Flaws Validation of Maze Mobility Model using Spatial-temporal

Synthetic Mobility Metrics

Nisrine Ibadah

1 a

, Khalid Minaoui

, Mohammed Rziza

, Mohammed Oumsis

1,2

and C

esar Benavente-Peces

3 b

LRIT Laboratory, Associated Unit to CNRST (URAC 29), IT Rabat Center,

Faculty of Sciences, Mohammed V University in Rabat, Morocco

High School of Technology, Mohammed V University in Rabat, Sale, Morocco

ETS Ingenier

ıa y Sistemas de Telecomunicaci

on, Universidad Polit

ecnica de Madrid,

Calle de Nikola Tesla sn., 28031 Madrid, Spain

Keywords:

Maze Mobility Model, Mobility Metric, Spatial Node Distribution, Speed Decay Problem, Density Wave

Phenomenon, Average Neighbor Percentage, Mobile Neighbors Range, Wireless Networks.

Abstract:

Mobility modeling represents a critical task in mobile wireless networks to improve the overall throughput.

This paper evaluates relevant spatial-temporal stochastic properties of the most frequently used synthetic mo-

bility models compared to a new efﬁcient mobility model named Maze Mobility Model (Maze MM). It imitates

a real-life movement according to diverse mobility features, as spatial and temporal dependencies with also

geographic restrictions. To demonstrate the efﬁciency of this new model, various metrics were validated such

as; the speed decay problem, the density wave phenomenon, the spatial node distribution, the average neigh-

bor percentage, and mobile neighbors range. Each mobility pattern may bear from diverse mobility ﬂaws, as

shown by network simulations. So, numerous metrics are employed to describe mobility features. The current

research aims to deeply understand mobility features of Maze MM with the aim to deduce a deﬁnite judgment

of each mobility metric, given that further this fact affects the whole network performances. The validation re-

sults are discussed to remark the effectiveness and robustness of Maze MM according to the validated mobility

metrics.

1 INTRODUCTION

Mobile devices become ubiquitous in all our daily

life activities. Among the principal challenging is-

sues of this recent revolution is how to provide pro-

tocols and applications adequate to a highly dynamic

mobile network. Researches objectives lean to deeply

innovate in all ﬁelds of expertise related to wireless

communications, that have achieved an unpredictable

growth of trafﬁc applications. They permanently sug-

gest and implement new mobility designs responding

to diverse mobility requirements for a high quality of

services. It must take into consideration speed, dis-

tance and time to reﬂect a real-life situation. The pre-

cision of these mobility decisions further conduct to

maximum save energy and moderate consumption of

mobile devices. Under assorted limitations, the mo-

bility Models (MMs) predict nodes movement from

https://orcid.org/0000-0002-3079-3115

https://orcid.org/0000-0002-2734-890X

one position to another within a given period. They

expect devices motions by changing speed and di-

rection with time. Mobility models are implemented

in the ground, airborne, space, and undersea where

nodes are mobile as for as mobile opportunistic net-

work, Mobile Ad Hoc Network (MANET), and ve-

hicular ad hoc network. Mobility modeling ﬁeld is

principally splitted into several major tracks;

• Evaluating performances of mobility models un-

der diverse scenarios,

• studying mobility traces of real human world de-

ployments,

• suggesting new mobility models

• Or, validating the robustness of synthetic mobility

models.

Each stumble of the adopted motion strategy oc-

curs one or several serious mobility ﬂaws, as an in-

admissible ﬂuctuation of neighbors’ number, an ir-

regular distribution of mobile nodes inside the net-

106

Ibadah, N., Minaoui, K., Rziza, M., Oumsis, M. and Benavente-Peces, C.

Flaws Validation of Maze Mobility Model using Spatial-temporal Synthetic Mobility Metrics.

DOI: 10.5220/0008168801060112

In Proceedings of the 9th International Conference on Pervasive and Embedded Computing and Communication Systems (PECCS 2019), pages 106-112

ISBN: 978-989-758-385-8

work ﬁeld, or the unsteadiness average speed within

the simulation time. These problems have ﬁrstly been

validated for only Random Waypoint Mobility Model

(RW MM). And then, they are veriﬁed for many other

mobility models, like: Manhattan Grid MM (MG

MM), Reference Point Group MM, Nomadic MM,

SLAW and SMOOTH example:

• The speed decay problem, depicted in (Pramanik

et al., 2016).

