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Utility-based Exploration for Performance
Enhancement in Opportunistic Mobile Networks
Barun Kumar Saha, Sudip Misra Senior Member, IEEE, and Sujata Pal Student Member, IEEE
Abstract—Opportunistic Mobile Networks (OMNs), which are formed by mobile devices carried by human users, present an interesting
communication paradigm in the absence of access to global network connectivity or any form of network infrastructure. In this work, we
combine the natural mobility of the human users – which has been shown to resemble Levy Walk – in OMNs, together with intentional
explorations. We consider the case where the human users in an OMN undergo explorations, i.e., occasionally visit a set of fixed Point
of Interests (PoI), for example, shopping malls. The objective of this work is two-fold – 1) Establishing that limited explorations of the
users can help in enhancing the performance of OMNs, and 2) Formulating a method to decide whether or not a user should undergo
exploration. In this regard, we propose two schemes based on Prospect Theory (PT) and Expected Utility Theory (EUT). The results
of extensive simulation-based performance evaluation indicate that limited exploration can promote the delivery ratio of messages
by large levels — about 7–33% depending on the number of randomly placed PoI, and about 36% depending upon the terrain size.
Moreover, the time spent in exploration, on an average, is negligibly small – a typical value is about 0.55% of the simulation duration,
which indicates its feasibility in real life.
Index Terms—Opportunistic Mobile Networks, Delay Tolerant Networks, Prospect Theory, Expected Utility Theory, Exploration.
F
1 INTRODUCTION
Opportunistic Mobile Networks (OMNs) (or Pocket
Switched Networks [1]) are formed among the mobile
and portable devices (such as, smartphones) carried by
human beings. Such devices are often equipped with Wi-
Fi and Bluetooth interfaces that help in communication.
In particular, two devices in an OMN communicate
when they come within the transmission range of one
another. Therefore, the consideration of how a user
moves directly affects message delivery in OMNs.
It has been found that human mobility pattern (specif-
ically, movement flight length and pause time at any
location) reflects characteristics similar to heavy-tailed
distributions such as, Levy flights [2], [3]. In particular,
Rhee et al. [2] analyzed several real-life location traces
collected from users across different cities. Consequently,
the authors proposed the truncated Levy Walk (TLW)
mobility model that can mimic human mobility in the
real world.
However, a few questions largely remain unaddressed
in this context. For example, whether or not intentional
exploration – visiting a place intentionally – by users
would be beneficial for OMNs? Moreover, what can
motivate such intentional explorations? In this work, we
attempt to investigate these two issues. It may be noted
that in the field of psychology, how agents (for example,
human beings, living organisms and autonomous soft-
ware systems) switch between exploration and exploita-
tion is largely projected as an open question [4], [5]. In
•The authors are with the School of Information Technology, Indian Insti-
tute of Technology Kharagpur, India. E-mail: {barun.kumar.saha, smisra,
sujatadas.pal}@sit.iitkgp.ernet.in
general, “exploitation” refers to utilizing opportunities
currently available at hand, which may not always be op-
timal; “exploration” refers to looking for new prospects,
which could be risky, but could be more rewarding at
the same time [4]. In our context, “natural” movement
of human beings amounts to exploitation, whereas ex-
ploration is analogous to intentional exploration.
In particular, we consider a set of human users moving
according to the TLW, together with a set multiple points
of interest (PoI). As shown in Fig. 1, although a PoI
can span over a vast area geographically (for example,
a cafeteria), from the point of view of the OMN, a
PoI’s geographic presence is small and limited by its
transmission range (to continue with the example, a
router inside the cafeteria).
Geographic
boundary of PoI
ε-neighborhood
of PoI
PoI
Mobile nodes
ε
Estimated
PoI location
ε
Fig. 1: Illustration of a PoI and its ε-neighborhood.
In other words, we differentiate between the geo-
graphic and network-centric notion of a PoI. We would
further elaborate on this later (in Section 3.2).
Unlike TLW, we consider a scenario wherein the mo-
Accepted Version (For personal use only)
2
bile users intentionally visit these PoI (in continuation
of our example, neighboring regions of the router in
the cafeteria) occasionally. More specifically, the mobile
devices of the users would recommend them – much
like mobile recommender systems used for tourism [6],
[7] – to possibly visit such locations. The underlying
objective is to attempt to maximize the delivery of the
messages generated in the OMN, as perceived by these
opportunistically networked devices.
A logical question that arises here is why (or how)
intentional explorations would be beneficial for the per-
formance of OMNs. It may be noted that by intentional
explorations, we are proposing a very subtle prospect.
Such explorations would often let multiple users con-
verge at different PoI, which increases the contact op-
portunities, as compared to TLW, with the PoI. Thus,
more messages can be passed on to the PoI from other
mobile devices. This, in turn, improves the chances of
message delivery in OMNs.
But in which scenarios would such intentional explo-
ration be useful? In the recent times, OMNs have found
several novel applications. Maggiorini et al. [8] consid-
ered the feasibility of opportunistic mobile games in
cities using public transportation. Intentional but infre-
quent visits – based on what the user’s device perceives
– to PoI might be helpful for the gaming experience since
more users would likely be present there. On the other
hand, tourist recommender systems [6], [7] can leverage
the tourist influx for message dissemination (similar to
the OMN in the RollerNet experiment [9]).
Fig. 2 provides a high-level functional overview of
this work. A human user can visually locate1a PoI
(with some error) and stores the location in his/her
device. Devices of the users, on the other hand, ex-
change the stored locations of PoI with one another.
Based on such locations known by a device, along
with other network parameters, a device recommends
its owner of possible exploration (to some nearby PoI’s
ε-neighborhood, discussed in Section 3.2) in order to
enhance the performance of the OMN. Finally, a user
himself/herself decides whether or not he/she should
undergo the recommended exploration.
1.1 Assumptions
The following assumptions are made in this work.
•All PoI know their exact location (coordinates).
•Distance between any two PoI device is much larger
than the transmission range of a device.
•A human user can perform visual discovery of PoI
any time during his/her flight.
•When an ordinary device (carried by a human user)
comes in contact with a PoI, the latter sends its
location to the ordinary device.
1. For example, several related Android apps are available
at https://play.google.com/store/search?q=object%20distance%
20estimator&c=apps&hl=en
Store estimated
location
Get exact PoI
location
Visually discover?
PoI with error ε
Resolve PoI
locations
Suggest
exploration
Perform
exploration
Exchange
locations
database
User PoI Device Other Device
Fig. 2: Sequence of interactions among users, their de-
vices, other devices and PoI.
•Any pair of devices (including a PoI device, from
the network-centric notion) can communicate when
they are within the transmission range of one an-
other. Such communication is possible irrespective
of whether a device is stationary or in motion.
•Users check their devices from time to time for
any recommendation for exploration. However, the
users themselves decide whether or not to undergo
such recommended exploration.
1.2 Contributions
The specific contributions of this work are summarized
below.
•Augmenting user movement with intentional explo-
ration, which is defined as visiting a (known) PoI
by a user intentionally, i.e., based on some purpose.
•Trading off a small fraction of “natural” movement
of users (according to the TLW model) with inten-
tional exploration.
