Modeling the Impact of Human Spontaneity inMobile Trajectories
Andrea G. RibeiroFaculdade Ideal (FACI)
Belem, Brazil
Abstract—Social mobility modeling has as motivation assist indeveloping mobile simulation environments, in order to providebetter grounds for the evaluation of mobile networks. Being anew trend with roots on social network theory, these modelsare still unable to capture a few relevant characteristics ofhuman movement, being one of them the impact of humanspontaneity in mobile trajectories. This paper proposes a wayto model such impact by providing nodes in movement with amechanism that captures changes of target based on the notion ofsocial attractiveness. We evaluate our proposal based on a socialmobility model standalone simulator, against realistic traces.
Index Terms—Wireless networks; human movement patterns;social mobility models.
I. INTRODUCTION
As wireless networks deployment expands, we assist to a
growth in User-Centric wireless Networks (UCNs), networking
architectures often based on end-user equipment such as
smartphones. These networks are user-centric in the sense
that as wireless devices are carried by humans, their motion
reflects the human behavior of their carriers (owners). They are
also user-centric in the sense that the underlying connectivity
graphs are a product of the social nature of relations between
the carriers, or at least of potentially shared interests that their
carriers may have, even without knowing each other.
Today and within the context of simulating and emulating
realistic networking environments, mobility models being de-
veloped contain rules that can be used to generate motion
and trajectories for mobile nodes, trying to predict the nodes’
future location [1], [2], [3]. Mobility models are helpful in
creating adequate environments to evaluate aspects related to
networking, e.g. evaluate the performance of routing protocols,
or of some resource management mechanism.
Out of the available mobility models, the ones that are
relevant to discuss in this paper have a root on social network
theory and are known as social mobility models [4], [5], [6].
These models are realistic enough to assist in modeling the
trajectory of nodes based on the notion of social attractiveness,i.e., a measure of the attraction that other nodes exert on a
specific node in movement. However, attempting to model
movement according to human motion behavior is a complex
aspect and hence social mobility models still have a few
gaps [7]. Within the context of this paper, we focus on an
identified gap, namely, the inability for nodes on the move
to change their trajectory before they reach the computed
target. In human motion, such changes are bound to occur,
as a basic feature of the human nature is free will (volition).Such human characteristic is of course highly complex to be
easily modeled, but nonetheless, in social mobility models
it is essential, for the sake of being as realistic as possible,
to consider a way to allow nodes to change their planned
trajectory on-the-fly, e.g. probabilistically.
Current social mobility models address trajectories having
a social flavor, but once a node is set in motion, it will not
stop until it reaches the selected destination. In some cases,
it may happen that due to some changes in the topology
or experimental environment, the selected goal looses its
properties as a potential goal during the node’s trajectory. For
instance, consider the case of a user on the move to meet a
group of friends. While he is going to meet its friends, he
receives a call/SMS saying that his friends are not anymore
at the previous place. That user will then make a decision on
whether or not to continue its expected trajectory depending
on the attractiveness of that target. This decision cannot be
captured today by available social mobility models.
In this context, the main goal of this work is to propose
a mechanism that is suitable to be applied on social mobility
models and which can assist them in capturing the potential
changes in destination that may occur while a node is moving.
The remainder of the paper is organized as follows. Section
2 covers related work. Our proposal is described in section
3. Section 4 describes the methodology of work. Section 5
provides an analysis of our proposal based upon an existing
social mobility model, against real traces. Finally, section 6
concludes this work and presents some future work.
II. RELATED WORK
A number of approaches have been dealing with the mod-
eling of accurate node mobility, and a specific set of models
are dealing with social aspects.
The Community Based Mobility Model (CMM) [4] was one
of the first mobility models to consider social relationships
among individuals as a way to select movement targets.