• The spatial node distribution, described in (Wang

et al., 2016).

• The density wave phenomenon, introduced

in (Noguchi and Kobayashi, 2017).

• The average neighbor percentage, proposed

in (Almomani et al., 2015).

• The mobile neighbors range, suggested by Ibadah

in (Ibadah et al., 2018).

Those mobility metrics are mandatory for the net-

work performance analysis. Network analysis is pri-

mary proceeded to evaluate the total network simula-

tion basing on suitable performance metrics to only

present a general view. However, mobility metrics

make possible to judge a speciﬁc simulation of a mo-

bility model without needing to implement it on a real

mobile wireless network. A correct mobility valida-

tion can strictly detect the real reasons of network im-

pairment without analyzing performances of the mo-

bile network. For these purposes, in this paper we

validate the previously suggested mobility metrics for

Maze MM comparing with some well-know synthetic

mobility models. Then, we verify the novel mobil-

ity metric called the ’node neighbors range’ for this

new mobility model. That profoundly exposes the no

equilibrium of mobility models during the experiment

time.

The rest of this paper is organized as follows. In

Section 2, we validate Maze MM according to some

mobility metrics. In Section 3, we present the Maze

MM features. And ﬁnally, we discuss a brief conclu-

sion.

2 MOBILITY MODELS

VALIDATION

This section will mainly focus on mobility metrics; as

spatial node distribution, speed decay problem, den-

sity wave phenomenon, Average node neighbor per-

centage and mobile neighbors range in order to de-

scribe more exact features of our current new model.

We compare Maze MM with RW MM and MG MM.

The previously mentioned metrics have already

been carried out for only RW MM. And newly,

they have been analyzed for other mobility models

by (Ibadah et al., 2018). In this section, we inquire

to validate the movement steadiness for Maze MM

compared to other synthetic mobility models. Us-

ing those mobility metrics, we can put up and under-

stand an accurate judgment of each mobility ﬂaw. The

adopted strategy of mobile nodes chieﬂy further af-

fects the whole network performances. These metrics

will offer precise explanations of models’ dissimilar-

ities from each other. The validation parameters are

presented in Table 1.

Table 1: Validation settings.

Parameters Values

Number of nodes 50

Speed 5 m/s

Pause time (s) 0

Mobility models Maze MM

RW MM

and MG MM

Mobility metrics Speed decay problem

Spatial node distribution

Density wave phenomenon

Average neighbor percentage

mobile neighbors range

Area 1030m × 1030m

Simulation time 1000 sec

Iterations 20 times

The aforementioned experimental settings are cor-

related to rectify all possible scenarios with the aim

to deduce a deep and precise knowledge of each mo-

bility unbalance. The simulation outcomes are dis-

played and examined by Figures 1 to 6 in the next

sub-sections.

Models themselves do not offer precise expla-

nations of how MMs are different from each other.

Hence, this part will be a hard task which will mainly

focus on mobility metrics in order to describe more

exact features of our current new model. Using Mat-

lab, we make the average of 20 MMs for each pattern

to have more rigorous results. Random Waypoint MM

as a reference of mobility modeling, suffers from sev-

eral problems. In this section, we must make sure to

learn more about Maze MM and compare it with RW

MM and MG MM.

2.1 Speed Decay Problem

Firstly, we start with ’speed decay problem’. Yoon

and al.(yoo, ) showed that average node speed consis-

tently decreases over time. And therefore, it should

not be used for simulation. It decays over time be-

fore reaching a steady-state, which contradicts the as-

sumption of having the same average speed during a

Flaws Validation of Maze Mobility Model using Spatial-temporal Synthetic Mobility Metrics

107

simulation time, as proved with the red line chart of

Fig. 1. We remark that RW MM obviously suffers

from speed decay problem. Speed is not steady dur-

ing simulation time, due to selecting randomly speed

and waypoint independently.