•Proposing Prospect Theory (PT)- [10] and Expected
Utility Theory (EUT)-based schemes that motivate
such intentional exploration in order to enhance
communication aspects in the OMN. In other words,
message delivery is the purpose of intentional ex-
plorations.
•Establishing via exhaustive simulations (using two
well known routing protocols for) that EUT- and
PT-based schemes ensure higher delivery of the
messages as compared to the TLW model.
•Moreover, showing that such improvements come
at a very low cost in terms of average exploration
time per user.
1.3 Organization
The remainder of this work is organized as follows.
Section 2 presents a survey of the contemporary works
in the related domains. Section 3 summarizes the TLW
mobility model. Consequently, it presents TLW with
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3
exploration, termed as TLWE, and discusses several
methods of PoI discovery. Finally, the motivation of users
for undergoing exploration in terms of users’ revenue
is discussed. Exploration schemes based on EUT and
PT are presented in Section 4. In Section 5, we discuss
the simulation setup used for performance evaluation.
Section 6 presents the simulation results and related
discussions. Finally, Section 7 concludes this work.
2 RE LATED WORK
A large number of works were dedicated to the charac-
terization of human mobility, the traces of which were
gathered based on experimentation. It was found that
the inter-contact times (ICTs) in such scenarios are not
exponential, but rather exhibit a heavy tail [1], [11].
Karagiannis et al. [11] observed that the distribution
follows power law up to a certain characteristic time, be-
yond which it exhibits exponential decay. Moreover, they
noted that the pairs of nodes tend to meet repeatedly at
some “home locations”. Casteigts et al. [12], on the other
hand, investigated a different aspect by measuring the
temporal lags in DTNs using time-varying graphs [13],
where the contact durations were variable.
Based on a set of real-life movement traces collected
using GPS, Rhee et al. [2] concluded that human move-
ment can be modeled using Levy Walk. Further, the au-
thors proposed a synthetic truncated Levy Walk (TLW)
model, which resembles movement of human beings
and generates ICT distribution similar to that discussed
above. Rhee et al. noted that real human movement and a
TLW process, however, have some differences, since hu-
man movement is not entirely random. Moreover, such
motion is affected by different parameters, for example,
home-coming tendencies and geographical constraints.
On a related note, Kosta et al. [14] proposed the small
world in motion (SWIM) mobility model capable of
producing realistic human contact events.
One of the fundamental objectives of any network,
including OMNs, is routing. In the recent past, sev-
eral routing protocols (for example, Spray-and-Wait
(SnW) [15], Probabilistic Routing Protocol based on His-
tory of Encounters and Transitivity (PRoPHET) [16],
Community-Aware Opportunistic Routing [17], and
hypercube-based routing [18]) have been proposed and
their performance has been evaluated. Mei et al. [19]
proposed a stateless routing protocol based on the obser-
vation that people with similar interest tend to meet each
other quite often. The authors considered the users in
the network having individual interest profiles. In such
a network, a message is routed to one or more users
based on their respective interest profiles.
Although OMNs are so-called unconventional net-
works, some innovative applications are already emerg-
ing, for example, opportunistic mobile games [8]. Mag-
giorini et al. [8] considered the feasibility of opportunistic
mobile games in cities using public transportation. The
results of performance evaluation based on simulations
hinted at such feasibility. The authors also outlined some
guidelines for any such deployment.
It may be observed here that intentional but infre-
quent visits – based on what the user’s device perceives
and user confirms – to PoI might be helpful for such
gaming experience. For example, let us consider a game
wherein daily top scores or leaderboard information are
exchanged among devices. Since PoI (in the geographical
sense) typically witness gathering of large number of
people, such locations may be helpful for opportunistic
synchronizations. In this context, the functionality of mo-
bile tourist recommender systems [6], [7] may be noted.
In essence, such systems recommend a tourist a place
that he could visit next. In our context, a device may
recommend its owner places which he could explore
next. Of course, it is up to the user of the device whether
or not he should comply with that recommendation.
In general, it may be noted that whether or not (lim-
ited) exploratory movements are beneficial to an OMN
largely remain unaddressed. The closest work in this
context – to the best of our knowledge – is perhaps
[20], where “purposeful mobility” of the nodes were
considered to reduce average power consumption. How-
ever, in [20], an end-to-end communication paradigm
was considered, and movement of the mechanical nodes
therein do not correspond to natural movement of hu-
man beings. Such a scenario thus, does not fit in the
context of OMNs considered here. Therefore, studying
the aspects of exploration by human users, and, in turn,
its effect on communication aspects (message delivery,
in particular) presents an interesting problem. This is
particularly relevant in the case of OMNs, where human
beings carry their devices and thus, are a part of the
network.
In this work, we, therefore, attempt to investigate two
questions:
1) Are intentional explorations by human users in
limited extent beneficial to the performance of an
OMN?
2) Can such explorations be motivated using some
decision theoretic framework?
We would explore these two issues in the remainder
of this work. In particular, we use Prospect Theory [10]
that was proposed to model human decision making,
which often is perceived far from rational. For the sake
of completeness, we also use Expected Utility Theory
that models decision making by rational agents.
For the benefit of the reader, we summarize the im-
portant notations used in the remainder of this work in
Table 1.
3 EXPLORATION AND POI DISCOVERY
In this Section, we summarize the truncated Levy Walk
(TLW) mobility model [2]. We, then, present a vari-
ation of the TLW, truncated Levy Walk with explo-
ration (TLWE), which couples TLW with probabilistic
exploration, in order to enhance the message delivery
performance of the OMNs.
Accepted Version (For personal use only)
4
TABLE 1: Summary of Notations
Notation Description
SP(t)Set of PoI known until time t
S0Set of PoI known from previous knowledge
SE(t)Set of PoI known by visiting them until time t
SV(t)Set of PoI known by visual discovery until time t
SK(t)Set of PoI known from encounter with other nodes until
time t
pEProbability of exploration
pVProbability of visual discovery
RVRadius of visual discovery
Tavg Average exploration time
v(·)Value/utility function
π(·)Probability mapping function
L, E Actions denoting movement with TLW and exploration,
respectively
D, F, X Outcomes representing delivery, forwarding and no
action taken, respectively
nj(·)Total number of messages delivered for a given action,
j∈ {D, F, X }
ˆnj(·)Expected number of messages to be delivered for a
given action, j∈ {D, F, X }
pj(·)Outcome probability for a given action, j∈ {D, F, X }
U(·)Utility of a gamble/lottery
w(·)Probability weighting function
3.1 Truncated Levy Walk
TLW [2] consists of a sequence of steps, where each step
is represented with a tuple S= (l, θ, ∆tf,∆tp). Here,
l > 0denotes the length of the flight; θ∈[0◦,360◦]de-
notes the direction; the flight time is denoted by ∆tf>0;
and ∆tp≥0denotes the pause time. The distributions
of the flight length and the pause time, p(l)and ψ(∆tp),
respectively, follow the Levy distribution: p(l)∼1/l(1+α)
and ψ(∆tp)∼1/∆t(1+β)
p, where 0< α, β < 2. In [2], the
authors, based on the experimental data, modeled the
flight time as ∆tf=kl(1−ρ), where kand ρare constants;
0≤ρ≤1. Thus, every time a traveler generates a
tuple S, so that 0< l ≤lmax, and waits for time
0≤∆tp≤∆tp,max after reaching the destination. The
step time, ∆ts= ∆tf+ ∆tp, gives the time spent by a
traveler for a given step.
