On Exploiting Few Strangers for Data Forwardingin Delay Tolerant Networks

Peiyan Yuan, Huadong Ma, Pengrui DuanBeijing Key Laboratory of Intelligent Telecommunications Software and Multimedia

Beijing University of Posts and Telecommunications

Beijing, China

peiyan@htu.cn, mhd@bupt.edu.cn, dpr@bupt.edu.cn

Abstract—Routing is one of the challenging tasks in DelayTolerant Networks (DTNs), due to the lack of global knowledgeand sporadic contacts between nodes. Most existing works takegreedy mechanism to forward messages, i.e., only nodes whichhave higher quality metrics than current carriers can be selectedas relays to final destinations. In this work, we explore theinfluence of strangers on routing performance under a morechallenging scenario of pure darkness. We first present a methodto identify the relationship between nodes (i.e., stranger orfriend). Second, we explore the optimized number of strangers wecan employ. Third, we propose a novel routing scheme which arecalled STRON in this paper by taking both the STRangers andtheir Optimized Number into account. We finally compare ourrouting scheme with the greedy mechanism through syntheticaland trace-driven simulations, the results show that our routingstrategy achieves a better performance, especially in terms ofcombined overhead/packet delivery ratio and the average numberof hops per message.

Index Terms—Stranger; Forwarding mechanism; Routing pro-tocol; Delay Tolerant Networks

I. INTRODUCTION

One of the most characteristics of Delay Tolerant Networks

is that an end-to-end path between source and destination is

rarely (if ever) existed at any moment, which makes routing

very challenging in DTNs [1]. In this work, we focus on the

influence of strangers on routing performance within a pure

darkness environment, where the mobility of nodes can not

acquire in advance and each node depends only on itself to

locally estimate the forwarding metric to destination.

Obviously, epidemic scheme [2] is a potential solution to

deliver messages under the above scenario as it tries to send

each message over all possible paths (i.e., multiple copies) in

the network. Thus, the message will be successfully received

so long as one of the copies reaches the destination. Whereas,

the immoderate spraying will incur a high price of system

resources, resulting in the splurge on energy and buffer space,

the rapid consumption of available bandwidth, and in turn,

the chance to impair the routing metrics such as the packet

delivery ratio and the average number of hops per message.

These deficiencies of epidemic have motivated researchers

to design other novel routing algorithms, most of which make

a better tradeoff between packet delivery ratio and cost by

making use of different contexts (e.g., [3] [4] [5] [6] [7]

[8]). For these schemes, the data forwarding performance

depends heavily on the contexts they exploited to evaluate

the potential relays to the final destination. Furthermore,

most existing schemes take a greedy mechanism to deliver

messages, i.e., only such which have higher quality metrics

than current carriers can be selected as relays to the final

destinations, hence, the strangers have no chance to help others

to communicate in the network. Whereas, routing performance

can be improved if permitting few strangers to participate

in the forwarding process of messages as that the strangers

have different spatiotemporal distributions from the current

carriers. Therefore, we need to address the problem of how

to integrate stranger into data forwarding algorithms in DTNs.

It is a critical while challenging question especially in a pure

darkness environment.

Recently, there is few work that explicitly takes stranger into

account (e.g., [9]). Whereas, the work of [9] needs to know

the mobility of each node and the global topology information.

For instance, the authors of [9] exploited the community-

detection mechanisms presented in [10] to classify nodes and

took low number of contacts and short duration as a baseline

to identify strangers, on the one hand, which requires the

detailed traces of each node (obviously, it may not be practical

when considering the problems such as privacy protection and

selfishness of nodes [11]), on the other hand, the distributed

community-detection mechanisms result in high cost due to

the information exchange and calculations, and the complexity

of adjusting several threshold parameters [12] [13]. Moreover,

we argue that how to ascertain the optimized values of several

key parameters such as contact frequency, short duration and

low number of contacts.