Figure 1: The Speed Decay Problem.

From the same Fig. 1, we observe that MG MM

is less steady comparing with Maze MM which have

stable speed during all simulation time. We conclude

that Maze MM does not suffer from this problem.

Due to every mobility decision is taken according to

the distance traveled, speed adopted and motion time.

If these three parameters are dependent by respecting

each other, we almost avoid speed decay problem in

a mobility pattern; as demonstrated for Maze MM in

Fig. 1.

2.2 Density Wave Phenomenon

Secondly, another mobility metric is validated which

is called ’density wave phenomenon’. It represents

the average number of neighbors for a particular node.

Royer, Melliar-Smith and Moser(Royer et al., 2001)

were observed this pathology of RW MM which peri-

odically ﬂuctuates along with time as exactly proved

in Fig. 2.

Figure 2: The Density wave phenomenon.

From Fig. 2, MG MM suffers too from this trouble

as shown with green line chart. We observe that, RW

MM and MG MM ﬂuctuate in a big range from 0 to 11

and from 0 to 9 respectively, and frequently without

any neighbor. But, this range is more precise (2-4)

with Maze MM which all the time has at least two

neighbors. This metric is too important, mostly, if we

applied for a MANET. If a mobile node send trafﬁcs

without any intermediate node, that will mainly in-

ﬂuence the Packet Delivery Ratio (PDR) in such net-

work.

From all these results, we conclude that RW MM

and MG MM have apparently this problem. However,

Maze MM is more stable with slight ﬂuctuation in a

reasonable range with some neighbors all the time.

2.3 Average Neighbor Percentage

Thirdly, we validate another mobility metric which

called ’average neighbor percentage’. In general, high

variability in average mobile node neighbor percent-

age will produce high variability in performance re-

sults (Almomani et al., 2015). In order to highly be

certain of the outcomes displayed in Figure 2, this

metric will give more rigorous view of neighboring

nodes changes in Figure 3.

• According to Figure 3b, the RW MM knows the

worst results. It oscillates in a range of 0–16%

with several existing moments of any neighbor.

That means any intermediate node will be de-

tected to forward packets which are sent by a def-

inite mobile node. This ﬂaw further raises the lost

packets which will reduces the packet delivery ra-

tio of this validated model.

• From Figure 3c, the MG MM presents small ﬂuc-

tuations in the range of 4–9%, in addition to more

than two neighbors are always present among the

total experimented nodes. This fact permits to this

pattern to outperform than the RW MM.

• Nevertheless, from Figure 3a, Maze MM have a

range of 3–6%. It produces the best obtained

results, with a continuous presence of neighbors

during the whole validation time. This particular-

ity lets them to highly outperform than other mod-

els (Ibadah et al., 2019). This mobility model is

more steady than the other models.

This property accords a global sight of the density

wave phenomenon within the validation period. That

mightily confesses the results depicted in Figure 2,

as outlined in Table 2.

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108

(a) Maze MM

(b) RW MM

Figure 3: The Average neighbor percentage. (a) Maze MM

(b) the RW MM; (c) the MG MM.

2.4 Spatial Node Distribution

Fourthly, we validate another mobility metric, as

the ’spatial node distribution’. Bettstetter (Bettstet-

ter et al., 2002), Blough and al. (blo, ) respectively

observed the non-uniform spatial distribution of RW

MM as proved in Fig. 4(b). At the steady state, the

node density is extreme in the center region, whereas,

it is almost few around the boundaries, as shown in

Fig. 4(b). We analyze this mobility metric at t = 0 and

when simulation time elapses.

In Fig. 4(a) at t = 0, we observe that Maze MM is

well distributed in the simulation ﬁeld when mobile

(a) Maze MM

(b) RW MM

Figure 4: The Spatial node distribution at t = 0s. (a) Maze

MM (b) the RW MM; (c) the MG MM.

nodes are located at the boundaries with some few

empty spaces comparing with Fig. 4(b) and Fig. 4(c).

That will be more obvious if we use a high mobile

node number.

