Efficient Routing in Delay Tolerant Networks withCorrelated Node Mobility

Eyuphan Bulut, Sahin Cem Geyik, Boleslaw K. SzymanskiDepartment of Computer Science and Center for Pervasive Computing and Networking

Rensselaer Polytechnic Institute, 110 8th Street, Troy, NY 12180, USA{bulute, geyiks, szymansk}@cs.rpi.edu

Abstract—In a delay tolerant network (DTN), nodes are con-nected intermittently and the future node connections are mostlyunknown. Since in these networks, a fully connected path fromsource to destination is unlikely to exist, message delivery relieson opportunistic routing. However, effective forwarding basedona limited knowledge of contact behavior of nodes is challenging.Most of the previous studies looked at only the pairwise noderelations to decide routing. In contrast, in this paper, we analyzethe correlation between the meetings of each node with othernodes and focus on the utilization of this correlation for efficientrouting of messages. We introduce a new metric calledconditionalintermeeting time, which computes the average intermeeting timebetween two nodes relative to a meeting with a third node usingonly the local knowledge of the past contacts. Then, we show howwe can utilize the proposed metric on the existing DTN routingprotocols to improve their performance. For shortest-path basedrouting protocols in DTNs, we propose to route messages overconditional shortest paths in which the link cost between nodesare defined by conditional intermeeting times. Moreover, formetric-based forwarding protocols, we propose to use conditionalintermeeting time as an additional delivery metric while makingforwarding decisions of messages. Our trace-driven simulationson three different datasets show that the modified algorithmsperform better than the original ones.

I. I NTRODUCTION

Delay tolerant networks (DTN) [1]-[3], also called as in-termittently connected mobile networks (ICMN), are wirelessnetworks in which at any given time instance, the probabilitythat there is an end-to-end path from a source to a destinationis low. This is caused by the high mobility and low density ofthe nodes in the network. This property makes the routing ofmessages in DTNs a challenging problem. The conventionalsolutions do not generally work in DTNs because they assumethat the network is stable most of the time and failures of linksbetween nodes are infrequent. Therefore, the routing problemis still an active research area in DTNs [4].

With the advent of DTNs, routing utilizingstore-carry-and-forward paradigm has been widely applied. When a node has

This research was sponsored by US Army Research Laboratory and theUK Ministry of Defence and was accomplished under Agreement NumberW911NF-06-3-0001 and under Cooperative Agreement Number W911NF-09-2-0053. The views and conclusions contained in this documentare those ofthe authors, and should not be interpreted as representing the official policies,either expressed or implied, of the US Army Research Laboratory, the U.S.Government, the UK Ministry of Defense, or the UK Government. The USand UK Governments are authorized to reproduce and distribute reprints forGovernment purposes notwithstanding any copyright notation hereon.

a message but no connection to any other node in the network,it stores the message in its buffer and carries the message untilit meets a new node that does not have this message. If theencountered node is assessed to be useful in the delivery of themessage, then the message is transferred to it. Several DTNrouting algorithms based on this paradigm have been proposedrecently. In each, different techniques (single-copy [5],multi-copy [6]-[8], erasure coding [9] [10]) with slightly differentgoals have been utilized. A survey of previous DTN routingalgorithms can be found in [11].

Since DTNs consist of mobile agents that contact inter-mittently, recent studies on DTN routing have focused onthe analysis of real mobility traces (human [16] [17], ve-hicular [18] etc.) and utilized extracted characteristicsof themobile objects on the design of forwarding algorithms forDTNs. These designs proposed in previous work led us tothe following conclusions:

• The pairwise intermeeting times between the nodes usu-ally follow a log-normal distribution [19] [20] so thatthey are not memoryless1. This makes future contacts ofnodes dependent on their past.

• Most of the previous routing protocols that make theforwarding decisions at node meetings use a metric(encounter frequency [15], time elapsed since last en-counter [21] [22], social similarity [23]-[25] etc.) com-puted from the pairwise relations of nodes with thedestination node only. They do not use the information of‘meeting with each other’ while computing their deliverymetrics.

• The mobility of many real objects are non-deterministicbut periodic [27]. For example, in a cyclic MobiS-pace [27], if two nodes were frequently in contact at aparticular time in previous cycles, then they are likely tomeet around the same time in the next cycle.

The above three key observations motivated us to do theresearch presented in this paper that utilizes the correlationbetween the meetings of nodes for designing more efficientrouting algorithms. Hence, we introduce a new link met-ric, conditional intermeeting time, that computes the averageintermeeting time between two nodes relative to a meeting

1Assume thatX is the random variable representing the intermeeting timebetween two nodes, then the meetings are memoryless ifP (X > s+t | X >

t) = P (X > s) for s, t > 0 holds.

with a third node using only the local knowledge of thepast contacts. For example, withτA(D,B), we define theconditional intermeeting time of nodeA with destinationD

given the condition that it has justB as the average time ittook in the past (computed from previous contact history) tomeet withD after its meeting withB. Hence, at each meetingof nodeA with a potential destination nodeD, we computethe meeting frequency ofA with D conditional on meetingswith all the other nodes nodeA met since its last meeting withnodeD. In the paper, we discuss how this metric addressesall the above mentioned three key observations.

Moreover, note that this definition of intermeeting times isalso meaningful in terms of the context of routing of messagesbecause the messages are received from a node and given toanother node on the way towards the destination. Moreover,the conditional intermeeting time represents the durationdur-ing which a node holds the message during routing.

We provide the analysis of conditional intermeeting timeand discuss when and why it can be beneficial for providingbetter information to nodes within the context of routing.We also present statistical results from three different datasets (RollerNet [20], Cambridge [30], Haggle [32]) whichcontain the contact traces of real objects logged during reallife experiments.