Fig. 3 shows a fundamental characteristic of the TLW
– the node diffusion distribution (Fig. 17 in [2]). With
the increasing α, the diffusion decreases. In other words,
with increasing α, the nodes have less movement. Here,
“RWP” indicates the Random Waypoint mobility model.
0
0.2
0.4
0.6
0.8
1
0 500 1000 1500 2000
P(X < x)
Distance x (meter)
α = 0.5
α = 1.0
α = 1.5
α = 2.0
RWP
Fig. 3: Truncated Levy Walk: diffusion of the nodes
increases as αdecreases.
3.2 Truncated Levy Walk with Exploration
We consider the nodes – human owners together with
their devices – in an OMN to move according to the TLW.
A person, who is moving normally, decides whether or
not to visit a PoI known by him/her.
Before proceeding further, we crisply define here the
notion of intentional exploration considered earlier. Unless
otherwise mentioned, the term exploration would hence-
forth refer to intentional exploration in the remainder of
this work.
Definition 1. Exploration: By exploration it is meant that
a node (user) in an OMN visits a known PoI with probability
pE∈[0,1] and continues moving according to the TLW with
the probability 1−pE.
Here, pEcaptures the interest of a user to deviate from
his/her natural movement and engage into exploration
to a PoI.
Two interesting questions arise here is. First, when
there are multiple known PoI, which PoI does a user
visit to as part of his/her exploration? On one extreme, a
user can visit the nearest PoI. However, there is a pitfall.
Since TLW fundamentally involves more flights with
shorter lengths, a user can end up visiting the nearest PoI
repeatedly. On the other hand, selecting a PoI purely on a
random basis for exploration is unrealistic. Therefore, we
choose the second-closest PoI (from the current location)
as the destination. Henceforth, whenever we say that a
node is exploring, we would mean that it is visiting its
second-closest PoI. Of course, if only one PoI is known,
then that is the only PoI that a node would visit.
Second, would exploration be performed at any time?
In other words, is exploration independent of the dis-
tance traveled by a user? In reality, it is not usually so.
A user typically travels his/her current neighborhood
(exploits) before embarking into exploration. To account
for this, we consider a parameter θE, the threshold flight
length for exploration. A user opts in for exploration if
the length of his/her last flight was more than θE. Thus,
pEand θEhelps to find a tradeoff between exploration
and exploitation.
As promised in Section 1, we distinguish between
the geographic and network-centric notion of PoI. As
depicted in Fig. 1, geographically, a PoI can span over
a large area. For example, let us consider a cafeteria
located at the center of a city. From the perspective of
a human being, the cafeteria serves as a PoI. Now, let
us consider that the cafeteria has a wireless hotspot or a
throwbox2[21]. In our context, such a throwbox serves as
a PoI from the point of view of the OMN. With reference
to Fig. 1, we also define the ε-neighborhood of a point
(location).
2. A throwbox is a battery-powered stationary device with storage,
processing capability and typically large transmission range. It was
found that placement of such devices can increase the capacity of
Delay Tolerant Networks by introducing contact opportunities among
the otherwise disconnected nodes.
Accepted Version (For personal use only)
5
Definition 2. ε-Neighborhood: The ε-neighborhood of a
given point is the circular area covered by a circle of radius ε
centered at the given point.
In the remaining of this work, whenever we say that
a node visits a PoI, the node actually visits a location in
the ε-neighborhood of the concerned PoI.
3.2.1 PoI Discovery
A mobile node in an OMN can know about the PoI in
one or more of the following four ways:
1) Previous knowledge: Let, S0be the set of PoI
known by a node, based on its previous knowl-
edge. For example, a person in a city knows the
locations of the nearby shopping malls and movie
theaters.
2) PoI encounter: When a node reaches a previously
unknown PoI as its destination location as part the
TLW mobility model, it stores that location. Let,
SE(t)be the set of all such PoI known by a mobile
node.
3) Visual discovery: Moreover, a node (user) can
locate a PoI, not known to it (him/her) yet, within
a radius RV>0, from its current location, with
a probability pV∈[0,1]. This probability accounts
for the cases when a node fails to visually locate
a PoI due to obstructions or otherwise. However,
since this is an estimated location, we consider
an error margin of ε, as shown in Fig. 1. Let,
SV(t)be the set of PoI discovered by a mobile
node in this way. This visual discovery mechanism,
which is unavailable in the communication devices,
highlights a typical context awareness of the human
beings.
4) Known from others: When two nodes encounter
each other – either mobile-mobile or mobile-PoI –
they exchange locations of the PoI known to each
other. This, in turn, helps the other nodes in the
geography concerned to learn about the location
of the PoI. The knowledge so gained helps the
(owners of the) mobile nodes in deciding their
future destinations. Let, SK(t)be the set of PoI that
a node knows till time t, through communication
with the other nodes.
Therefore, at any time instant t, the set of PoI known
by a node is given by SP(t) = S0∪SE(t)∪SV(t)∪SK(t).
For the PoI themselves, SE(t) = ∅and SV(t) = ∅.
It may be noted here that the visually estimated lo-
cation of a PoI can be different from the actual location
(Fig. 1). However, we assume that a PoI knows its own
location precisely. Therefore, when a device comes in
contact with a PoI, the device stores the actual location
of the PoI.
This would be an appropriate place to discuss about
the control overhead in exchanging PoI locations. We
argue that such overhead can be neglected in comparison
with “actual” data exchange in an OMN. This can be
justified in several ways. First, the number of PoI in
a geographic region is finite and small, which makes
the number of records to be stored (and exchanged)
manageable. Second, the amount of space required for
storing a single PoI location is negligibly small. For
example, if we represent the latitude and longitude (up
to 4decimal places3) of a PoI as a string, it would
take less than 20 bytes4to store a single PoI’s location.
Moreover, it is possible to compress such (serialized)
text before transmitting. To summarize, it is feasible to
reduce the volume of control data exchanged. Therefore,
the bandwidth “wastage” for exchanging control infor-
mation5can be practically ignored. This also makes the
proposed scheme scalable with an increase in size of
terrain or number of PoI. In fact, after a certain threshold
time, when a node knows about “enough” PoI, it can
pause receiving PoI updates from other nodes. However,
due to space constraints, we refrain from elaborating
further on this.
3.2.2 Movement of the nodes
The subsequent movement of the mobile nodes is a mix
of normal TLW and exploration – they visit a randomly
chosen PoI from their database with a probability pE,
and move according to the TLW with probability 1−pE.
For simplicity, we assume that the decision whether
to explore or not is taken after reaching its current
destination location.
It may be noted that the movement of the nodes is
entirely distributed and decentralized. In other words,
only the nodes themselves decide on how to move. The
following concretely defines the terminologies used in
this work.