We analyze this mobility metric when simulation

time elapses. In Fig. 5(a), we observe that Maze

MM has always the best spatial distribution. It is

well distributed in the simulation ﬁeld with some mo-

bile nodes at the boundaries. It has some few empty

spaces comparing with Fig. 5(b) and Fig. 5(c). If

a MM has this phenomenon during simulation time,

nodes will suffer from ’Density wave phenomenon’

all the time, as shown in Fig. 2.

Flaws Validation of Maze Mobility Model using Spatial-temporal Synthetic Mobility Metrics

109

(a) Maze MM

(b) RW MM

Figure 5: The Spatial node distribution at t = 1000s. (a)

Maze MM (b) the RW MM; (c) the MG MM.

2.5 Mobile Neighbors Range

A new metric was recently suggested surmounting

limitations of the other metrics which have been sug-

gested previously, such as the spatial node distribu-

tion, density wave phenomenon and average neighbor

percentage. This new metric is called ’mobile neigh-

bors range’. It gives a right conduct of mobility mod-

els ﬁrmness for all mobile nodes within the valida-

tion period. It inspects neighboring changes basing

on a speciﬁc propagation range whatever the time in-

stant, the targeted model, and the inspected node, are.

This feature is prosperous for each instant by show-

ing a range of recorded neighbors for the mobility

pattern. Meanwhile, this metric points out the advan-

tages and disabilities of each mobility issue which has

been highlighted previously. The validation outcomes

of this mobility metric are shown in Figure 6.

(a) Maze MM

(b) RW MM

Figure 6: The Mobile neighbors range. (a) Maze MM (b)

the RW MM; (c) the MG MM.

We remark that:

• According to Figure 6b, the RW MM reports the

worst pattern based on this property. It bears

perceptibly from the number of neighbors vari-

ation during time. That occurs a worse mobil-

ity pattern with an irregular gap of mobile neigh-

bors range that reﬂects the unsteadiness behavior

within time.

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• The MG MM deﬁnes more appropriate ﬂuctua-

tions with a regular gap of 0–9, with several mo-

ments with no detected neighbors. That ﬁrmly en-

dorses the previous results of prior validated met-

rics, as the density wave phenomenon and the av-

erage neighbor percentage.

• Figure 6 shows that RW MM and MG MM have

obviously this issue. However, the Maze MM out-

perform at this feature where the calculated range

is too promptly converges in a regular margin.

In addition to during all validation time, mobile

nodes detect some neighbors to forward packets to

their destinations with no losses. This speciﬁcity

is not spoted for the other validated model. That

hugely reﬂects that the validated mobility model

is more steady and stable which lead to satisfac-

tory results in the performance analysis (Ibadah

et al., 2017) .

This metric furnishes rise precision compared to

the others. The mobile neighbors range reasons that

it handles ﬂaws of all prior mobility metrics by vali-

dating all deployed nodes within all validation period

for all mobility models. We conclude that Maze MM

offers the best results than RW MM and MG MM in

the ﬁve analyzed mobility metrics. It keeps:

• The same speed during the simulation time, due

to, its respecting to the motion laws, as shown for

the ’speed decay problem’ in Fig. 1.

• Maze MM has the best ’spatial node distribution’

before moving, as conﬁrmed in Fig. 4. And also,

when the simulation time elapses, as proved in

Fig. 5.

• All the time, Maze MM has a few ﬂuctuations of

density neighbors comparing to RW MM and MG

MM, as demonstrated in Fig. 2, for the ’density

wave phenomenon’.

• Maze MM maintains the same rhythm of the av-

erage neighbor percentage, as shown by Figure 3.

• Moreover, Maze MM offers the best recorded Mo-

bile neighbors range with high satisfactory results,

as exactly deﬁned in Figure 6.

Based on these metrics, we can divine perfor-

mances of the mobility models with no need to sim-

ulate them into a wireless network, as mostly done to

judge the mobility model. This policy is more precise

to only yield the correct behavior of only the motion

strategy adopted. These metrics highlight integral as-

pects with the aim of correctly extract outlook of mo-

bility issues. Due to these ﬂaws, the choice of a wrong

mobility model deeply affect the whole network per-

formances with undesirable consequences. After sim-

ulating 60 ﬁles corresponding to the three mobility

models, we deduce that we can classify them accord-

ing to their results as recapitulated in Table 2. The

best outcomes are shown in green cells(1), acceptable

shifts are shown in yellow colored cells(2), and the

worst results are shown in red colored cells(3).