To show the benefit of this metric, we propose im-provements on existing DTN routing protocols. Firstly, forthe algorithms which route messages over shortest paths(SP) [12] [14], we propose to use conditional intermeetingtimes rather than standard intermeeting times and route themessages over conditional shortest paths (CSP). Secondly,for the algorithms which make message forwarding decisionsdepending on a delivery metric (we call them metric-basedforwarding algorithms), we propose to use conditional inter-meeting time as a secondary delivery metric and allow theforwarding of messages if and only if both the algorithm’soriginal delivery metric and conditional intermeeting timesuggest to forward the message to the encountered node.

Through real-trace-driven simulations on three data sets,we compare the modified protocols with the original ones.The results show that modifications improve performances ofthose protocols. This shows that the conditional intermeetingtime represents inter-node link costs well (in the context ofrouting) guiding forwarding decisions effectively while routinga message.

In short, the contributions of this paper are four-fold:1) A new metric, conditional intermeeting time is proposed;

it computes the average intermeeting time between twonodes relative to a meeting with a third node using onlythe local knowledge of the past contacts.

2) The analysis of the proposed metric is presented to showsignificance of the metric for routing.

3) Modification of the existing DTN routing protocols byusing conditional intermeeting time metric is discussed.

4) Real-trace-driven simulations are performed and the per-formance improvement achieved in the updated versionsof the existing algorithms on three different data sets

are shown. Thus, the benefit of conditional intermeetingtime in making effective decisions in DTN routing isshown experimentally.

The remaining of the paper is organized as follows. InSection II, we describe the proposed metric in detail andexplain how a node can compute it from its previous contacts.In Section III, we give the analysis of proposed metric. InSection IV, we describe how the conditional intermeetingtime can be used to modify existing DTN routing algorithmsfor performance improvement. In Section V, we present thedetails of real-trace-driven simulations in which we comparethe performance of modified algorithms with the performancesof original algorithms. Finally, we offer conclusion and outlinethe future work in Section VI.

II. CONDITIONAL INTERMEETING TIME

Recently, the research community working on routing algo-rithms in DTNs has focused on the analysis of real mobilitytraces to understand the main characteristics of mobile ob-jects. Many experiments in different environments (office [19],conference [32], city [30], skating tour [20]) with differentobjects (human [16], bus [18], zebra [31]) and with variablenumber of attendants were performed. From the analysis of thedata sets collected during these experiments, significant resultsabout the aggregate and pairwise mobility characteristicsofreal objects were obtained.

As opposed to the random mobility models [26] accordingto which the intermeeting time between pairs follow an expo-nential distribution, recent analysis [19] [20] on real mobilitytraces showed that the intermeeting times between most (morethan99% in many datasets) of the node pairs fit to log-normaldistribution. However, this revokes the validity of a commonassumption [8] [13] [22] that the pairwise intermeeting timesare exponentially distributed and memoryless, and it makesthe pairwise contacts between nodes dependent on their pasts.

As a first consequence of this, the residual time until thenext meeting of two nodes can be predicted more accuratelydepending on the condition that they have not met duringthe lastt time units [19]. However, the dependence of futurecontacts on the past of nodes can provide more than this. Thenodes can also benefit from their past contacts to predict theirfuture contacts more accurately.

Previous work have used pairwise node relations in thedesign of DTN routing protocols while making effectiveforwarding decisions. The more frequently a node meets withdestination, the higher probability it can deliver a messageto the destination. Therefore, in the meeting of two nodes,keeping the message in the node with smaller average inter-meeting time with destination increases the delivery probabil-ity. However, an important aspect here is that nodes receivemessages from a node and forward it to another node. Thatis, the duration that a node holds a message is between itscontacts with two different nodes.

Depending on the above facts, we propose a new metriccalled conditional intermeeting timeto define the node rela-tions more precisely within the context of routing. This metric

4 time units/cycle3 time units/

2 time unitsA

B

C

cycle

cycle

Fig. 1: A physical cyclic MobiSpace with a common motioncycle of 12 time units.

computes the average intermeeting time between two nodesrelative to a meeting with a third node using only the localknowledge of the past contacts2.

The proposed metric can also provide more accuracy if thenodes move in a cyclic MobiSpace [27]. According to thedefinition of cyclic MobiSpace, if two nodes contact frequentlyat a particular time in previous cycles, the probability thatthey will be in contact around the same time in the nextcycle is high. In Figure 1, a sample cyclic MobiSpace withthree objects is illustrated. The common motion cycle is 12time units. In this example, the discrete probabilistic contactsbetweenA and B happen in every 12 time units (1, 13,25..) and the discrete probabilistic contacts betweenB andC occur in every 6 time units (2, 8, 14..). When we considerintermeeting time between nodesB andC, we can expect thatnodeB will forward its message to nodeC in 6 time units,however conditional intermeeting time ofB with C based onthe condition that it has met (received the message from) nodeA lets us know that the message will be forwarded to nodeC

within 1 time unit.In a DTN, each node can keep and update the list of its

contacts and the previous meeting times with each of themduring its lifetime. Then, utilizing this information, each nodecan find the values of both of their standard and conditionalintermeeting times with their neighbors.

Let τA(B|C) denote the conditional intermeeting time ofnodeA with nodeB given that it has met nodeC. It representsthe average time that elapses from the timeA has metC tothe time it first meetsB. Hence, the standard intermeetingtime betweenA andB can be denoted asτA(B|B) (or shortlyτA(B)). To find the conditional intermeeting time ofτA(B|C),each time nodeA meets nodeC, it starts a different timer.When it meets nodeB, it takes the sum of the values on thesetimers and also notes the number of timers it has started beforedeleting them. This computation is repeated again each timenodeC is encountered. Then, dividing the sum of time values

2Note that, the proposed metric is different thanconditional residual time(CRT) proposed by Srinivasa et al. in [19]. While CRT computes the remainingtime for the meetings of two nodes based on the condition that the nodes havenot met each other for some time, our metric computes the residual time tothe next meeting of two nodes based on the condition that one ofthe nodesmet with a third node. As we will see in analysis section, CRT isa specialcase of conditional intermeeting time in which the distribution of passed timesince the last meeting is not considered.