Definition 3. Simple exploration (TLWE): A user in an
OMN, who knows about at least a single PoI, explores at the
end of his/her current flight. In case the user knows about only
a single PoI and reaches there at the end of his/her current
flight, the subsequent flight is according to the TLW without
exploration.
Definition 4. Improved (utility-based) exploration: A
user in an OMN, who knows about at least a single PoI,
explores at the end of his/her current flight based on a certain
utility. In other words, a utility – defined as a function of the
outcome of the exploration – decides whether a user should
explore or not.
Definition 5. Exploration time: Let, T={t1, t2,· · · , tf}
be the set of flight times of a mobile node (user). Let, TE⊂
Tdenote the set of flight times corresponding to the node’s
exploration to the PoI. The total exploration time is given
by Pti∈TEti. Thus, the average exploration time per node is
Tavg =Pti∈TEti
|NM|.
3. This can give a precision of around 10 m – see https://en.
wikipedia.org/wiki/Decimal degrees
4. Represent the location as xx.xxxx,yyy.yyyy
5. It may be noted that several routing protocols (e.g., PRoPHET
[16]) exchange control information at every contact.
Accepted Version (For personal use only)
6
3.3 Motivation of Users for Exploration
An interesting question is why users should explore?
Alternatively, how users can be motivated to undergo
intentional explorations to PoI? It may be noted that
today, several services do exist that provide users with
some form of incentives for performing some specified
actions. For example, Amazon Mechanical Turk6can be
used to crowdsource tasks among human users and pay
them accordingly for their efforts.
Similarly, certain services (such as, FreeCharge7) offer
coupons for talk time recharge of mobile phones. Ama-
zon also provides a service to send gift coupons as email
to a person.
We envision that similar incentive schemes can be
leveraged to motivate the users. A measure of users’ con-
tribution is required for this purpose. A simple scheme
would be to, at each PoI, keep track of the number of
contact with different nodes. Subsequently, for each user
i, the frequency of contacts, ci(t), until time instant tcan
be translated into “points” (or revenue) using a concave
utility function, for example, r(ci(t)) = log(ci(t)), where
ci(t)>0. A user can then redeem the points so collected
using some of the above discussed incentive schemes
such as, talk times or coupons for shopping malls.
4 EXPLORATION BASED ON UTIL ITY THEO -
RIES
Although the above discussed exploration model is
probabilistic in nature, a question, however, still persists
– should the nodes (users) always undergo explorations
simply based on random chances? In real life, actions
are often based on self-evaluation of past information
[22] or associated with some form of utility, for example,
incentive offered to the nodes for cooperating [23]. To
decide on and justify the exploratory actions, we, there-
fore, formulate a model of exploration based on two
popular utility theories – Expected Utility Theory (EUT)
and Prospect Theory (PT) [10].
EUT has been predominantly used in the context of
decision making process. However, it has been shown
that the human decision making process violates the
commonly used EUT [10]. Since, we consider that the
decision making is performed by human users in the
OMN, we propose an exploration scheme based on PT.
For the sake of completeness, however, we also consider,
and contrast the performance with, a similar EUT-based
scheme. Before proceeding further with the individual
theories, we present the general terminologies and nota-
tions below.
4.1 Actions and Outcomes
Let, (x1, x2,· · · , xn)be a set of outcomes correspond-
ing to a lottery/gamble with respective probabilities
6. https://www.mturk.com/mturk/welcome
7. https://www.freecharge.in/
TABLE 2: Utility and probability mapping functions
EUT PT
Outcome
utility/value v:x→u(x)∈Rv:x→u(x)∈R
Probability
mapping π:p→p π :p→w(p)∈(0,1)
(p1, p2,· · · , pn). The utility of this lottery has the follow-
ing general form:
U=
n
X
i=1
v(xi)×π(pi),(1)
where v(·)is a value/utility function defined on the
domain of outcomes, and π(·)is a probability mapping
function. When multiple such lotteries are available, the
one having the maximum utility Ushould be chosen.
To summarize the difference between EUT and PT, the
specific nature of v(·)and π(·)are shown in Table 2.
In particular, an utility is assigned to the value of each
outcome. Moreover, unlike EUT, PT uses a probability
mapping function, w(·), that transforms the individual
objective probabilities into the subjective ones.
We now model the problem at hand using the utility
theory. The specific nature of the problem based on PT
would be presented subsequently.
Let us consider the set A={E=Explore, L=
Truncated Levy Walk}, where the elements of the set
indicate the possible actions taken by a node.
It may be noted that the movement of a node and
the subsequent encounters result in one or more of the
following three different outcomes – 1) Delivery of mes-
sage(s) to their destination, 2) Forwarding/replication
of message(s), and 3) No action taken on message(s).
Thus, for each of the above noted actions, we have
the following set of outcomes: O={D=Deliver kD
messages, F=Forward kFmessages, X=No action on
kXmessages};kD≥0, kF≥0, kX≥0. Let, pD(E), pF(E)
and pX(E), respectively, be the probabilities of having
the outcomes D, F and Xfor the action E. Similarly,
pD(L), pF(L)and pX(L)are defined.
Further, let U(E)and U(L)be the utilities correspond-
ing to the two actions Eand L, respectively. Then, at
any instant of time, the action Eis chosen over L, if
U(E)> U(L); otherwise, Lis the preferred action.
4.2 Outcome Probabilities
Every time a device communicates with another device,
it is considered to maintain a record (bi, fi, di, ei)in
its storage. Here, biindicates the number of messages
stored in the node’s buffer before the beginning of the
ith communication event; fiand di, respectively, indicate
the number of messages delivered and forwarded during
this event. The relevant counts are obtained after a
communication link is terminated. The state variable ei
indicates whether or not the corresponding movement
of the node is exploration.
Accepted Version (For personal use only)
7
Let, R(t) = {(bi, fi, di, ei)}be a set of records observed
by a node till any time instant t. Also, let us define
nD(E) = Pidi∈R(t) : ei=T rue, i.e., nDgives the
total number of messages delivered while undergoing
exploration till the time instant t. The total number of
messages delivered while undergoing TLW is given by
nD(L) = Pidi∈R(t) : ei=F alse. Thus, the total
number of messages delivered till time tis nD=nD(E)+
nD(L). Similarly, nF(E),nF(L),nX(E)and nX(L)are
defined; nFand nXare obtained accordingly. Further,
let b(E) = Pibi∈R(t) : ei=T rue, and b=b(E) + b(L).
Then, the outcome probabilities are determined as:
pD(E) = nD(E)
b(E)
pF(E) = nF(E)
b(E)
pX(E)=1−pD(E)−pF(E)
pD(L) = nD(L)
b(L)
pF(L) = nF(L)
b(L)
pX(L)=1−pD(L)−pF(L)
(2)
Let, at that time instant t, a device has nmessages
in its buffer. Then, using (2), the estimated number of
messages that would be delivered, forwarded, or neither,
respectively, for the two actions Eand Lare given as:
ˆnD(E) = pD(E)×n
ˆnF(E) = pF(E)×n
ˆnX(E) = pX(E)×n
ˆnD(L) = pD(L)×n
ˆnF(L) = pF(L)×n
ˆnX(L) = pX(L)×n
(3)
Therefore, at the end of this event about nD(E) +
ˆnD(E)will be delivered due to exploration, while
nD(L) + ˆnD(L)messages will be delivered if the node
undergoes TLW.