Taking all above issues into account, in this paper, we

investigate stranger from the following two aspects within

a pure darkness environment. (i) Identifying stranger: The

strangers are likely to be more useful for bringing messages

to different parts of the deployed region, which potentially

increases the probability to meet up destinations. Thus, we

focus on how to differentiate strangers from a large amount

of nodes. (ii) The number of strangers we can exploit, which

has a big influence on the routing performance. Making it

too few results in little improvement of routing performance,

making it too much results in deteriorating the performance

of data forwarding algorithm. As such, we have to ascertain

the optimized number of strangers before integrating them into

routing metric.

2011 Seventh International Conference on Mobile Ad-hoc and Sensor Networks

978-0-7695-4610-0/11 $26.00 © 2011 IEEE

DOI 10.1109/MSN.2011.51

283

2011 Seventh International Conference on Mobile Ad-hoc and Sensor Networks

978-0-7695-4610-0/11 $26.00 © 2011 IEEE

DOI 10.1109/MSN.2011.51

282

2011 Seventh International Conference on Mobile Ad-hoc and Sensor Networks

978-0-7695-4610-0/11 $26.00 © 2011 IEEE

DOI 10.1109/MSN.2011.51

282

In this paper, we propose an adaptive solution to address

these challenges. First, we utilize local observations of each

node to estimate the similarity between them (i.e., each node

only records contact duration between itself and others). We

average these contact durations and use this mean as a baseline

to identify strangers. Furthermore, each time a new contact

was observed, the sum of the contact durations should be

updated. Thus, the change rate of similarity between nodes

can be reflected dynamically. Second, we count the number

of strangers which act as relays for other nodes on all shortest

paths and use the mean ratio (i.e., the number of these

strangers over that of all relays ) to explore the optimized

number of strangers we can employ. Finally, we design our

routing metric by taking both strangers and their number

into account. Our main contributions can be summarized as

follows:

∙ We study DTNs routing in a more challenging scenario

and consider the influence of strangers.

∙ We discuss the effect of the number of strangers on the

routing performance and propose a method to explore the

optimized number of strangers we can exploit.

∙ We conduct extensive simulations to compare our rout-

ing metric with greedy mechanism based on synthet-

ical mobility model and real DTNs traces, simulation

results show that our algorithm largely outperforms the

greedy mechanism, especially in terms of combined over-

head/packet delivery ratio and the average number of

hops per message.

The remainder of this paper is organized as follows. Section

II reviews the related work. In Section III, we discuss how to

integrate strangers into STRON. We first introduce the greedy

mechanism which has been applied into many DTNs routing

metrics in Section III.A. In Section III.B and Section III.C, we

explore how to identify strangers and ascertain the optimized

number of strangers we can employ, respectively. We present

our routing metric in Section III.D and have a discussion

in Section III.E. In Section IV, we make a performance

evaluation. Finally, we conclude our paper and discuss some

future research areas in Section V.

II. RELATED WORK

Routing messages through intermittently connected network

is challenging. In the past few years, researchers have proposed

several strategies to solve this issue. According to the contexts

they exploited, these solutions can be classified into the

following two categories.

A. Routing without stranger

Routing with extra nodes: Several projects try to deliver

messages by the help of extra nodes which are called data

MULEs or message ferries [14] [15] [16] [17] [18].

The authors of [14] first utilized mobile MULEs to collect

data for sparse sensor networks. The MULEs have large

storage capacities and renewable power, which make them

have the ability to buffer data for a relatively long time and

thus can be used in a delay tolerant environment. The data

MULEs scheme provides opportunistic forwarding between

static sensor nodes and the mobile MULEs, whereas, they

neglect the influence of the mobility of MULEs on routing per-

formance. On the contrary, the message ferries scheme (e.g.,

[15] [16] [17]) goes further in exploiting special mobile nodes

which are called ferries to deliver message by assuming control

or influence over ferries movements. For example, the authors

of [15] proposed the idea of exploiting controlled mobility of

extra nodes to facilitate message transmission in disconnected

Mobile Ad hoc Networks. W. Zhao, M. Ammar and E. Zegura

[16] designed two kinds of no-random movements to forward

data in DTNs. The first is node initiated mobility, where ferries

move around the deployed region according to conventional

routes. The second is ferry initiated mobility, where a ferry

will adjust its trajectory to meet up the node when receiving

a request from that node. They also evaluated the tradeoff

between the incurred cost of extra ferries and the improved

performance in [17]. Besides, the authors of [18] further

relaxed the assumptions used in [16] [17] and depended only

on partial observations and statistical information of nodes

mobility to enable ferries navigate themselves intelligently.