AB

5

C

11

C

14

B

16

C

23

B

25

B

30

C

34 time

6 units 7 units 4 units

9 units

5 units

2 units 2 units

0

Fig. 2: Example meeting times of nodeA with nodesB andC.While the values in the upper part are used in the computationof τA(B|C), the values in the lower part are used in thecomputation ofτA(C|B).

collected from each timer by the total count of all timers usedgives the value ofτA(B|C). We can also use a sliding windowwith an appropriate size over the past contacts [14] to makethe conditional intermeeting value more local and current.

Consider Figure 2 which shows the sample contact timesof a nodeA with its neighborsB and C. Node A meetswith node B at times {5, 16, 25, 30} and with nodeC attimes {11, 14, 23, 34}. Then, following the procedure de-scribed above,τA(B|C) = 3 andτA(C|B) = 6.5 units.

III. A NALYSIS

In this section, we give the analysis of conditional intermeet-ing time and show why it is significant in accurate predictionof future meetings within the context of routing.

Assume that nodeA has two different contacts,B andC,and the setsSB andSC include the meeting times of nodeAwith nodesB and C in order during the time frame [0,T ],respectively.

SB = {B1, B2, B3, . . . Bn}, n meetings

SC = {C1, C2, C3, . . . Cm}, m meetings

Furthermore, assume that the intermeeting time of nodeA with node B is well represented by a random variableX1 while the intermeeting time of nodeA with C is wellrepresented by a random variableX2 with the CDF D2(x)and probability densityd2(x) = D′

2(x).To find τA(C|B), we need to compute the following (with-

out loss of generality, we assume thatCm ≥ Bn):

τA(C|B) =

∑mk=1(Cd(k) − Bk)

m,

where,d(k) = min{i : Ci ≥ Bk}.The conditional intermeeting time of nodeA with nodeC

under the condition that it has met nodeB is then a randomvariable that we will denote asY . Then τA(C|B) = E[Y ].Let’s considerjth meeting of nodeA with nodeB and denotet = Bj − Cd(j)−1. Consider a family of random variablesY (t)’s with CDFsDt(x) and probability densitiesdt(x), then:

Dt(y) =D2(y + t) − D2(t)

1 − D2(t)

dt(y) =d2(y + t)

1 − D2(t)

0

20

40

0

20

400

2

4

6

8

10

12

x 104

B

Haggle Traces

C

Co

nd

itio

na

l In

term

ee

ting

tim

e (

sec)

B

C

C−Map of node 21 in Haggle traces

0 10 20 30 400

5

10

15

20

25

30

35

40

(a) C-Map of node 21 in Haggle traces

020

4060

0

20

40

600

500

1000

B

RollerNet Traces

CC

on

diti

on

al I

nte

rme

etin

g tim

e (

sec)

B

C

C−Map of node 33 in RollerNet traces

0 10 20 30 40 50 600

10

20

30

40

50

60

(b) C-Map of node 33 in RollerNet traces

010

2030

0

10

20

30

0

1

2

3

x 105

B

Cambridge Traces

C

Co

nd

itio

na

l In

term

ee

ting

tim

e (

sec)

BC

C−Map of node 2 in Cambridge traces

0 5 10 15 20 25 30 350

5

10

15

20

25

30

35

(c) C-Map of node 2 in Cambridge traces

Fig. 3: C-Maps of popular nodes in three datasets. In figures,B represents the id of the node already met andC representsthe id of the node to be met.

E[Y (t)] =

∫ ∞y=0

yd2(y + t)dy

1 − D2(t)

=

∫ ∞y=t

(1 − D2(y))dy

1 − D2(t)

WhenX1 andX2 are exponentially distributed random vari-ables, thenDt(x) = D2(x), showing the memoryless propertyof exponential distribution. However, as the previous worksuggests,X1 and X2 fit well with log-normal distribution.Then:

E[Y (t)] =eµ2+

σ22

2

[

1 − erf(

ln t−(µ2+σ2

2)

σ2

√2

)]

1 − erf[

ln t−µ2

σ2

√2

] − t

where erf is error function andµ2 and σ2 are mean andvariance ofX2, respectively. Since in this case, as well ingeneral, the expected value ofY (t) depends on the value oft,then, denoting bydACB(t) the probability density of the timedifference between the meeting of nodeA with C to time ofmeeting of nodeA with B beforeA meetsC, we get:

E[Y ] =

∫ ∞

t=0

∫ ∞y=t

(1 − D2(y))dy

1 − D2(t)dACB(t)dt

Clearly, E[Y ] depends on probability density functiondACB(t) that is defined by the correlation between the meet-

ings of nodeA with nodesB and C. Due to the nature ofDTNs, and also the possible cyclic behavior of nodes [27],there is often a repeating pattern between the meetings ofnode A with node B and C, creating a strong correlation.Consequently,E[Y ] strongly depends on the aforementionedcorrelation.

Given A, to see the distribution ofτA(C|B) according todifferentB andC nodes, we computed the average conditionalintermeeting time maps (C-Map) of the most popular nodes(having the highest total meeting count with other nodes) inthree different datasets. In Figure 3, we show these results.For each dataset, the upper plot shows the 3D view ofτA(C|B) and the lower plot shows the contour plot displayingthe isolines ofτA(C|B). The darker the color in the plots,the smaller theτA(C|B) values. Interestingly, the diagonalsand theAth row and column in the plots are the darkestplaces becauseτA(C|B) values are assumed zero in thesecases. Moreover, if there is no instance of the case in whichnode A meets nodeC after it meets nodeB, we assumedτA(C|B) = −1.