In other words, nodes move towards other nodes or other
communities based upon probabilities and taking into account
a form of social strength between nodes which the authors
have named social attractiveness. There are several works that
propose improvements to CMM ([8], [5]); however, there are
key aspects that these mobility models still do not provide,
namely: pauses, when a node reaches its goal (destination) or
2013 IEEE 9th International Conference on Wireless and Mobile Computing, Networking and Communications (WiMob)
978-1-4799-0428-0/13/$31.00 ©2013 IEEE 507
the needs to change their trajectory; preventing collisions, or
changing a route while moving.
The Self-similar Least Action Walk (SLAW) mobility model
[9] is one of the more complete mobility models in the
sense that it contains several properties that are left aside on
other models, for instance, pause time modeling; providing
individual nodes with a travel plan modeling “preferential”
locations. Pause time is, however, modeled in an artificial way
based on a global routine (12 hours), out of which pause times
are probabilistically selected. However, despite the SLAW
consider some important features, it still does not consider
that nodes can change their trajectory on motion.
The Heterogeneous Human Mobility (HHM) model [10]
considers the node’s popularity index to define the movement
pattern. A simple observation in social network theory (some
people are more popular and have more opportunities to meet
others) is taken into account to define the node’s movement.
The authors define overlapping communities showing that if
a node belongs to more than one community, it has the
opportunity to meet people in multiples communities; however,
if a node belongs to only one community, its movement is kept
confined. Still, this model does not take into consideration the
spontaneity in decision making, and which is a relevant trait
in human nature.
The Sociological Interaction Mobility for Population Sim-ulation (SIMPS) model [11], relies on two main features of
nodes: their social interaction level, for instance, personal
status (e.g. age and social class); and the social interaction
needs, i.e. the need of individuals to make acquaintances. The
authors show that these two components can be translated into
a coherent set of behaviors, called sociostation. The nodes
movement occurs based on these two definitions, where a node
is attracted by acquaintances, in order to socialize; or a node
is repulsed by strangers, in order to isolate. However, nodes
will not change their routes once movement is started.
GeSoMo (GEneral SOcial MObility) [12] is a social mobil-
ity model, which has the differentiating aspect of considering
social interaction analysis as an input to modeling mobility.
It relies also on the strength of an association between nodes
derived from the strong assumption that the number of contacts
between nodes should be proportional to the strength of the
association between those nodes. GeSoMo does not, similarly
to the other models consider pause modeling; obstacle avoid-
ance; or changes of trajectory while the node is moving.
In prior work [13] we have analysed CMM as one of the
models that was the closest to the notions of social movement
[4]. We have improved it by providing pause time modeling
based on the notion of social attractiveness and on the fol-
lowing thinking: if a node has a higher social attractiveness
for a specific target, then it normally spends more time on the
selected target [14]. We have noticed, however, that in several
cases, when arriving to the selected target, that area no longer
held the social attractiveness properties that initially attracted
the node. In other words: while the node was moving towards
its target, the surrounding conditions changed. Hence, the
work presented in this paper proposes an improvement which
Figure 1. An example of node and community mobility.
addresses this particular aspect: modeling potential changes of
target while the node is on the move.
III. CAPTURING TRAJECTORY CHANGES
In social mobility modeling, the line of thought currently
being followed is: humans organize themselves into groups
which only have a meaning at some instant in time and in
space. These groups, known as communities, have a spacial
and temporal correlation (e.g. affiliation; family; club).
Nodes carried by humans therefore exhibit a pattern of
movement which relates to this social notion of community.
For instance, a person moves to work. Hence, humans move
according to the “social attractiveness” of their targets. Targets
are nodes of a cluster, but can represent locations. Moreover,
there is another human characteristic that impacts movement:
volition. Capturing volition is not an easy task, but the
capability to allow nodes on the move to change their target
should be modeled by current social mobility models, even if
a node has already selected its target.