Routing with periodic mobility of nodes: In some other sce-

narios (e.g., bus transportation system [19] and interplanetary

internet [20]), the mobility patters of nodes have periodicity,

which motivates researchers to design periodic information

based routing scheme [21] [22] [23]. Most of them took a

modified Dijkstra algorithm to compute shortest paths between

sources and destinations and designed routing table based on

intermediate nodes along those paths. That is, each node has

a global view on network structures. For instance, S. Merugu

et al. [21] delivered messages over a space-time routing table

which was derived from the mobility of nodes and carried

by each node. S. Jain et al. [22] computed the shortest path

between transceivers by utilizing the periodicity of nodes

movements. Besides, the authors of [23] proposed a source

routing in DTNs, they exploited the expected minimum delay

(EMD) as forwarding metric and applied the Markov decision

process to derive the EMD of messages at particular times.

Routing with partial observations: Sometimes, it is difficult

or impractical to acquire global information of the network,

this is mainly because of the problems such as time-varying

topology, privacy protection or selfishness of nodes etc. In

these scenarios, different local contexts can be exploited to

improve routing performance. For example, by exploiting past

traces of buses to predict future behavior, MaxProp [3] shows

better performance than protocols that have proactive knowl-

edge. The authors of [4] presented SimBet, which exploited

neighbor’s adjacency matrix to compute the centrality and

similarity of nodes and then utilized these social attributes to

predict the best relay to the final destination. The adjacency

matrixes should be swapped and updated each time two nodes

have a contact. Different from the solutions of [3] and [4], the

authors of [5] proposed PER, a prediction and relay algorithm

for DTNs, which considered the time of a contact. A. Lindgren

et al. [6] presented PROPHET, in which the transitive property

and an aging constant were both considered to try to accurately

284283283

predict the probability of future encounters. Similar to [6],

CAR (context aware routing) was proposed in [7], which

exploited the context information such as the changing rate of

neighbors of a node and its current energy level to estimate the

delivery probability. In addition, J. Leguay et al. [8] presented

MobySpace, a high-dimensional Euclidean space constructed

by the past motion patters of nodes.

B. Routing with stranger

Note that most aforementioned schemes do not take stranger

into account, i.e., most existing schemes take a greedy mecha-

nism to deliver messages, thus, only such which have a higher

quality metric than current carriers can be selected as relays

to the final destinations. Whereas, routing performance can be

improved if permitting few strangers to participate in routing

process as the strangers are likely to be more useful for bring

messages to different parts of the deployed region, which

potentially increases the probability to meet up destinations.

Recently, there is few work that tries to explore the influence

of stranger on routing performance. For example, the authors

of [9] took low number of contacts and short duration as a

baseline to identify strangers and integrate the strangers into

their routing metric by assuming that the mobility of each

node/person can be acquired in advance. We argue that it

may not be practical since people always are reluctant to

expose their daily routines. On the other hand, the distributed

community-detection mechanisms used in [9] result in high

cost due to the information exchange and calculations, and

the complexity of adjusting several threshold parameters [12]

[13]. Moreover, we wonder that how to ascertain the optimized

values of several key parameters such as contact frequency,

short duration and low number of contacts.

Note that the obvious difference between our work and

the aforementioned works [9] comes from the fact that we

address a more challenging scenarios, where each node only

depends on itself to locally estimate the forwarding metric

to destination. Furthermore, we explore the influence of the

number of strangers on routing performance, rather than pure

strangers.