If there were no correlation between the meetings of node Awith other nodes,τA(C|B) would have been the same for allB’s other thanA or C and entire rows would have been of thesame color in contour plots. In contrast, we observe different

colors within the rows, demonstrating that the meetings ofnode A with different nodes are not independent of eachother. Indeed this result matches with real world scenarios. Forexample, consider the meetings of a man who goes from hometo work every morning. After meeting his family members(while leaving home), he meets later his office friends. Yet,on the way to his office, he meets the security guard at thegate of his workplace a few moments before meeting his officefriends. In other words, the meetings of the man with his officefriends is correlated with his meetings with security guard.

IV. PROPOSEDALGORITHMS

In this section, we present two different utilization of con-ditional intermeeting time in existing DTN routing algorithms.In the first part, we look into the shortest path based routingalgorithms and propose to use conditional shortest paths toroute messages. Then, in the second part, we propose to re-vise message forwarding decision of metric-based forwardingalgorithms by including the conditional intermeeting time.

A. Shortest Path based Routing

1) Overview: Shortest path routing (SPR) protocols forDTNs are based on the designs of routing protocols fortraditional networks. The links between each pair of nodes areassigned a cost and messages are forwarded over the shortestpaths between the source and the destination. Furthermore,thedynamic nature of DTNs is also addressed in these designs.Two of the common metrics used to define the link cost areminimum expected delay (MED [14]) and minimum estimatedexpected delay (MEED [14]). These metrics compute theexpected waiting time plus the transmission delay betweeneach pair of nodes. However, while the former uses the futurecontact schedule, the latter uses only observed contact history.

In this paper, we are interested in neither the suitability ofSPR algorithms for DTNs nor the scalability and complexity oftheir designs as the papers introducing the original algorithmsinclude elaborate discussions of these issues. In this paper,we focus on the enhancements of the performance of SPRalgorithms achieved by utilizing our metric, conditional inter-meeting time, rather than using standard intermeeting time.To this end, in the rest of this section, we show the necessarychanges to the current designs of SPR algorithms.

2) Network Model:We model a DTN as a graphG = (V ,E) where the mobile nodes are represented by vertices (V ) andthe possible connections between these nodes are representedby the edges (E = Eu ∪ Eb), which, unlike previous DTNgraph models, allows for multiple and both unidirectional (Eu)and bidirectional (Eb) edges between the nodes. The neighborsof a nodei are denoted byN(i) and the edge sets are givenas follows:

Eb = {(i, j) | ∀j ∈ N(i)} where,w(i, j) = τi(j) = τj(i)

Eu = {(i, j) | ∀j 6= k ∈ N(i)} where,w(i, j) = τi(j|k)

Note that there can be multiple unidirectional edges (Eu)between any two nodes but these edges differ from each other

A

BD

C

TA(D)

TA(D|C)

TA(D|B)TA(B|D)TA(B|C)

TA(C|B)TA(C|D)

TA(B)

TA(C)

Fig. 4: A sample DTN graph with four nodes and nine edges.

in terms of their weights (w(i, j)) and the corresponding thirdnode which is the reference point used while computing theconditional intermeeting time. In Figure 4, we illustrate asample DTN graph with four nodes and nine edges. There arethree bidirectional edges with weights of standard intermeetingtimes and six unidirectional edges with weights of conditionalintermeeting times.

3) Conditional Shortest Path Routing:Our algorithm basi-cally finds conditional shortest paths (CSP) for each source-destination pair and routes the messages over these paths. Wedefine the CSP from a noden0 to a nodend as follows:

CSP (n0, nd) = {n0, n1, . . . , nd−1, nd | ℜn0(n1|t) +

d−1∑

i=1

τni(ni+1|ni−1) is minimized.}

Here, t represents the time that has passed since the lastmeeting ofn0 with n1 andℜn0

(n1|t) is the expected residualtime to the next meeting ofn0 and n1 given that they havenot met in the lastt time units.ℜn0

(n1|t) can be computedas in [19] with parameters of distribution representing theintermeeting time betweenn0 andn1. It can also be computedin a discrete manner from the observed intermeeting times ofn0 and n1. Assume thatn0 observedk intermeeting timeswith n1 in the past. Letτ1

n0(n1), τ2

n0(n1),. . .τk

n0(n1) denote

these values. Then, discrete computation ofℜn0(n1|t) can be

defined formally as follows:

ℜn0(n1|t) =

∑ks=1 fs

n0(n1)

|{τsn0

(n1) ≥ t }|where,

fsn0

(n1) =

{

τsn0

(n1) − t if τsn0

(n1) ≥ t

0 otherwise

If none of thek observed intermeeting times is bigger thant

(this case occurs less likely as the the contact history grows),ℜn0

(n1|t) becomes0, which is a good approximation.Next, we give an example to show the benefit of CSP over

SP. Consider the DTN shown in Figure 5. The weights of edges(A, C) and (A, B) show the expected residual time of nodeA

with nodesC andB, respectively, in both graphs. The weightsof edges (C, D) and (B, D) are different in both graphs. Whilein the left graph, they show the average intermeeting times ofnodesC andB with D respectively, in the right graph, theyshow the average conditional intermeeting times of the same

A D

B

C30= C

(D)

15= B(D)=25A(B|t)R

=20A(C|t)R

A D

B

C10= C

(D|A)

12= B(D|A)=25A(B|t)R

=20A(C|t)RT

T T

T

Fig. 5: An example case where CSP can be different than SP.

nodes withD relative to their meeting with nodeA. From theleft graph, we conclude that SP(A, D) is (A,B,D). Thus, itis expected that on average a message from nodeA will bedelivered to nodeD in 40 time units. However this may not bethe actual shortest delay path. As the weight of edge (C, D)states in the right graph, nodeC can have a smaller conditionalintermeeting time (than the standard intermeeting time) withnode D assuming that it has met nodeA. In other words,nodeC understands its faster transfer capability of messages(received from nodeA) to nodeD. Hence, in the right graph,CSP(A, D) is (A,C,D) with the path cost of 30 time units.