To better explain our rationale, Figure 1 illustrates the
impact that free will may have in the trajectory of nodes. We
consider four mobile nodes A, B, C, and D, where two of
them (B and C) are friends of A. A is at home and nodes B
and C are at a coffee-shop. Based on the fact that the social
attractiveness of B and C is the highest, node A is moving
towards the coffee-shop and therefore, at instant t = t0 selects
as next target this location, which we identify as (6). At instant
t = t1 node A is still moving and nodes B and C also start to
move towards another place, in the direction of node D, for
instance. Considering what could happen in real life, node B
or C would notify node A that they now go somewhere else
(e.g. call/sms) and then node A could decide whether or not to
move, towards B and C. From a modeling perspective, node
A should in fact recompute its new target, as cell (6) social
attractiveness will change once B and C move out. Hence, at
instant t = t2, node A actually decides to follow nodes B
and C - from a modeling perspective, what occurs is that by
recomputing the social attractiveness of potential targets node
A realizes that cell 6 is no longer the cell holding the greater
attractiveness and instead, that cell is now (8).
508
As described in section II none of the available mobility
models consider the possibility of nodes changing their tra-
jectory before arriving at the computed goal. Hence, current
social mobility models would compute cell 6 as original target
at instant t = t0. When node A reaches cell 6, its social
attractiveness has decreased as nodes B and C have already
moved. Yet, the current models cannot detect this behavior.
The consequence is that often a node moves towards a cell
that should not be the target anymore.A. Our Proposal
In order to provide social mobility models with the capa-
bility to trigger route changes while nodes are moving, one
simple improvement is to have a way for nodes in active
trajectories to recompute social attractiveness periodically.To provide a dynamic way of splitting the time a node
may take in its trajectory, we consider the euclidean distance
between the node’s origin and its chosen target, as well as
the average speed si at which a node i is moving to compute
the estimated trajectory duration Li, as provided in Equation
1, where ‖xi − yi‖ corresponds to the euclidean distance in
meters between node i current position (xi) and its target
position (yi).
Li =‖xi − yi‖
si(1)
Hence, we consider a time-window based mechanism. The
time-window is adjusted based upon Equation 2, where α is
the Exponential Moving Average (EMA) factor to be chosen
between 0 and 1; and Lt is the time interval to verify if
changes occur in the node’s i target.
Lt = (1− α)Lt−1 + αLi
2(2)
The mechanism works as follows. Once a node i starts its
trajectory, it computes the target and the estimated trajectory
duration, Li considering node’s speed (si) at that moment.
Whenever the time-window (Lt) expire, the probabilistic social
attractiveness function used to compute a new target is re-
calculated to check whether the target was a change (e.g.
number of nodes at destination, social attractiveness). If every-
thing has the same value or have higher value (i.e. number of
nodes at destination or social attractiveness), then node i keepsmoving towards its target. However, if target’s behavior was
changed to lower values, which means that its friends may
have left that community, a new target is computed, having
three main possibilities for selecting a new target: The first
one is the node i keeps moving to toward its previous target,
for reason not related with its social relationship, however
because that place; the second is the possibility of node i selectthe same destination that its friends, being this the highest
probability mainly due to its social relationship; and the last
possibility is the node i selects a completely different target.
IV. METHODOLOGY
The methodology described in this section has been carried
out having as benchmark the CMM standalone simulator [4],
where we have considered this model and added our modeling
to allow trajectory changes, which we refer to as CMM-v2.
A. Benchmark: CMM
In this section we briefly introduce CMM as it is the model
that we have considered as benchmark for evaluation purposes.
We suggest the reader to consider the original work [4] for
further details.
CMM models movement of nodes towards a target based
on the notion of affinities between nodes. From an operational
perspective, CMM assumes that each node cluster (commu-
nity) is assigned to an individual cell in a grid. It should be
highlighted that CMM does not take into consideration the
geographical position of nodes.
For a node i located on a specific cell the computation of a
next target involves computing the Social attractiveness (SA)of each set of nodes positioned in a cell, towards node i.
SA corresponds to the social attractiveness that a specific
set of nodes has to a node i, which in a way measures the
social relevancy of such cell to node i. Such attractiveness is
a product of the nodes that are, at a specific instant in time, in
such cell. SA is therefore computed based on the sum of the
cost of associations between i and each of the nodes j in the
cell, wi,j . This sum is then normalized by the number of nodes
associated to the specific cell, n. An empty cell has SA equal
to 0. The choice of a specific target relies on the computation
of SA and also on a probabilistic selection.