III. IMPLEMENTING STRANGER INTO STRON

In this section, we discuss how to integrate strangers into

STRON. We first introduce the greedy mechanism which has

been applied into many DTNs routing metrics in Section III.A.

In Section III.B and Section III.C, we explore how to identify

strangers and ascertain the optimized number of strangers we

can employ, respectively. In Section III.D, we present our

routing metric. Finally, we have a discussion in Section III.E.

A. Greedy mechanism

In the past few years, researchers have proposed a large

number of routing metrics in DTNs. Although they exploited

different kinds of contexts (e.g., similarity [4], intra-contact

time [6], energy level [7] and virtual community [24] etc.),

most of them took a greedy forwarding mechanism. That is,

when two nodes have a contact, a node with a lower quality

metric to the destination will forward messages to the node

with higher quality. For ease of presentation, in this paper, we

take intra-contact time as an example to illustrate the main

difference between the greedy mechanism and the STRON.

Let random variable 𝑋𝑖 denote the intra-contact time be-

tween node 𝑖 and other nodes, let 𝑥𝑖(𝑑) denote the intra-

contact time between node 𝑖 and any node 𝑑. Let 𝑁 denote

the set of nodes in the network. The notations used in this

paper are listed in Table I.

TABLE INOTATION SUMMARY

NOTATION Explanation

𝑁 The set of nodes∥𝑁∥ The number of nodes in the network𝑖, 𝑗 Two randomly chosen nodes𝑥𝑖(𝑗) Intra-contact time between node 𝑖 and node 𝑗𝑚𝑑 The destination of message 𝑚

𝐷𝑠(𝑖, 𝑗) The degree of strangeness between two nodes𝑃𝑖𝑗 Shortest path from 𝑖 to 𝑗𝑆𝑖𝑗 The number of strangers in 𝑃𝑖𝑗

𝑅𝑖𝑗 The number of relays in 𝑃𝑖𝑗

𝑅𝑠 The mean of 𝑆𝑖𝑗/𝑅𝑖𝑗

𝐼𝑠 The number of strangers which carry 𝑚𝑇𝑠 The threshold of 𝐼𝑠𝑓𝑝 Forwarding probability

We outline the greedy mechanism in Algorithm 1, which

summarizes the communication process between two ran-

domly chosen nodes 𝑖 and 𝑗. Take node 𝑖 as an example.

When meeting up node 𝑗, for any message 𝑚 that 𝑖 carries, if

its destination 𝑚𝑑 is node 𝑗, node 𝑖 delivers it to node 𝑗 and

removes it from 𝑖’s buffer. Otherwise, if node 𝑗 does not hold

this message, the two nodes swap their own quality metric. If

𝑥𝑖(𝑚𝑑) is smaller than 𝑥𝑗(𝑚𝑑), node 𝑖 forwards 𝑚 to node

𝑗, where nodes 𝑖, 𝑗 and 𝑚𝑑 ∈ 𝑁 .

Algorithm 1 Greedy mechanism, pseudo-code of node 𝑖

1: upon meeting up node 𝑗 do

2: for any message 𝑚 in 𝑖’s buffer do3: if 𝑚𝑑 == 𝑗 then4: 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑀𝑠𝑔(𝑚)5: 𝑟𝑒𝑚𝑜𝑣𝑒(𝑚)6: else if 𝑚 /∈ 𝑗 then7: 𝑖← 𝑥𝑗(𝑚𝑑)8: if 𝑥𝑖(𝑚𝑑) < 𝑥𝑗(𝑚𝑑) then9: 𝑓𝑜𝑟𝑤𝑎𝑟𝑑𝑖𝑛𝑔𝑀𝑠𝑔(𝑚)

10: end if11: end if12: end for

B. Identifying strangers

We use the mean of intra-contact time as threshold to

identify strangers. Let 𝐸(𝑋𝑖) denote the mean of 𝑋𝑖, we have

𝐸(𝑋𝑖) =

∑𝑖,𝑘∈𝑁,𝑖 ∕=𝑘

𝑥𝑖(𝑘)