4.3 Expected Utility Theory
In EUT, the expected utility of any action is computed
based on the utility of the final status considering the
current outcome. Each action (or gamble), Eand L,
probabilistically add to/deduct from the node’s current
utility after an action has been chosen. Using (2) and (3),
the expected utilities of any node corresponding to the
two actions are given by:
U(E) = pD(E)×uD(nD(E) + ˆnD(E))+
pF(E)×uF(nF(E) + ˆnF(E))+
pX(E)×uX(nX(E) + ˆnX(E))
U(L) = pD(L)×uD(nD(L) + ˆnD(L))+
pF(L)×uF(nF(L) + ˆnF(L))+
pX(L)×uX(nX(L) + ˆnX(L))
(4)
The utility functions, ∀x≥0, corresponding to the de-
livery, forwarding and no action are defined as follows:
uD(x) = log(1 + x)
uF(x) = log(1 + x/2)
uX(x) = 0.01 −0.01
e−(−log(1+√x))2
(5)
It is easily observed from (5) that uD(·),uF(·)and
uX(·)ensure the preference of any user that the delivery
of xmessages is preferred to their forwarding, which
is, of course, preferred to no action being taken, i.e.,
the ordering DFXprevails. Moreover, uX(·)
is slightly negative underscoring the fact that when no
action is taken on any message, it does not help toward
its delivery, but reduces the chance to some extent.
Theorem 1. Let, A1be an action that has no chance of
message forwarding. Also, let, A2be another action for which
only forwarding is possible. Given uD,uFand uX, the ratio
uF−uX
uD−uXdetermines the minimum fraction of messages that
should be delivered in A1below which A2will be preferred.
Proof: Let, (pD(A1), pF(A1), pX(A1)) =(q, 0,1−q).
Further, we have (pD(A2), pF(A2), pX(A2)) =(0,1,0).
Then, U(A1) = q×uD(d) + (1 −q)×uX(x), and U(A2) =
uF(f), where d,fand xare the number of messages
on which the corresponding utility functions act. So that
A2is preferred to A1, we should have U(A2)> U(A1).
That is, q×uD(d) + (1 −q)×uX(x)< uF(f). This gives
q < uF(f)−uX(x)
uD(d)−uX(s). However, since q≤1, the inequality
becomes q < min{1,uF(f)−uX(x)
uD(d)−uX(s)}. Thus, when at least a
fraction qof the messages have a possibility of delivery,
A1will be the preferred action.
Theorem 2. When the “no action” outcome has zero utility,
i.e., uX(x) = 0, the fraction qis solely determined by the
relative magnitude of uFwith respect to uD.
Proof: From Theorem 1, when uX(x)=0, we get q <
uF(f)/uD(d). So, an action with at most uF(f)/uD(d)
chance of only forwarding is preferred to any other
action with the only possibility of message delivery.
4.4 Prospect Theory
While EUT is based on rational decision making, PT [10]
acknowledges the fact that decisions made by the human
beings are not always rational, but often biased. People
are found to consider the subjective value rather than
the objective utility. Moreover, decision making is also
influenced by the reference frame chosen. It has been
found that, in the domain of loss, people are risk seeking.
But, in the domain of gains, people are risk averse.
Thus, the value function, v(·), is concave for gains and
convex for losses. Moreover, losses hurt more than gains.
Therefore, the convex segment of v(·)is steeper than its
concave segment. Finally, the probability decision weight
function, w(·), is S-shaped reflecting that people tend to
overweight small probabilities, but underweight larger
probabilities.
Accepted Version (For personal use only)
8
Based on [24], [25], we consider the subjective proba-
bility function as follows:
w(p) = e−(−ln p)a,(6)
where 0< a < 1. The parameter acontrols the distor-
tion of subjective probability, w(p), with respect to the
objective probabilities, p, as shown in Fig. 4.
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Subjective probability
Objective probability
p
a = 0.3
a = 0.7
Fig. 4: Subjective probabilities for different values of a.
The value functions vD(·),vF(·), and vX(·)are given
by:
vD(x) = xb, x ≥0
=−λ×(−x)c, otherwise
vF(x) = (0.7x)b, x ≥0
=−λ×(−0.7x)c, otherwise
vX(x) = (0.1x)b, x ≥0
=−λ×(−0.1x)c, otherwise
(7)
We took a= 0.5, and b=c= 0.88, λ = 2.25
as mentioned in [26]. The latter values indicated were
the median of the corresponding parameters obtained
using a nonlinear regression-based estimation of those
parameters.
The utilities corresponding to the actions Eand Lare
given by:
U(E) = w(pD(E)) ×v(nD−nD(E)−ˆnD(E))+
w(pF(E)) ×v(nF−nF(E)−ˆnF(E))+
w(pX(E)) ×v(nX−nX(E)−ˆnX(E))
U(L) = w(pD(L)) ×v(nD−nD(L)−ˆnD(L))+
w(pF(L)) ×v(nF−nF(L)−ˆnF(L))+
w(pX(L)) ×v(nX−nX(L)−ˆnX(L))
(8)
Equation (8) depicts the choice of dynamic reference
point in use, and valuation of the outcomes as a relative
change. For instance, in the case of message delivery
under exploration, we consider the difference between
nD– the total number of messages delivered until a
particular time instant – and nD(E) + ˆnD(E), i.e., the
approximate number of messages that are to be deliv-
ered under exploration, if the current action taken is
exploration. Similarly, the difference between nDand
nD(L)+ˆnD(L)is considered for the outcome correspond-
ing to the action L.
4.5 Algorithm Design
We now discuss how the nodes make a preference
between TLWE and utility-based exploration. To give
a fair chance to both the schemes, a node continues
to explore with probability pEuntil there is a positive
chance of messages either being delivered or forwarded
for both the TLWE and utility-based scheme, i.e., either
pD(E)>0or pF(E)>0and pD(L)>0or pF(L)>0.
Once this criteria is satisfied, a node makes its decision
based on (4) and (8), respectively, for the EUT- and
PT-based schemes. Thus, up to a certain time instant
t, a node moves according to TLWE, beyond which
its motion is guided by either TLWE or the concerned
utility-based scheme.
Algorithm 1 summarizes the PT-based decision mak-
ing process of any node. In particular, the for loop at
the beginning iterates over each record to compute the
different counters to be used with (2). Since, at a given
instant, every node iterates over R(t), the time com-
plexity of this algorithm is O(Q), where Qdenotes the
number of connection up/down events in the network.
The sparse connectivity in DTNs/OMNs ensures that
such a computation is feasible. This complexity, however,
can be easily reduced to O(1) when only two set of
counters are maintained to store – 1) The cumulative
sum until now and 2) The counts obtained at the end
of the current communication event. Moreover, storage
overhead would also be reduced.