To attempt to model some predictability due to human
routine, CMM uses a reconfiguration interval variable. To
assist in the development of stronger or weaker associations
between the different clusters.
Despite the fact that we are using CMM mobility model,
we believe that the trajectory change mechanism can also
be used in any social mobility model which consider social
graph to model nodes’ movement, given that we are not using
none specific parameter of CMM model. To implement this
new mechanism in any social mobility model, we only need
to know the number of nodes that had direct impact on the
node’s movement toward to a specific target (n), and the social
attractiveness (SA), which is provided by:
SA =
n∑
j=1
wi,j
n(3)
where wi,j represents a cost of the association (links of
social graph) from its origin node (i) toward its destination
nodes (j), and n is the number of nodes in the cluster target.
B. Scenarios
To evaluate our mechanism in realistic settings, we have
considered traces provided by [15]; from three different types
of environments. The first one is an University Campus(NCSU), the second corresponds to traces obtained from NewYork City (NYC) and the last one is from University of Milano.
1) NCSU Scenario Settings: The NCSU scenario has been
selected as an example of an environment with dense wireless
coverage. In the traces it corresponds to a rectangular area
where the X length is of 2586.85 meters, while the Y length
is of 2347 meters - we have modeled it as 2500 meters per
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Table IPARAMETERS NECESSARY FOR SIMULATIONS AND RESULTS ANALYSIS.
2500 meters. The traces represent 20 participants out of a set
of students sharing a common interest, i.e., enrolled on the
computer science department and the trace set comprises 35
files. Hence, more than one node contributed to different trace
files; however, there is no possibility to distinguish and to
understand which node provided which trace and therefore,
we considered 20 nodes with a range of 250 meters - we have
split the area into cells of 250 meters per 250 meters, to be
compatible with CMM. Following the traces data, the 20 nodes
have been provided with 1 m/s speed.
2) NYC Scenario Settings: We chose the NYC scenario as a
not so dense wireless environment. The NYC scenario is based
on a rectangular area where the X length is of 31432 meters,
while the Y length is of 18900 meters - for simplification
reasons, we modeled the grid as of 31,000 meters per 19,000
meters. However, to ensure that we have longer distances than
in the NCSU setting we consider that each cell in the square
has 500 meters per 500 meters.
The NYC traces are based on 10 volunteers living in
Manhattan or vicinities. These volunteers work mostly in Man-
hattan, and employ different transports, e.g. subway, buses, or
pedestrian walking [16].
3) University Milano Scenario Settings: We chose this
other scenario, which is also available in [17], where encoun-
ters are recorder between groups of people from University
of Milano to evaluate some important metrics for routing
protocols. This dataset contains mobility traces from 44 mobile
devices at University of Milano.
The University Milano scenario is based on the University
area, where some of the classes take place in different building
3.5 Km away. Hence, we modeled the grid as 4000 X 4000
meters. The data was collected during 19 days [18].
V. RESULTS AND DISCUSSION
Tests on the outcome of trajectory changes mechanism have
been conducted considering realistic scenarios as aforemen-
tioned. The general parameters used by our benchmark are
shown in Table I.
A. Target Selection Error Margin
A first aspect that we want to understand is the improvement
that our mechanism introduces in terms of allowing nodes to
reach the most adequate destination, according to the measure
of social attractiveness that models such as CMM base their
movement modeling function upon. Hence, we have computed
the number of times that nodes truly reach a target that still
has the original social attractiveness level.
To evaluate the target selection error margin we run mobility
simulations using various parameters allowed by CMM, to try
Table IINUMBER OF TIMES THE NODES REACH TARGETS WITHOUT AN ADEQUATE
SOCIAL ATTRACTIVENESS.
understand if any specific aspect can provide some changes in
our mechanism.