A node-specific view of the network using the aforemen-tioned network model is formed at each node and the standardand conditional intermeeting times of other nodes are collectedvia epidemic link state protocol as it is described in originalstudy [14]. However, once the weights are known, it is notas easy to find CSPs as it is to find SPs. Consider Figure 6where the CSP(A, E) follows path 2 and CSP(A, D) follows(A, B, D). This situation is likely to happen in a DTN,if τD(E|B) ≥ τD(E|C) is satisfied. Running Dijkstra’s orBellman-Ford algorithm on the current graph structure cannotdetect such cases and concludes that CSP(A, E) is (A, B,D, E). Therefore, to obtain the correct CSPs for each sourcedestination pair, we propose the following transformationonthe current graph structure.

Given a graphG = (V,E), we obtain a new graphG′ =(V ′, E′) where:

V ′ ⊆ V × V and E′ ⊆ V ′ × V ′ where,

V ′ = {(ij) | ∀j ∈ N(i)} andE′ = {(ij , kl) | i = l}

where,w′(ij , kl) =

{

τi(k|j) if j 6= k

τi(k) otherwise

Remark that the edges inEb (in G) are made directional inG′. Also the unidirectional edges (Eu) between the same pairof nodes inG are separated inE′. This graph transformationkeeps all the historical information that conditional intermeet-ing times require and also keeps only the paths with a validhistory. For example, if a pathA,B,C,D is chosen, then anedge like (CD,DA) cannot be chosen because of the edgesettings in the graph. Hence, only the correctτ values will beadded to the path calculation. To solve the conditional shortestpath problem however, we add one vertex for sourceS (apartfrom its permutations) and one vertex for destination nodeD.We also add outgoing edges fromS to each vertex(iS) ∈ V ′

EA D

C

Path 1

Path 2

B

Fig. 6: Path2 may have smaller conditional delay than path1even though CSP fromA to D is throughB.

with weight ℜS(i|t). Furthermore, for the destination node,D, we add only incoming edges from each vertexij ∈ V ′

with weight τi(D|j) and fromS with weightℜS(D|t).In Figure 7, we show a sample transformation of a clique

of four nodes to the new graph structure. In the initial graph,all mobile nodesA to D meet with each other, and we set thesource node toA and destination node toD (we did not showthe directional edges in original graph for brevity). Note thatwe set any path to begin withA on transformed graphG′, butwe also put the permutations ofA, B andC with each other.

Running Dijkstra’s shortest path algorithm onG′ given thesource nodeS and destination nodeD will give shortestconditional path. InG′, |V ′| = O(|V |2) and|E′| = O(|V 3|) =|E|3/2, and therefore Dijkstra’s algorithm will run inO(|V |3)(with Fibonacci heaps) while computing the original shortestpaths (with standard intermeeting times) takesO(|V |2).

Using conditional intermeeting times instead of standardintermeeting times only requires (over original design) extraspace to store the conditional intermeeting times and additionalprocessing as complexity of running Dijkstra’s algorithm in-creases fromO(|V |2) to O(|V |3). We believe that in currentDTNs, wireless devices have enough storage and processingpower not to be unduly taxed with such an increase. Moreover,to lessen the burden of collecting and storing link weights,an asynchronous and distributed version of the Bellman-Fordalgorithm can be used, as described in [28].

B. Metric-based Forwarding Algorithms

1) Overview: In DTNs, a common routing method is toforward the message to the encountered node that is morelikely to meet with destination than the current message carrier.However, making effective forwarding decisions in single-copy based routing in DTNs is a challenging task. When twonodes meet, one of them forwards a message to the other oneif it decides that the message will have a higher chance to bedelivered to destination at the other node.

In previous work, depending on the observed contact historybetween nodes, several metrics have been used to definethe delivery quality of nodes. Some of the popular onesare encounter frequency [15], time elapsed since last en-counter [21] [22], residual time [19] and social similarity[23]-[25]. For example, in Prophet [15], messages are forwardedto the nodes meeting the destination more frequently.

BA

BC

CA

CB

AB

AC

DA

A(D|t)

A(C|t)

A(B|t)

C

(C | B)

C(B | A)

(D | B)

A

B(A | C)

A(D | B)

A(D | C)

B(D | C)

C(D | A)

B(D | A)

A

A

B C

D

Source

Destination

A, B, C and D all meet with each other

R

R

R

T

T

T

T

T

T

T

T

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Fig. 7: Graph transformation to solve CSP with 4 nodes whereA is the source andD is the destination.

2) Proposed Revision:According to most of the deliverymetrics proposed previously, two encountering nodes makethe message forwarding decision depending on their individualrelations with the destination node. In some algorithms suchas [15] [22], transitivity rule is utilized to reflect the effectof other nodes on the delivery quality of a node but such anapproach can be applied to all delivery metrics and it does notreflect the metric’s own feature.