Algorithm 1: Exploration based on PT
1for each record ∈R(t)do
2Compute the cumulative sums of bi,diand fi
separately for ei=T rue and F alse
3Compute the outcome probabilities according to (2)
4Compute the subjective probabilities according to (6)
5if (pD(E)>0or pF(E)>0)and (pD(L)>0or
pF(L)>0)then
6Determine U(E)and U(L)according to (8)
7if U(E)> U(L)then
8Undergo exploration
9else
10 Undergo TLW
11 else
12 Undergo exploration
5 SIMULATION
This Section discusses the experimental setup and the
metrics used for performance evaluation.
5.1 Simulation Setup
The ONE simulator [27] was used to evaluate the effects
of TLWE and utility-based exploration schemes. We used
an implementation of the TLW mobility model by Massri
Accepted Version (For personal use only)
9
et al. [28]8with certain corrections. Specifically, the code
for generation of flight lengths and pause times was
altered. The flight lengths were based on the truncated
Pareto distribution: p(l) = αlα
minl−α−1
1−(lmin/lmax )α, where αand
lmin, respectively, are the shape and scale parameters.
The parameter lmin (lmax) indicates the minimum (max-
imum) distance traveled by a node. To generate a flight
length, we selected a uniform random number u∈
[0,1), and applied the inverse transformation so that
l=F−1(u), where F(l)denote the CDF of p(l). Similarly,
the pause times were generated. As mentioned in [2],
we took k= 18.72,ρ= 0.79 when l < 500 m; k= 1.37,
ρ= 0.36, otherwise.
We individually considered the effects of different
parameters as summarized in Table 3. The “Default
value” column in the Table 3 indicates the values of the
corresponding parameters when they were not varied.
The movement speeds correspond to the average
walking speed of human beings (∼0.5−2m/s). The
pause time of the mobile nodes was distributed between
0–1000 s. The minimum distance of separation among
the PoI was taken to be 600 m. We assumed S0=∅in
all the cases. The threshold flight length for exploration,
θE, was taken to be 250 m.
The Spray-and-Wait [15] routing protocol was used
by the nodes in binary mode with C= 16 copies.
Messages in the network were generated by the PoI
every 10–15 minute in the first 12 hour of the simulation.
The destination of a message was selected at random
from all the nodes. We also investigated and compared
the performance with another state-of-the-art routing
protocol, PRoPHET [16].
We also considered a case where all the nodes – the
mobiles as well as the PoI – offered traffic to the OMN.
In this case, the TTL of the messages were taken to be
infinite to discount its effects, if any, on the message
delivery.
5.2 Performance Metrics
Performance evaluation was conducted with respect to
the following metrics:
•Delivery ratio of the messages,
•Fraction of PoI known per mobile node,
•Average exploration time per node, and
•Total revenue earned by users on an average.
The delivery ratio gives the fraction of the created
messages that are delivered to the respective destina-
tions. Let, ncand nd, respectively, denote the number of
messages created and delivered in the OMN. Then, the
delivery ratio of the messages is defined as nd/nc∈[0,1].
The fraction of PoI known per mobile node is evalu-
ated as 1
|NM|×Pi∈NM|Si
P|
|NP|∈[0,1], where | · | indicates
the count of elements in a given set, and Si
Pdenotes the
set of PoI known by the ith mobile node, ∀i∈ NM. A
8. https://code.google.com/p/evolving-dtn-routing/source/
browse/src/movement/LevyWalk.java, accessed 29 June 2013
TABLE 3: Simulation Parameters
Parameter Range of Values Default Value
Transmission speed,
range 2Mbps, 10 m
No. of mobile nodes 50
∆tp,max 1000 second
Message generation
interval and duration Every 10 −15 minute for the first 12 hour
α0.5–1.0 1.0
lmax 400–800 m 500 m
No. of PoI 5–25 10
Visual discovery
probability 0.3–0.7 0.5
Visual discovery ra-
dius 100–150 m150 m
Exploration probabil-
ity 0.01–0.7 0.1
SnW (binary mode) C 8–32 16
Terrain size (sq. m)
2000 ×2000,
3000 ×3000,
4000 ×4000
2000 ×2000
Simulation duration 12–60 hour 24 hour
higher value of this fraction implies higher number of
unique contacts with the PoI per mobile node, which, in
turn, enhances the delivery of the messages. The average
exploration time per node gives insight on to what extent
the exploration is justified.
The total revenue earned by users in an OMN, on an
average, was determined by mapping total number of
contacts with PoI into revenue, as discussed in Section
3.3.
The ensemble average of the results were taken over 30
random scenarios and the 95% confidence interval was
calculated.
6 RE SULTS
At first, we look into the performance of the OMN when
the nodes moved using TLW. Fig. 5 shows the message
delivery ratio obtained using TLW for different node
densities, terrain sizes and lmin. It can be observed that
as lmin increased, the delivery ratio increased, too. This is
due to the reason that each node, on an average, traveled
more and, therefore, had more contact opportunities to
deliver the messages. On the other hand, increasing
terrain sizes reduced the chances of meeting among the
nodes and hence, the delivery ratio decreased.
6.1 Effect on the Delivery Ratio of the Messages
Fig. 6 shows the delivery ratio of the messages obtained
when the nodes moved according to TLW and TLWE
in terrains of different dimensions. It can be observed
that, for the terrain size of 2000 ×2000 sq. m., there
is a significant improvement of the delivery ratio with
TLWE, as compared to TLW. The enhancement, however,
relatively degraded for larger terrains. Nevertheless,
TLWE fared much better than TLW for all the terrain
sizes considered.
In Fig. 7 it can be observed that with the increasing
simulation time, the performance improved for both
Accepted Version (For personal use only)
10
0
0.5
1 (i)
500×500
1000×1000
2000×2000
0
0.5
1
5 10 15 20
lmin (meter)
(ii)
Fig. 5: Delivery ratio of the messages using TLW for (i)
40 and (ii) 100 mobile nodes in three different terrains
for different values of lmin.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
2000,2000 3000,3000 4000,4000
Delivery ratio
Terrain size (sq. m)
TLW
TLWE
Fig. 6: Effects of terrain dimensions on the delivery ratio
of messages.
TLW and TLWE. When the messages had a finite TTL
(12 hour), the performance improvement for TLWE is
notably high. However, it is interesting to note that even
in the case of messages with infinite TTL, TLWE offered
better message delivery ratio than TLW. All other factors
remaining the same, this, indeed, is a direct consequence
of intentional exploration.
0
0.2
0.4
0.6
0.8
1
12 24 36 48 60
Delivery ratio
Simulation time (hour)
TLW
TLW, TTL = ∞
TLWE
TLWE, TTL = ∞
Fig. 7: Variation in the delivery ratio of the messages
with simulation duration (with TTL = 12 hour and ∞).
Fig. 8 shows that an increase in lmax also helped
in the improvement of message delivery ratio in the
OMN. In simple terms, if users plan to travel longer
distances, on an average, they are expected to have more
communication opportunities with – and hence, more
message forwarding chances to – other devices.
0.8
0.85
0.9
0.95
1
1.05
400 500 600 700 800
Delivery ratio
Maximum flight length (m)
TLW
TLWE
Fig. 8: Changes in the delivery ratio of the messages due
to variation in the maximum flight length.
