎦

+

Ton∫τ

dTa

⎡⎣ τ∫

0

dt+

Ta∫τ

(t

τ

)−k

dt+ Ton − Ta

+

T+Ta−Ton∫Ta

(t

τ

)−k

dt

⎤⎦⎫⎬⎭

=1T 2

{τk

[T 2−k − (T − Ton)

2−k]

(1 − k)(2 − k)

+ 0.5T 2on − τTon

1 − k+ τTon

}. (23)

Similar to the calculating process given, according to (3), wecan obtain that Pc3 = Pc1.

When Ton < τ ≤ T − Ton and T − Ton < τ ≤ T , similar tothe calculating process given and according to (2) and (3), wecan obtain that the expressions of Pc1 and Pc3 are the same asthe expression when 0 < τ ≤ Ton. Thus, Pc can be expressedas (10).

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Huan Zhou is currently working toward the Ph.D.degree with the Department of Control Scienceand Engineering, State Key Laboratory of IndustrialControl Technology, Zhejiang University, Hangzhou,China.

From November 2012 to May 2013, he wasa Visiting Scholar with Temple University,Philadelphia, PA, USA. He is currently a memberof the Networked Sensing and Control Group,Key Laboratory of Industrial Control Technology,Zhejiang University. His research interests include

data transmission and energy saving in mobile social networks and opportunis-tic mobile networks.

Jiming Chen (M’08–SM’11) received the B.Sc. andPh.D. degrees in control science and engineeringfrom Zhejiang University, Hangzhou, China, in 2000and 2005, respectively.

In 2006, he was a Visiting Researcher with theNational Institute for Research in Computer Scienceand Control (INRIA), Paris, France; in 2007, withthe National University of Singapore, Singapore;and, from 2008 to 2010, with the University ofWaterloo, Waterloo, ON, Canada. He is currentlya Full Professor with the Department of Control

Science and Engineering and the Coordinator of the Networked Sensing andControl Group with the State Key Laboratory of Industrial Control Tech-nology, Zhejiang University, Hangzhou, China. His research interests includeestimation and control over sensor networks, sensor and actuator networks, andcoverage and optimization in sensor networks.

Dr. Chen currently serves as an Associate Editor for several internationaljournals, including the IEEE TRANSACTIONS ON PARALLEL AND DISTRIBU-TION SYSTEMS, the IEEE TRANSACTIONS ON INDUSTRIAL ELECTRONICS,and IEEE NETWORKS. He is a Guest Editor for the IEEE TRANSACTIONS

ON AUTOMATIC CONTROL, Computer Communication (Elsevier), WirelessCommunication and Mobile Computer (Wiley), and the Journal of Networkand Computer Applications (Elsevier). He has also served as a Cochair of theAd hoc and Sensor Network Symposium of the IEEE Global CommunicationsConference in 2011, the General Symposium Cochair of the Association forComputing Machinery International Wireless Communications and MobileComputing Conference in 2009 and 2010, the Medium Access Control TrackCochair of the International Wireless Internet Conference in 2010, the PublicityCochair of the IEEE International Conference on Mobile Ad hoc and SensorSystems (IEEE MASS) in 2011, the Publicity Cochair of the IEEE InternationalConference on Distributed Computing in Sensor Sytems in 2011, the PublicityCochair of the IEEE International Conference on Distributed Computing Sys-tems (IEEE ICDCS) in 2012, and a Technical Program Committee memberof IEEE ICDCS 2010, IEEE MASS 2010, the IEEE Communications SocietyConference on Sensor, Mesh and Ad Hoc Communications and Networks in2011, the IEEE International Conference on Computer Communications in2011 (IEEE INFOCOM), IEEE INFOCOM 2012, IEEE ICDCS 2012, amongothers.

Hongyang Zhao received the B.E. degree in automa-tion from Shanghai Jiaotong University, Shanghai,China, in 2011. He is currently working toward theM.S. degree with the Department of Control Scienceand Engineering, State Key Laboratory of IndustrialControl Technology, Zhejiang University, Hangzhou,China.

He is currently a member of the Networked Sens-ing and Control Group, State Key Laboratory ofIndustrial Control Technology, Zhejiang University.His research interests include delay-tolerant net-

works and mobile social networks.

Wei Gao (M’12) received the B.E. degree in electri-cal engineering from the University of Science andTechnology of China, Hefei, China, in 2005 and thePh.D. degree in computer science from PennsylvaniaState University, University Park, PA, USA, in 2012.

He is currently an Assistant Professor with theDepartment of Electrical Engineering and ComputerScience, University of Tennessee, Knoxville, TN,USA. His research interests include wireless andmobile network systems, mobile social networks,cyber–physical systems, and pervasive and mobile

computing.

Peng Cheng (M’10) received the B.E. degree in au-tomation and the Ph.D. degree in control science andengineering from Zhejiang University, Hangzhou,China, in 2004 and 2009, respectively.

He is currently an Associate Professor with theDepartment of Control Science and Engineering,Zhejiang University. His research interests includenetworked sensing and control, cyber–physical sys-tems, and robust control.

Dr. Cheng served as the Publicity Cochair for theIEEE International Conference on Mobile Ad hoc

and Sensor Systems in 2013.

on exploiting contact patterns for data forwarding in duty ...weigao/publications/tvt13.pdf ·...

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