∥𝑁∥ (1)

285284284

0 10 20 30 400

0.2

0.4

0.6

0.8

1

Contact times

Degr

ee o

f stra

ngen

ess

(a) CMM (NodeID=11)

1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

Contact times

Degr

ee o

f stra

ngen

ess

(b) KAIST (NodeID=21)

Fig. 1. Degree of strangeness vs Contact times

Hence, whenever node 𝑖 meets up node 𝑗, if 𝑥𝑖(𝑗) is smaller

than 𝐸(𝑋𝑖), we call that node 𝑗 is a stranger to node 𝑖.Let 𝐷𝑠(𝑖, 𝑗) denote the degree of strangeness between node 𝑖and node 𝑗, let function 𝑓 denote the mapping from 𝑥𝑖(𝑗) to

𝐷𝑠(𝑖, 𝑗), we have

𝑓 : 𝑥𝑖(𝑗)→ 𝐷𝑠(𝑖, 𝑗) (2)

Obviously, 𝑓 is a decreasing function, that is, the bigger the

value of 𝑥𝑖(𝑗) is, the smaller the value of 𝐷𝑠(𝑖, 𝑗) should be. It

is difficult and impractical to obtain an optimized 𝑓 , due to the

intermittent connectivity in DTNs. Whereas, it is possible to

gain some qualitative insights on roles of different functions,

we experimented the following three types: convex, linear and

concave in this paper.

𝐷𝑠(𝑖, 𝑗) =√

1− (𝑥𝑖(𝑗)/𝐸(𝑋𝑖))2 (3)

𝐷𝑠(𝑖, 𝑗) = 1− 𝑥𝑖(𝑗)

𝐸(𝑋𝑖)(4)

𝐷𝑠(𝑖, 𝑗) = 1−√

1− (1− 𝑥𝑖(𝑗)/𝐸(𝑋𝑖))2

(5)

To make the above equations hardness, we set 𝑥𝑖(𝑗) =𝐸(𝑋𝑖) if 𝑥𝑖(𝑗) > 𝐸(𝑋𝑖). Fig.1 portrays the behavior of

𝐷𝑠(𝑖, 𝑗) at different contact times when using Equation (4),

where the ID of node 𝑖 is set to 0 and two other nodes are

randomly chosen as partners, besides, CMM [27] denotes the

community mobility model and KAIST [25] presents a real

DTN trace (please refer to Section IV). Obviously, it shows

a close match to the Equation (4) (i.e., a linearly decreased

trend).

C. The optimized number of strangers we can employ

In this paper, we first count the number of strangers which

act as relays for other nodes on all shortest paths and then use

the mean ratio 𝑅𝑠 (i.e., the number of these strangers over that

of all relays ) to explore the optimized number of strangers

we can employ in STRON. Let 𝑃𝑖𝑗 denote the shortest path

from node 𝑖 to node 𝑗, let 𝑆𝑖𝑗 denote the number of strangers

which participate in 𝑃𝑖𝑗 and 𝑅𝑖𝑗 denote that of total relays,

we have

𝑅𝑠 =∑∀𝑖∈𝑁

∑∀𝑗∈𝑁,𝑗 ∕=𝑖

𝑆𝑖𝑗

R𝑖𝑗(6)

According to Equation (6), we get the values of 𝑅𝑠 are

0.7044 and 0.0435 in community mobility model and KAIST,

respectively. Interestingly, we discover that the value of 𝑅𝑠 in

synthetical mobility model is much bigger than that in real

DTNs trace. It is reasonable since that nodes in the latter

show bursty dispersion [25], instead of randomly selecting one

community and going ahead as in the former. Furthermore, the

authors of [26] indicated that the “Spray and Wait” scheme

can retain good performance under CMM by only assigning

a limited number of copies (about 5%∼10%) for each mes-

sage. Considering this fact, the threshold of the number of

strangers (𝑇𝑠) used in this paper is ∥𝑁∥ × 10%× 70.44% =∥𝑁∥× 7.044% under CMM and ∥𝑁∥× 4.35% under KAIST,

respectively.