To make forwarding decisions of these algorithms moreeffective, thus to improve their performance, we propose touse conditional intermeeting time as an additional deliverymetric. That is, when two nodes meet, they will also comparetheir conditional intermeeting times with destination andif thecurrent carrier of the message learns that other node has alsoshorter remaining time (according to conditional intermeetingtime) to meet the destination than itself, the message isforwarded. At first glance, this additional condition seemstocut down the number of times the message is forwarded sothat the probability of delivery will be reduced. However, assimulation results show, the necessary number of hops arepreserved and the less beneficial ones are not performed.Therefore, more effective forwarding decisions are made sothat the cost of message delivery declines while the deliveryratio and average delay are maintained (in some cases, eventhe delivery ratio increases and average delay decreases).

V. SIMULATIONS

To evaluate the performance of proposed modifications ofalgorithms, we have built a Java based DTN simulator whichuses the traces of real objects. We used traces from threedatasets which include the contact times and durations of realobjects logged in different DTN environments and we set thenetwork parameters (number of nodes etc.) accordingly.

A. Algorithms in Comparison

In simulations, we compared existing DTN algorithms withtheir modifications utilizing conditional intermeeting time intheir designs. First, we compared Shortest Path Routing (SPR)with Conditional Shortest Path Routing (CSPR) which is de-scribed in Section IV-A3. Then, we compared the existing and

revised versions of two metric-based DTN routing algorithms:Prophet [15] and Fresh [21]. When two nodes,A andB, meet,in ProphetA forwards its message toB if and only if itspredicted time of delivery to destinationD is smaller thanB’spredicted time of delivery. In Fresh,A forwards the messageto B only if B has a more recent meeting with destinationD than itself. In the revised versions of these algorithms(we refer to them as C-Prophet and C-Fresh to underlinethat they use conditional intermeeting time),A forwards themessage toB if τA(D|B) > τB(D|A) is also satisfied (inaddition to algorithm’s own forwarding condition). Althoughwe obtained results (showing performance improvement) withmany metric-based algorithms (including [19]), we show onlythe results of two benchmarking algorithms due to lack ofspace. However, we give the results obtained by EpidemicRouting [6] since it achieves the optimum delivery ratio anddelay (at high cost, however).

B. Data Sets

To evaluate the proposed algorithms, we used traces fromthe following three data sets.

1) RollerNet Dataset [20]: It includes the opportunisticsightings of Bluetooth devices distributed to 62 rollerbladersin the 3 hour roller tour of Paris in August 20, 2006.

2) Cambridge Dataset [30]:This data includes a number oftraces of Bluetooth sightings by 36 students from CambridgeUniversity who were asked to carry the iMotes with them atall times for the duration of the experiment that started onOctober 28, 2005 and ended on December 21, 2005.

3) Haggle Project Dataset [32]:Among the different ex-periments performed within Haggle Project, we selected theBluetooth sightings recorded between the iMotes carried by41attendants of Infocom’05 Conference held in Miami. Deviceswere distributed on March 7th, 2005 between lunch time and5pm and collected on March 10th, 2005 in the afternoon.

C. Performance Metrics

We use the following three metrics to compare the algo-rithms: message delivery ratio, average cost, and routing effi-ciency. Delivery ratio is the proportion of messages delivered

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Fig. 8: Comparison of SPR and CSPR: Message delivery ratio vs. time.

to their destinations among all messages generated. Averagecost (which is a good indicator of the total power consumptionin the network) is the average number of forwards done permessage before delivery. Finally, routing efficiency [33] isdefined as the ratio of delivery ratio to the average cost. Inthe results, we did not give separate plots for delivery delaybecause they can be obtained from the delivery ratio plots.

D. Results

To collect several routing statistics, we have generated trafficfrom the traces of three data sets. For each simulation run,after a warm up period, we generated 5000 messages froma random source node to a random destination node at eacht seconds. In RollerNet, since the duration of experiment isshort, we sett = 1s, but for Cambridge and Haggle data sets,we sett = 1min andt = 30s, respectively. We assume that thenodes have enough buffer space to store every message theyreceive, the bandwidth is high and the contact durations ofnodes are long enough to allow the exchange of all messagesbetween nodes3. These assumptions are reasonable in view oftoday’s technology capabilities and are also used commonlyinprevious studies [29]. Besides, we compare all algorithms inthe same conditions. Any change in the current assumptionsis expected to affect the performance of compared algorithmsin the same way since they use one copy of the message.Moreover, we used a simple MAC model similar to CSMAmodel. We ran each simulation 10 times with different seedsand in each run we collect statistics by running each algorithmon the same set of messages. All results plotted in figures showthe averages of results obtained in all runs (we did not plotthe error bars since they were very small).

1) Comparison of CSPR and SPR:Figure 8a shows thedelivery ratios achieved in CSPR and SPR algorithms withrespect to time (i.e. TTL of messages) in RollerNet traces.Clearly, CSPR algorithm delivers more messages to theirdestinations than SPR algorithm. Moreover, it achieves loweraverage delivery delay than SPR algorithm. For example,CSPR delivers80% of all messages after 17 minutes with

3We also performed simulations with limited resources (e.g. buffer, band-width) and obtained results showing better (but different)performance im-provement in revised algorithms over original algorithms. However, we presentthem in the extended version of the paper due to the lack of space here.

an average delay of almost 6 minutes, while SPR achieves thesame delivery ratio only after 41 minutes and with an averagedelay of 12 minutes. Moreover, although we did not show ithere for brevity, average costs in SPR and CSPR are very close(1.48 and 1.52 respectively) to each other (and much smallerthan the average cost in epidemic routing which is around 25).

We also see the better delivery ratios achieved by CSPRalgorithm in Cambridge and Haggle traces in Figure 8b andFigure 8c, respectively. In Cambridge traces, after 6 days,CSPR delivers78% of all messages with an average delay of2.6 days, however SPR can only deliver62% of all messages totheir destination with an average delay of 3.2 days. Moreoveraverage costs in SPR and CSPR are 1.73 and 1.78 respectivelywhile it is around 16 in epidemic routing. Similarly, in Haggletraces, with an average cost close to each other, CSPR delivers87% of all messages by the end of simulation whereas SPRcan only achieve 78% delivery ratio. To put this in perspective,compared to Epidemic routing with the highest achievabledelivery ratio (94% in Haggle traces with current setting),CSPR lost only 7% of messages, while SPR lost 16% so CSPRachieved more than 55% improvement over SPR.