We have considered the scenarios described in section IV-B,
and have set α in Equation 2 to be equal to 0.2 and 0.8.
Moreover, we also set different number of clusters. To be
as fair as possible in a realistic comparison, we also divided
the traces in cells with 250 and 500 meters for NCSU and
NYC traces respectively; and for NCSU scenario we randomly
selected only 20 trace files and for NYC 10 files.
The results are provided in Table II, where rows correspond
to simulated scenarios and the traces values; while columns
correspond to the number of times that the nodes reach a
target that does not hold anymore an adequate level of social
attractiveness, the total number of times that nodes reach their
destination, and the last column corresponds to error margin.
Overall, CMM-v2 provides a lower target selection error
margin. For the NCSU scenario (standing for a dense network)
the improvement provided seems to be higher, as it reduces
around 20.00% in both scenarios. We believe that in future
work the error margin can be lowered with an even better
fine-tuning of the time-window.
The target error margin improvement the NYC scenario
seems to be smaller but this is also a consequence of a not so
dense environment: nodes often have as targets empty areas,
and our proposal disregards such situations as the SA does
not change. We have only one error, when we are using
the trajectory changes mechanism in NYC scenario, which
happened, because a node has chosen its next destination
inside the own cell, having a very short trajectory duration,
and given that the time window mechanism use the previous
time window value, and usually in a larger scenario, we have a
high value for the time window, the time window had a higher
value than the trajectory duration in this case.
The trajectory changes mechanism showed a constant be-
havior in all scenarios, even with different number of clusters
and in both alpha values we have smaller error margin.
B. Impact on Trajectory Duration
In addition to the number of times that nodes reach their
adequate target destination, another aspect that we would like
to understand is the impact that a change of target while on the
move may have on the overall trajectory duration. We highlight
that the baseline here are not the number of hops but trajectory
510
Figure 2. Trajectory duration example. Node in black originally selects atarget in cell 4; later it selects a target in cell 2.
time, as allowing a node to change target during an active
trajectory implies an investment in terms of time. This is an
important metric to evaluation, given that the possibility of
nodes change their trajectory on motion, could greatly reduce
their trajectory duration.
We have again considered the NCSU and NYC scenarios.
We highlight that to be as accurate as possible the duration of
the trajectory is measured from the moment a node starts its
movement until it reaches a target that still holds the previously
computed number of nodes or more (social attractiveness). An
example for this line of thought is provided in Figure 2, where
the black node is the node moving and a node in cell 4 rep-
resents the target. During movement the social attractiveness
of the target (cell 4) decreases, having as consequence the
selection of a new target (cell 2), then the trajectory duration
is equal to t−x+y. If the node does not change its movement,
the trajectory duration is equal to t. Assuming the case that a
node arrives at its original target and this cell holds a lower
social attractiveness, then the trajectory duration is equal to
t+ t1.Figure 3 provides the average trajectory duration results
in minutes, considering all simulated scenarios, where each
scenario is represented by a set of three bars. The first two
sets in “x” axis, represent the results for NCSU scenario
with 5 and 10 clusters of nodes, respectively. Considering
these first results, we can see that there is no clear difference
between the trajectories duration, as was expected; i.e. even
when the trajectory changes mechanism is added, we still have
the same behavior for the social mobility model, having a
large proximity to NCSU traces. When looking into the results
obtained in the NYC scenario (the last two sets of bars),
we have a greater difference between NYC traces and our
simulated results. This difference can be explained, due to the
fact that in NYC traces the travel also include subway, trains
and buses; containing relatively long distance travels [15].
C. Influence on Network Operations
Predictability of the user’s mobility pattern is relevant for
the optimal allocation of resources in the access network, in
order to guarantee continuity of the session while moving [19].
Besides to assist in the resource management of the wireless
mobile networks, the mobility modeling can also assist routing
protocols in terms of the need and the timing for route re-
computation. An even more relevant case to cite in regards to
routing is the message forwarding in DTNs (Delay-Tolerant
Networking), where data messages are carried by nodes (e.g.
mobile devices carried by humans) and exchanged whenever
Figure 3. Impact on trajectory duration for NCSU and NYC Traces, andSimulation results for CMM and CMMv2 with α = 0.2 and 0.8.