D. STRON

In this subsection, we discuss how to integrate the strangers

and their number into STRON. We also take two nodes 𝑖 and 𝑗as samples. When node 𝑖 meets up node 𝑗, for any message 𝑚in 𝑖’s buffer, if its destination 𝑚𝑑 is node 𝑗, node 𝑖 delivers it to

node 𝑗 and removes the message from its buffer. Otherwise,

if node 𝑗 does not hold this message, node 𝑖 will make a

forwarding decision based on the following two situations:

∙ If 𝑥𝑖(𝑚𝑑) is bigger than 𝑥𝑗(𝑚𝑑) and node 𝑗 is a

stranger to node 𝑖 and the number of strangers that

have received the message is smaller than 𝑇𝑠, the node

𝑖 forwards 𝑚 to node 𝑗 with a probability 𝑓𝑝 =𝐷𝑠(𝑖, 𝑗) (𝑥𝑗(𝑚𝑑)/(𝑥𝑖(𝑚𝑑) + 𝑥𝑗(𝑚𝑑))).

∙ If 𝑥𝑖(𝑚𝑑) is smaller than 𝑥𝑗(𝑚𝑑) and node 𝑗 is

not a stranger to node 𝑖, the forwarding probability

is (𝐸(𝑋𝑖)/𝑥𝑖(𝑗)) (𝑥𝑗(𝑚𝑑)/(𝑥𝑖(𝑚𝑑) + 𝑥𝑗(𝑚𝑑))), other-

wise, if the number of strangers that have received the

message is smaller than 𝑇𝑠, the forwarding probability is

set to 1.

We list the above communication process in Algorithm 2,

where 𝐼𝑠 denotes the number of infected strangers.

E. Possible limits and issues

In this paper, we discuss the influences of the strangers and

their number on routing performance in DTNs. We do not

focus on the correlations among strangers, that is, we only

choose 𝑘 strangers out of ∥𝑁∥ nodes in the network (𝑘 < 𝑇𝑠),

we do not ascertain which 𝑘 strangers should be selected. We

think it deserves separate study and leave it for future work.

In addition, researchers have proposed lots of metrics to

weigh the importance of nodes, we think all of them should

be esteemed, whereas, since we mainly focus on the strangers

and their optimized number, we here only take intra-contact

time as an sample and will evaluate other metrics in future

work.

IV. PERFORMANCE EVALUATION AND ANALYSIS

A. Mobility model, DTNs trace and system parameters

In this paper, we use a synthetical mobility model which

are called community mobility model (CMM) [27] and a real

DTNs trace called KAIST [25] to evaluate the performance of

greedy mechanism and STRON.

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Algorithm 2 STRON mechanism, pseudo-code of node 𝑖

1: upon meeting up node 𝑗 do

2: for any message 𝑚 in 𝑖’s buffer do3: if 𝑚𝑑 == 𝑗 then4: 𝑑𝑒𝑙𝑖𝑣𝑒𝑟𝑀𝑠𝑔(𝑚)5: 𝑟𝑒𝑚𝑜𝑣𝑒(𝑚)6: else if 𝑚 /∈ 𝑗 then7: 𝑖← 𝑥𝑗(𝑚𝑑)8: if 𝑥𝑖(𝑚𝑑) > 𝑥𝑗(𝑚𝑑)

⋀𝑥𝑖(𝑗) < 𝐸(𝑋𝑖)

⋀𝐼𝑠 < 𝑇𝑠

then9: 𝑚→ 𝑗 with a forwarding probability 𝑓𝑝

10: if 𝑓𝑜𝑟𝑤𝑎𝑟𝑑𝑒𝑑 then11: 𝐼𝑠 ← 𝐼𝑠 + 112: end if13: end if14: if 𝑥𝑖(𝑚𝑑) < 𝑥𝑗(𝑚𝑑) then15: if 𝑥𝑖(𝑗) > 𝐸(𝑋𝑖) then16: 𝑚 → 𝑗 with a forwarding probability