6.2 PoI known by the Mobile Nodes
Fig. 9 shows the fraction of PoI known per mobile node,
on an average, when the simulation duration was varied.
It is evident that probabilistically exploration under the
TLWE scheme helped in discovering more PoI. The
higher value of this metric for TLWE resulted in more
messages delivered, as can be verified from the previous
Figures.
0.85
0.9
0.95
1
1.05
12 24 36
Fraction of PoIs known
Simulation duration (hour)
TLW TLWE
Fig. 9: Fraction of PoI known per mobile node.
6.3 Impact of αand Visual Discovery
Fig. 10 (a) shows the delivery ratio of the messages
obtained for the two terrain sizes considered for different
values of α. As shown in Fig. 3, diffusion of the nodes
increased with a decrease in α. Thus, for a given terrain
size, the delivery ratio of the messages increased with
decreasing α. It is interesting to note that TLWE provided
considerable improvement over TLW even when a larger
terrain size was considered together with higher value
of α, i.e., lower diffusion.
We also considered the effect of radius of visual dis-
covery (RV) upon the performance. However, as shown
in Fig. 10 (b), we could not find any significant difference
in the message delivery ratio with increasing RV. In
particular, when visual discovery was taken into account
(i.e., RV>0), the message delivery ratio was found
to be about 3% greater than when visual discovery
was not considered (i.e., RV= 0). Therefore, the effect
of visual discovery on the performance of the OMN
remained inconclusive. However, when visual discovery
was performed, the number of mobile nodes that knew
Accepted Version (For personal use only)
11
0.2
0.4
0.6
0.8
1
0.5 0.75 1.0
Delivery ratio
α
2000×2000 (TLW)
3000×3000 (TLW)
2000×2000 (TLWE)
3000×3000 (TLWE)
(a)
0.8
0.85
0.9
0.95
1
1.05
50 100 150 200
Delivery ratio
Radius of visual discovery (m)
pV = 0.3 pV = 0.4 pV = 0.5
(b)
Fig. 10: Effects of (a) αand (b) visual discovery on the
delivery ratio of the messages. Here, pVindicates the
probability of visual discovery.
of at least a single PoI, on an average, in the terrain largely
increased, as depicted in Table 4 (here, pVwas taken as
0.3).
TABLE 4: Fraction of nodes knowing at least a single PoI
No visual discovery RV= 90 RV= 150
0.2427 0.6500 0.7400
6.4 Effect of the Traffic Sources
Fig. 11 shows the variation in the message delivery ratio
when the messages were created by (a) all the nodes,
(b) only by the PoI, and (c) only by the mobile nodes. It
can be observed that the delivery ratio of the messages
obtained on using TLWE was always greater than when
TLW was used. The difference was in the range 7–33%.
Two interesting trends can be observed here.
•When all the nodes in the OMN created messages,
the delivery ratio showed a decreasing trend, in
general, with the increase in the number of PoI in
case of both TLW and TLWE. To understand this,
we look at the next observation.
•When only the PoI generated messages, the delivery
ratio decreased in case of TLWE with the increasing
number of PoI. This is due to the reason that with
increasing number of PoI, the number of messages
created also increased. However, due to movement
constraints, not all such PoI could be visited by the
mobile nodes at appropriate time, and, therefore, on
an average, less number of messages were delivered.
This, in turn, also accounts for the case when all
nodes in the OMN generated messages.
It also can be noted that statistically significant differ-
ence (based on the confidence intervals) in the delivery
ratio could not be observed in the case of TLW. So, the
conclusion is that increasing the number of (randomly
placed) PoI in a terrain may not improve the perfor-
mance of an OMN in terms of message delivery ratio.
0.4
0.6
0.8
1
5 10 15 20
(a)
TLW TLWE
0.4
0.6
0.8
1
5 10 15 20
Delivery ratio
(b)
0.4
0.6
0.8
1
5 10 15 20
No. of PoIs
(c)
Fig. 11: Delivery ratio of the messages when they were
created by (a) All nodes, (b) Only PoI, and (c) Only
mobile nodes. |NM|= 50, in a terrain of size 3000 ×3000
sq. m.
6.5 Effect of the Exploration Probability
Fig. 12 shows the variation in the delivery ratio of
messages obtained for different probabilities of explo-
ration (pE) when TLWE, EUT-, and PT-based exploration
schemes were used. The corresponding delivery ratio
obtained using TLW was about 0.7719. It may be noted
that when pE= 0, TLWE degenerates into TLW. Since we
have already presented exhaustive performance evalua-
tion results concerning TLW and TLWE until now, we
skip the results pertaining to TLW (which does not vary
with pE) here for clarity.
Fig. 12 indicates that the message delivery ratio was
close to unity even for a very small value of pE. An
increasing trend in the performance can be observed up
to pE= 0.1. Moreover, the performance of the EUT-
and PT-based schemes were close to that of TLWE with
random exploration, if not more.
Fig. 13 (a) compares the time spent in exploration by
any node, on an average, for the different schemes when
the simulation duration was 24 hours. The Fig. clearly
indicates that TLWE often resulted in spending a larger
time in exploration, on an average, as compared to the
ET- and PT-based schemes. This is due to the reason that
TLWE cannot pre-judge whether or not the subsequent
exploration would reap any benefit. The time difference
was minor for very low values of pE(say, pE= 0.05),
Accepted Version (For personal use only)
12
0.86
0.88
0.9
0.92
0.94
0.96
0.98
1
1.02
0.01 0.05 0.1 0.3 0.5
Delivery ratio
Exploration probability
TLWE EUT PT
Fig. 12: Variation in the delivery ratio of the messages
with pEin a terrain of size 2000 ×2000 sq. m.
but considerable for moderate values say, when pE>
0.1. In particular, note that the average exploration time
when pE= 0.1was merely about 0.55% of the simulation
duration (24 hour).
Similar conclusion is drawn for the maximum time
spent on exploration, on an average, as shown in Fig. 13
(b).
10
20
30
40
50
60
70
0.01 0.05 0.1 0.3 0.5
Avg. exploration time (min)
Exploration probability
TLWE
EUT
PT
(a)
20
40
60
80
100
120
140
0.01 0.05 0.1 0.3 0.5
Max. exploration time (min)
Exploration probability
TLWE
EUT
PT
(b)
Fig. 13: (a) Average and (b) maximum time spent by the
nodes under the three exploration schemes in a terrain
of size 2000 ×2000 sq. m.
6.6 Effects of Routing Protocols
We looked into the performance of TLW and the pro-
posed mobility schemes (TLW and PT-based) using two
different routing protocols – SnW and PRoPHET, in a
terrain of size 3000 ×3000 sq. m. The second column
in Table 5 shows the delivery ratio obtained using SnW,
while the fourth column shows for PRoPHET.