These results show that in the context of routing, conditionalintermeeting time provides a better representation of linkcostthan standard intermeeting time. Therefore, in CSPR, moreeffective paths with similar average hop counts are selectedduring the routing of a message towards the destination.Thus, higher delivery ratios with lower end-to-end delays areachieved. In SPR and CSPR algorithms here, we used source-routing [12] and let the messages follow the paths which aredecided at the source nodes. We also observed similar resultsin our simulations with other routing approaches (per-hop andper-contact routing).

2) Comparison of revised and original versions of metric-based algorithms:In Figure 9a, we show the delivery ratiosachieved in RollerNet traces. Clearly, the modified algorithmsprovide higher delivery ratio than the original ones. Moreover,as Figure 9b shows, average cost is lower for the modified ver-sus the original algorithms. For example, C-Prophet delivers90% of all messages after 23 minutes with average delay of 7.8minutes and average cost of 4.83 hops. However, the originalProphet reaches the same delivery ratio only after 33 minuteswith average delay of 13.5 minutes and 17.02 average cost. A

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Fig. 11: Comparison of metric-based forwarding algorithmsusing Haggle Project traces

similar situation is also observed between C-Fresh and Fresh.Consequently, routing efficiency is increased more than100%.

When we look at the results obtained from Cambridgeand Haggle traces in Figure 10 and Figure 11, we observea different improvement. As it is seen in Figure 10a andFigure 11a, revised and original versions of algorithms havesimilar delivery ratios (and therefore similar average delays).However, as Figure 10b and Figure 11b show, average costsin modified versions are lower than they are in originalones. Moreover, in Cambridge traces, the mean hop countsof Prophet, C-Prophet, Fresh and C-Fresh are 5.21, 2.48,3.83 and 2.53, respectively and in Haggle traces, they are12.7, 4.98, 5.23 and 3.44. This shows that when conditionalintermeeting time is used as an additional delivery metric,

the nodes choose their next hops more effectively so thatthe cost is decreased while still keeping the original deliveryratio. Therefore, again more than100% gain is achieved inrouting efficiency. From the above results, we see the benefitof conditional intermeeting times in metric-based forwardingalgorithms clearly. Moreover, we also observe that in differentenvironments, the improvements obtained thanks to utilizationof conditional intermeeting times can be different. In RollerNettraces, we observed improvement in all metrics. However,in Cambridge traces we observed an improvement only inaverage cost, thus, in routing efficiency. From our initialanalysis of the traces, we conclude that this is caused bythe repetitive contacts between objects in RollerNet traces.That is, as it is stated in [20], during the tour, fluctuations

in the motion of the rollerbladers cause a typical accordionphenomenon (the topology expands and shrinks with time).When the topology shrinks, nodes are in contact which eachother, but when the topology expands, they are disconnected.This property in the contacts of nodes creates a cyclic behaviorand lets the proposed algorithms perform better. However,in Cambridge and Haggle traces, the repetitive behavior ofnode meetings is not clearly detected. From these results, weconclude that the benefit of using conditional intermeetingtimes in metric based algorithms becomes more pronouncedin the environments in which the repetitive motion of nodesis clearly observed. However, even in the environments wherethis is not the case, average cost of routing can be decreasedand routing efficiency can be improved remarkably thanks touse of conditional intermeeting times.

VI. CONCLUSION AND FUTURE WORK

In this paper, we focused on the routing problem in delaytolerant networks (DTN). First, inspired by the results of therecent studies showing that intermeeting times between nodesare not memoryless and the motion patterns of mobile nodesare frequently repetitive, we introduced a new metric calledconditional intermeeting time which is the average time thatpasses from the time a node meets with a neighbor nodeuntil the time it meets another one. Next, we presented ananalysis of this metric showing why it can be beneficial inproper representation of node relations. Then, we looked attheeffects of this metric on existing DTN routing algorithms. Tothis end, we modified their current designs using conditionalintermeeting time. Finally, through real-trace-driven simula-tions, we evaluated the modified algorithms and demonstratedthe superiority of them over original ones.

As a future work of our study, we would like to extendthe definition of conditional intermeeting time by using moremeetings from the contact history. For instance, assume thata nodeA wants to compute its conditional intermeeting timewith a nodeB after the time it has met another nodeC. Here,we want to differentiate the following two cases which areconsidered together in our current approach; when nodeA

has met nodeD before nodeC and when nodeA has metnodeE before nodeC. To apply this algorithm in our work,we plan to use probabilistic context free grammars (PCFG)and utilize the construction algorithm presented in [34].

REFERENCES

[1] P. Juang, H. Oki, Y. Wang, M. Martonosi, L. S. Peh, and D. Rubenstein,Energy-efficient computing for wildlife tracking: design tradeoffs andearly experiences with zebranet, in Proceedings of ACM ASPLOS, 2002.

[2] Disruption tolerant networking, http://www.darpa.mil/ato/solicit/DTN/.[3] J. Ott and D. Kutscher,A disconnection-tolerant transport for drive-thru

internet environments, in Proceedings of IEEE INFOCOM, 2005.[4] Delay tolerant networking research group, http://www.dtnrg.org.[5] J. Burgess, B. Gallagher, D. Jensen, and B. N. Levine,MaxProp:

Routing for Vehicle-Based Disruption- Tolerant Networks, in Proc. IEEEInfocom, April 2006.