(𝐸(𝑋𝑖)/𝑥𝑖(𝑗)) (𝑥𝑗(𝑚𝑑)/(𝑥𝑖(𝑚𝑑) + 𝑥𝑗(𝑚𝑑)))17: else if 𝑥𝑖(𝑗) < 𝐸(𝑋𝑖)

⋀𝐼𝑠 < 𝑇𝑠 then

18: 𝑚→ 𝑗 with a forwarding probability 1

19: 𝐼𝑠 ← 𝐼𝑠 + 120: end if21: end if22: end if23: end for

The system parameters used in CMM are listed below. The

simulation area is 600𝑚 × 600𝑚 and is divided into 9 sub-

communities. We randomly place 60 mobile nodes at the area.

Each node randomly selects one community as its hometown

that it is more likely to visit than other communities. The

mobility of a node is that it randomly selects a point of a

community as its potential destination, moves there, pauses

there for a while and selects a new destination. If it is at

hometown, it still stays in hometown with a high probability

𝑝 and visits other communities with a probability 1− 𝑝. If it

is away from hometown, it will return hometown with a high

probability 𝑞 and other communities with a probability 1− 𝑞.

The values of 𝑝 and 𝑞 are set to 0.8 and 0.9, respectively,

two default values also adopted in [6]. The mobility speed

is between 10m/s and 30m/s. The pause time is 1s and the

communication range is 30m.

In KAIST, 34 volunteers carried the GPS devices (GPS

60CSx) from 2006-09-26 to 2007-10-03 and altogether 92

daily traces were gathered. Each individual trace consists

of a sequence of three-tuples (Timestamp, X-coordinate, Y-

coordinate), which denotes a stay point recorded every 30

seconds. The communication range of nodes in KAIST is set

to 250m, a typical value of WiFi.

For the two scenarios, each source sends one message to a

randomly chosen destination and altogether 1200 messages are

generated. Besides, since each relay needs to buffer packets

for a long period of time in order to cope with the intermittent

connections, we compare the two routing strategies in a buffer

space constrained system to better understand and observe

their performance. The simulation results are the average

over 20 runs. The evaluation metrics are packet delivery ratio

(PDR), average cost and average number of hops per message.

Notice that we here use a correlative factor (average cost)

to further illustrate the performance of two strategies, which

means a message needs to be forwarded how many times

before it is received by the destination node, hence, we have

average cost =forwarded messages

received messages

Obviously, the bigger the value is, the lower the efficiency of

a protocol should be.

B. Performance evaluation

In the following figures, we use terms “Convex”, “Linear”

and “Concave” to denote the three kinds of decreased function

used in STRON respectively. Fig.2 and Fig.3 illustrate the

performance of packet delivery ratio when increasing the

size of buffer space. It’s obvious to see that the buffer size

has a heavy effect on the PDR metric. When buffer size

is relatively small, STRON shows better performance than

greedy mechanism. Compared to the greedy mechanism, it

achieves up to a 70-150% improvement in PDR under CMM

and 20-800% under KAIST when the size of buffer space

is smaller than 400. This is mainly because that STRON

consumes fewer resources, thus, the impact of buffer size

on it’s performance is very slight. For example, when the

buffer size exceeds 700 and 500 under the two scenarios

respectively, the PDR performance dominated by STRON is

almost freedom from the buffer size. In addition, we notice

that the greedy mechanism slightly outperforms STRON when

the buffer size is bigger than 600 under KAIST scenario. This

outlier is, we conjecture, mainly because the connectivity of

KAIST is poorer than that of CMM used in this paper, hence,

the forwarding probability will play a critical role in PDR

performance when the buffer size is relatively big.

