Modeling the Impact of Human Spontaneity inMobile Trajectories

Andrea G. RibeiroFaculdade Ideal (FACI)

Belem, Brazil

andrea.ribeiro@ieee.org

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

509

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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