TABLE 5: Delivery ratio with SnW vs. PRoPHET
Scheme SnW Scheme PRoPHET
TLW 0.4912 TLW 0.1930
TLWE 0.8772 TLWE 0.7368
PT 0.8947 PT 0.7719
It can be observed the TLWE and PT-based exploration
scheme resulted in much higher delivery of messages as
compared to TLW. The performance of TLWE and PT-
based scheme were close. The performance of PRoPHET
was found to be poor than that of SnW. This can be
accounted to the fact that a larger terrain size reduced the
node density, and hence, communication opportunities
among the nodes. This, in turn, affected the predictability
computations employed by PRoPHET. To confirm this,
we also simulated the scenario with a smaller terrain
size. In that case, we could not find any significant
difference between the performance of the two routing
protocols.
The exploration schemes proposed in this work are,
in fact, independent of any routing protocol. For this
reason, we did not investigate the performance related
to the routing protocols any further.
6.7 Revenue of Users
Fig. 14 plots the delivery percentage of the messages, the
number of contacts between mobile nodes and PoI, on
an average, for different scenarios. The numbers inside
the plot indicate the average users’ revenue (see Sec-
tion 3.3) for the corresponding scenarios. For example,
when TLWE was considered in an OMN of terrain size
1000×1000 sq. m. consisting of 5PoI (labeled with 1000-
5-TLWE along the x-axis), the average users’ revenue9
was about 5.87. It can be observed that when TLWE was
considered, the number of contacts with PoI (and thus,
user revenue), as well as, the message delivery ratio,
increased as compared to TLW.
0
0.2
0.4
0.6
0.8
1
1000-5-TLW
1000-5-TLWE
2000-10-TLW
2000-10-TLWE
3000-10-TLW
3000-10-TLWE
100
150
200
250
300
350
400
Delivery ratio
# of contacts
★★
★★
★
★
Delivery ratio
# of contacts
5.795
5.870
5.629
5.766
4.913
5.227
Fig. 14: Delivery ratio of the messages, number of con-
tacts and corresponding users’ revenue under different
scenarios.
9. The revenue values are not plotted as per the scale.
Accepted Version (For personal use only)
13
6.8 Observations: Should the users explore?
The observations from this Section can be summarized
in the following points:
•Devices with low transmission range (for example,
Bluetooth with 10 m) lower the chances of mes-
sage delivery when large terrain sizes and TLW
are considered. Such performance degradation can
be arrested with little exploratory movement of the
nodes.
•Increasing the number of (randomly placed) PoI (for
example, throwboxes) may not necessarily increase
performance in terms of message delivery ratio.
(We, however, did not consider the case of PoI with
larger transmission ranges or their placement at
“popular” areas of a city/terrain.)
•Exploration – whether simple (TLWE) or utility-
based (EUT and PT) – provides optimal perfor-
mance when pE≤0.1.
•The EUT- and PT-based exploration schemes re-
sult in lower exploration time, on an average, as
compared to the random exploration of the TLWE
scheme.
•Finally, evaluation of the utility functions and the
subsequent decision making do not involve network
communication. Therefore, the energy implication is
minimal.
Therefore, a little exploration would be deemed useful
for the OMN concerned.
7 CONCLUSION
In this work, we considered an OMN formed of a set
of mobile nodes moving according to the TLW mobility
model, together with a set of stationary nodes, termed
as PoI. The mobile nodes – devices together with their
human carriers – occasionally explore by probabilisti-
cally visiting the PoI known to them. We considered
a randomized model of exploration (TLWE) and con-
trasted it with similar schemes based on EUT and PT.
We evaluated the performance of the concerned OMN
through extensive simulations. The results indicate that
the delivery ratio of the messages largely increases when
the mobile nodes engage in even a small amount of
exploration.
This work can be extended along various directions.
First, we considered here the locations of the PoI to be
random. In future, different algorithms for PoI placement
can be used to evaluate the performance. Second, a
major consideration would be taking into account the
presence of multiple PoI devices in a single geographic
PoI, for example, multiple throwboxes in a cafeteria.
Next, it would be interesting to take into consideration
when a user is willing (or not) to explore. For example,
users might have work schedules and may not engage
in exploration all the time. Moreover, consideration of
users’ interest profile and how much time a user is
willing to spend for exploration would add another
interesting dimension to this work. Finally, it would be
interesting to perform real-life experiments based on this
work and compare the resulting performance.
ACKNOWLEDGEMENT
We are thankful to the anonymous reviewers for their
insightful comments that have helped us in enriching
this work.
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Barun Kumar Saha (http://barunsaha.me/) is
pursuing his PhD at the Indian Institute of Tech-
nology Kharagpur, India. Prior to that, he re-
ceived his MS degree in 2014 from the same
institute, and BTech from Haldia Institute of
Technology, West Bengal, India, in 2007. His
research interests include Delay Tolerant Net-
works, Mobile Ad hoc Networks, and use of
technology for advancing education. He is the
lead developer of the Software Engineering and
Advanced Network Technologies Vir tual Labs.
He maintains a widely popular blog on DTNs at http://delay-tolerant-
networks.blogspot.com/.
Sudip Misra is an Associate Professor in the
School of Information Technology at the Indian
Institute of Technology Kharagpur. He received
his Ph.D. degree in Computer Science from Car-
leton University, in Ottawa, Canada. His current
research interests include algorithm design for
emerging communication networks. Dr. Misra is
the author of over 230 scholarly research pa-
pers. He was awarded the IEEE ComSoc Asia
Pacific Outstanding Young Researcher Award at
IEEE GLOBECOM 2012, Anaheim, California,
USA. He was also the recipient of several academic awards and
fellowships such as the Young Scientist Award (National Academy
of Sciences, India), Young Engineers Award (Institution of Engineers,
India), (Canadian) Governor Generals Academic Gold Medal at Carleton
University, the University Outstanding Graduate Student Award in the
Doctoral level at Carleton University and the National Academy of
Sciences, India Swarna Jayanti Puraskar (Golden Jubilee Award).
He was awarded the Canadian Governments prestigious NSERC Post
Doctoral Fellowship and the Humboldt Research Fellowship in Ger-
many. Dr. Misra is the Editor-in-Chief of the International Journal of
Communication Networks and Distributed Systems (IJCNDS), Inder-
science, Switzerland. He has also been serving as the Associate Editor
of the Telecommunication Systems Journal (Springer SBM), Security
and Communication Networks Journal (Wiley), International Journal of
Communication Systems (Wiley), and the EURASIP Journal of Wireless
Communications and Networking. Dr. Misra has 8 books published by
Springer, Wiley, and World Scientific. Dr. Misra was also invited to deliver
keynote/invited lectures in over 30 international conferences in USA,
Canada, Europe, Asia and Africa.
Sujata Pal is currently pursuing her PhD degree
from the School of Information Technology at the
Indian Institute of Technology Kharagpur, India.
She received the MTech degree from the West
Bengal University of Technology, India, in 2007,
and the BE degree in CSE from the North Orissa
University, India, in 2002. She got the eminent
TCS scholarship award for 4 years for doing her
PhD, and was awarded the Schlumberger Fac-
ulty For The Future fellowship for the year 2015–
2016. She has more than 6 years of teaching
experience. Her current research interests are DTNs and MANETs. She
is a student member of IEEE and ACM.
Accepted Version (For personal use only)