0 200 400 600 800 1000 12000

0.2

0.4

0.6

0.8

1

Buffer space

PDR

ConvexLinearConcaveGreedy

Fig. 2. Packet delivery ratio (CMM)

Fig.4 and Fig.5 portray the performance of routing cost.

It’s interesting to note that increasing the buffer size results

in different influences on cost metric. Generally speaking,

287286286

0 200 400 600 800 1000 12000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Buffer space

PDR

ConvexLinearConcaveGreedy

Fig. 3. Packet delivery ratio (KAIST)

STRON first shows an increasing trend and then reaches

stable state. Compared with greedy mechanism, it at least

reduces the communication cost by 25-67% under CMM and

almost 30% under KAIST when both reach stable state. From

Algorithm 2, we know that STRON considers the strangers

and their numbers. On the one hand, the several strangers

can bring messages into different subareas of the network,

which increases the probability to meet up destinations. On

the other hand, it delivers messages with different forwarding

probabilities according to the degree of strangeness between

nodes and the limited number of strangers, which reduces the

number of redundant copies, thus, alleviating the overhead of

the network.

0 200 400 600 800 1000 120010

20

30

40

50

60

Buffer space

Cos

t

ConvexLinearConcaveGreedy

Fig. 4. Cost (CMM)

Fig.6 and Fig.7 demonstrate the average number of hops per

message. It seems like increasing the buffer size also increases

the average hops. The reason behind this is that more messages

are delivered. These extra delivered messages are those which

could be dropped at smaller buffer spaces, but now are able to

stay in the buffer space long enough to be delivered to their

destinations, which results in a longer hops for those messages.

Compared with greedy mechanism, STRON still exhibits a

good behavior. It almost reduces half of the average hops

caused by the former. For instance, at KAIST, when both reach

0 200 400 600 800 1000 12000

20

40

60

80

100

Buffer space

Cos

t

ConvexLinearConcaveGreedy

Fig. 5. Cost (KAIST)

stable state (i.e, when the buffer size is bigger than or equal

to 800), the average number of hops per message achieved

by STRON is near to 3.2 (“Concave”), whereas the greedy

mechanism leads to longer routing paths almost resulting in

an average hop value of 5.

Looking more closely at the variants of STRON. When

integrating all of the above three metrics, we see that concave

scheme is most the best of the STRON strategy due to the

more refined forwarding probability it used.

0 200 400 600 800 1000 12002

2.5

3

3.5

4

Buffer space

Ave

rage

Hop

s per

Mes

sage

ConvexLinearConcaveGreedy

Fig. 6. Average number of hops per message (CMM)

V. CONCLUSION

In this paper, we study DTNs routing within a more

challenging scenario. We explore the influence of strangers

and their number on routing performance. We present an

adaptive solution to identify strangers and propose a statistical

method to estimate the optimized number of strangers we can

employ. Based on this heuristic number, we integrate strangers

into DTNs routing. That is, when two nodes meet up, we

take different forwarding probability based on the degree of

strangeness between them and the current number of infected

strangers. We finally compare STRON with the greedy mech-

anism through synthetical and trace-driven simulations, the

results show that our routing strategy has a better performance,

288287287

0 200 400 600 800 1000 12001.5

2

2.5

3

3.5

4

4.5

5

Buffer space

Ave

rage

Hop

s per

Mes

sage

ConvexLinearConcaveGreedy

Fig. 7. Average number of hops per message (KAIST)

especially in terms of combined overhead/packet delivery ratio

and the average number of hops per message.

One significant topic for future work is to study the influ-

ence of different 𝑘 strangers on the STRON performance.

ACKNOWLEDGMENT

We acknowledge the support of the National 973 Project

of China under Grant No.2011CB302701, the National Sci-

ence Fund for Distinguished Young Scholars under Grant

No.60925010, the National Natural Science Foundation of

China under Grant No.60833009, the 111 Project under Grant

No. B08004 and the Fundamental Research Funds for the

Central Universities (2011RC0205). We also wish to thank the

reviewers for their valuable comments and the CRAWDAD

archive project for making the DTNs traces available to

research community.

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