Flaws Validation of Maze Mobility Model using Spatial-temporal
Synthetic Mobility Metrics
Nisrine Ibadah
1 a
, Khalid Minaoui
1
, Mohammed Rziza
1
, Mohammed Oumsis
1,2
and C
´
esar Benavente-Peces
3 b
1
LRIT Laboratory, Associated Unit to CNRST (URAC 29), IT Rabat Center,
Faculty of Sciences, Mohammed V University in Rabat, Morocco
2
High School of Technology, Mohammed V University in Rabat, Sale, Morocco
3
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
a
https://orcid.org/0000-0002-3079-3115
b
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
Copyright
c
2019 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
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
(c) MG 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
(c) MG 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
(c) MG 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
(c) MG 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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