Figure 4. The Contact Duration distribution for the University Milano Traces;CMM; and CMMv2 with α = 0.2 and α = 0.8.
possible; connectivity is intermittent. Adequate mobility mod-
els can therefore, improve routing protocols in DTNs due to
the fact that such modeling can predict future encounters.
This work considers two routing metrics (contact duration
and number of encounters) to evaluate the impact of the human
volition on network operation.
1) Contact Duration: The contact duration is a key factor
in DTNs, given that this metric determines how much data
can be exchanged during a contact. In this Section we will
evaluate the influence of trajectory changes mechanism using
the parameters cited on Table I for the Milano Traces.
Figure 4 shows the results obtained for the University
Milano traces [18], CMMv2 with α = 0.2, CMMv2 with
α = 0.8, as well as for the CMM mobility model, where the X
axis represents the contact duration in seconds and the Y axis
holds the Complementary Cumulative Distribution Function(CCDF) representation of the probability of occurrence of the
different contact duration.
Analyzing the results for contact duration (c.f. Figure 4),
the CMMv2 in both cases (α = 0.2 and α = 0.8) have higher
contact duration than CMM, as was expected. These experi-
ments confirm our hypothesis that if a node anticipates any
changes in the trajectory, it will stay for a longer period with
its friends, due to the fact that it reduces the unnecessary visits
to its previous destination. Moreover, we can see that CMMv2,
511
Figure 5. Number of Encounters, University Milano Traces, CMM; andCMMv2 with α = 0.2 and α = 0.8.
also in both cases, has a better proximity to University Milano
traces, having a slight difference when the contact duration in
traces is higher than 80.000 seconds. We believe that this is
because in the simulation scenario is difficult that two nodes
remain in contact during a entire day, i.e. 86.400 seconds.
2) Number of Encounters: Another important metric to
routing protocols in opportunistic networks, is the number of
encounters between nodes. According [20], the humans regular
behavior can help to predict future opportunistic encounter,
identifying better candidates for relaying the data towards the
destination. Based on this, we also evaluated the mean of the
number of encounters between nodes for the Milano scenario.
Figure 5 provides the mean of the number of encounters in
the University Milano Traces (dashed horizontal line in 15.6),
as well as the mean for the simulated scenario considering the
CMM, CMMv2 with α = 0.2 and CMMv2 with α = 0.8.
As we can see, the CMM has a higher number of encounters
when compared with both cases of CMMv2, however, it is
important to say that it does not means that is better, given that
sometimes these encounters last only few seconds, making it
impossible to exchange messages. Moreover, when compared
to real traces, CMMv2 again shows a better proximity.
VI. CONCLUSIONS AND FUTURE WORK
In this paper, we present a new mechanism to model tra-
jectory changes while nodes are on the move, which consider
social human behavior. We show that one of the characteristics
of humans is to change your mind based on some factors, such
as; meet a friend or changes in their destinations. In this work,
we developed a new mechanism that allows nodes change their
movement before they reach at their destination.
We have validated the mechanism based on three realistic
scenarios (NCSU, NYC and University Milano) using as
benchmark the community based mobility model (CMM).
Such validation has been performed based on simulations,
and we have shown that there is a significant improvement
in terms of target selection error margin and considering the
trajectory duration, we can maintain the same pattern observed
in the CMM. We also evaluated the influence of the trajectory
changes mechanism on the network operations analyzing the
contact duration and the number of encounters, and we can
conclude that the mechanism has a positive influence on
overall context of the network operation.
As future work, we are considering alternative time-window
mechanisms. Moreover, another start point to change nodes
movement; e.g. if a node meet a friend on the way.ACKNOWLEDGMENT
This work is supported by Fundação para a Ciência e
Tecnologia (FCT) under a BD scholarship grant reference
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