[6] A. Vahdat and D. Becker,Epidemic routing for partially connected adhoc networks, Duke University, Tech. Rep. CS-200006, 2000.

[7] T. Spyropoulos, K. Psounis,C. S. Raghavendra,Efficient routing in inter-mittently connected mobile networks: The multi-copy case, IEEE/ACMTransactions on Networking, 2008.

[8] E. Bulut, Z. Wang, and B. Szymanski,Cost-Effective Multi-PeriodSpraying for Routing in Delay Tolerant Networks, to appear inIEEE/ACM Transactions on Networking, 2010.

[9] Y. Wang, S. Jain, M. Martonosi, and K. Fall,Erasure coding basedrouting for opportunistic networks, in Proceedings of ACM SIGCOMMworkshop on Delay Tolerant Networking (WDTN), 2005.

[10] E. Bulut, Z. Wang, B. Szymanski,Cost Efficient Erasure Coding basedRouting in Delay Tolerant Networks, in Proceedings of ICC 2010.

[11] I. Psaras, L. Wood and R. Tafazolli,Delay-/Disruption-Tolerant Net-working: State of the Art and Future Challenges, Technical Report,University of Surrey, UK, 2010.

[12] S. Jain, K. Fall, and R. Patra,Routing in a delay tolerant network, inProceedings of ACM SIGCOMM, Aug. 2004.

[13] T. Spyropoulos, K. Psounis,C. S. Raghavendra,Spray and Wait: AnEfficient Routing Scheme for Intermittently Connected Mobile Networks,ACM SIGCOMM Workshop, 2005.

[14] E. P. C. Jones, L. Li, and P. A. S. Ward,Practical routing in delaytolerant networks, in Proceedings of ACM SIGCOMM workshop onDelay Tolerant Networking (WDTN), 2005.

[15] A. Lindgren, A. Doria, and O. Schelen,Probabilistic routing in in-termittently connected networks, SIGMOBILE Mobile Computing andCommunication Review, vol. 7, no. 3, 2003.

[16] A. Chaintreau, P. Hui, J. Crowcroft, C. Diot, R. Gass, and J. Scott,Impact of Human Mobility on the Design of Opportunistic ForwardingAlgorithms, in Proceedings of INFOCOM, 2006.

[17] T. Karagiannis, J. Boudec, and M. Vojnovic,Power Law and ExponentialDecay of Inter Contact Times Between Mobile Devices, in Proceedingsof MobiCom, 2007.

[18] X. Zhang, J. F. Kurose, B. Levine, D. Towsley, and H. Zhang, Studyof a Bus-Based Disruption Tolerant Network: Mobility Modeling andImpact on Routing, in Proceedings of ACM MobiCom, 2007.

[19] S. Srinivasa and S. Krishnamurthy,CREST: An Opportunistic Forward-ing Protocol Based on Conditional Residual Time, in Proceedings ofSECON, 2009.

[20] P. U. Tournoux, J. Leguay, F. Benbadis, V. Conan, M. Amorim,J. Whitbeck,The Accordion Phenomenon: Analysis, Characterization,and Impact on DTN Routing, in Proceedings of Infocom, 2009.

[21] H. Dubois-Ferriere, M. Grossglauser, and M. Vetterli,Age Matters:Efficient Route Discovery in Mobile Ad Hoc Networks Using EncounterAges, in Proceedings of ACM MobiHoc, 2003.

[22] T. Spyropoulos, K. Psounis, and C. Raghavendra,Spray and Focus:Efficient Mobility-Assisted Routing for Heterogeneous andCorrelatedMobility, in Proceedings of IEEE PerCom, 2007.

[23] E. Daly and M. Haahr,Social network analysis for routing in discon-nected delay-tolerant manets, in Proceedings of ACM MobiHoc, 2007.

[24] P. Hui, J. Crowcroft and E. Yoneki,BUBBLE Rap: Social Based For-warding in Delay Tolerant Networks, in Proceedings of ACM MobiHoc,2008.

[25] E. Bulut, Z. Wang and B. Szymanski,Impact of Social Networks inDelay Tolerant Routing, in Proceedings of Globecom, 2009.

[26] T. Spyropoulos, K. Psounis,C. S. Raghavendra,Performance Analysis ofMobility-assisted Routing, MobiHoc, 2006.

[27] C. liu, J. Wu and I. CardeiMessage Forwarding in Cyclic Mobispace:the Multi-copy case, in Proceedings of the Sixth IEEE InternationalConference on Mobile Ad-hoc and Sensor Systems (MASS), 2009.

[28] D. Bertsekas, and R. Gallager,Data networks (2nd ed.), 1992.[29] C. Liu and J. Wu,An Optimal Probabilistically Forwarding Protocol in

Delay Tolerant Networks, in Proceedings of MobiHoc, 2009.[30] J. Leguay, A. Lindgren, J. Scott, T. Friedman, J. Crowcroft and P. Hui,

CRAWDAD data set upmc/content (v. 2006-11-17), downloaded fromhttp://crawdad.cs.dartmouth.edu/upmc/content, 2006.

[31] Y. Wang, P. Zhang, T. Liu, C. Sadler and M. Martonosi,http://crawdad.cs.dartmouth.edu/princeton/zebranet, CRAWDAD dataset princeton/zebranet (v. 2007-02-14), 2007.

[32] A European Union funded project in Situated and Autonomic Commu-nications,www.haggleproject.org.

[33] J. M. Pujol, A. L. Toledo, and P. Rodriguez,Fair routing in delaytolerant networks, in Proc. IEEE INFOCOM, 2009.

[34] S. Geyik, and B. Szymanski,Event Recognition in Sensor Networks byMeans of Grammatical Inference, in Proc. of INFOCOM, Brazil, 2009.