Table 2: The validated mobility model classiﬁcation.

Mobility models

Mobility Metrics Maze MM RW MM MG MM

Speed decay 1 3 2

problem - - -

Density wave 1 3 2

phenomenon - - -

Average neighbor 1 3 2

percentage - - -

Spatial node 1 3 2

distribution - - -

Mobile neighbors 1 3 2

range - - -

These validations of the Maze MM is too sufﬁ-

cient to judge Maze MM robustness and effectiveness

comparing to other patterns. The aim of this inves-

tigation is to prove that the realistic combination of

Maze MM approach that take into consideration all

parameters to perform an efﬁcient and ﬂexible mobil-

ity pattern which can be deployed in complex situa-

tions to afford the best performances, as proved by its

high-performance outcomes (Ibadah et al., 2019).

3 MAZE MOBILITY MODEL

FEATURES

The main faced challenge of Maze MM is how, we

can deduce the most convenient trajectory to a def-

inite destination into a complex ﬁeld to lead nodes

with to correctly move in presence of various mobil-

ity restrictions (paths, walls, and intersections). Some

previously suggested mobility patterns mimic various

real-life situations, but they are not ﬂexible with envi-

ronment.

The Maze MM owns a set of substantial charac-

teristics that adjust the entire adopted motion policy.

It is characterized by many remarkable aspects:

• Maze MM abides by the physical laws of mo-

tion. That considers the elemental relations be-

tween speed, time, and distance. As opposed to

RW MM, for example, which randomly chooses

speed and destination independently of each other.

That further produces an unrealistic model.

• It is a mobility model with spatial dependencies,

i.e., the next mobile node location can only be in

one of the four directions (top, left, down, or right)

basing on to the last position.

• It is also a mobility model with temporal depen-

dencies, i.e., the present instant mainly related to

Flaws Validation of Maze Mobility Model using Spatial-temporal Synthetic Mobility Metrics

111

the previous time instant.

• Due to the uniform grids, the ﬂight length is

steady between two successive grids.

• The visiting frequency and return time are proba-

bilistically distributed with relevance to the resti-

tuted trajectory.

• For the ﬁrst period, it has a spatial distribution ac-

cording to white grids. And subsequently, the ob-

tained trajectory must be only shaped by pathways

with no walls. This condition reﬂects a realistic

motion of daily life behavior.

The outstanding outcomes offered by Maze MM

have been resulted thanks to its logical process, its

conception, and the consideration of real-life move-

ments. These features make this model more efﬁcient

and stable, even in the presence of diverse mobility

restrictions.

4 CONCLUSION

The noticeable results sown in this paper has re-

marked the relevance of mobility models in mobile

networks to improve the overall throughput by sup-

porting routing protocols. Given the results obtained

in the proposed approach and shown and discussed

in this paper, we conclude that a new ﬂexible mo-

bility model is developed which offers the best result

at the most confronted mobility problems, like speed

decay problem, spatial node distribution and density

wave phenomenon, average neighbor percentage, spa-

tial node distribution, and mobile neighbors range.

Due to walls used inside the simulation area, Maze

MM can be classiﬁed as a mobility model with geo-

graphic restrictions. And also, it can be considered

as a hybrid entity synthetic mobility pattern. It com-

bines a random distribution at the beginning, a tem-

poral dependency based on the instant of the previous

decision motion, and a spatial dependency while the

next position depends on the last one. For all that,

this pattern mimics real-life movement especially in

a complex area without spending the time to move

to a wrong destination. This pattern can be used for

mobile devices like robots which have problems of

energy consumption.

ACKNOWLEDGEMENTS

This paper was supported by the project ”PPR2-6-

minaoui” of Mohammed V University and LRIT Lab-

oratory, Rabat.

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