Mobility Models in Mobile
Ad Hoc Networks
What is Mobile Network? Why is it called
Ad Hoc?

Mobile Ad Hoc Networks (MANET) is a
network consisting of mobile nodes with
wireless connection (Mobile) and without
central control (Ad Hoc)
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Self-Organized Network
Each mobile node communicates with other
nodes within its transmitting range
Transmission may be interrupted by nodal
movement or signal interference
It seems that something is watching
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Sensor Network is recently a hot topic
Specified Application in MANET
Nodes are equipped some observation devices
(GPS, Temperature, Intruder Detection and so on)
Nodes may move spontaneously or passively
There are more restrictions in Sensor Networks
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Power
Transmission Range
Limited Computation Power
Moving Speed (if does)
Realistic Mobility Model is better than
Proposed Mobility Models
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Although MANET and Sensor Network are being researched for
a while, there do not exist many realistic implementation
To implement a real MANET or Sensor Network environment for
emulation is difficult
 Signal Interference
 Boundary
We will need to evaluate MANET by simulation
To have useful simulation results is to control factors in
simulation
 Traffic Pattern
 Bandwidth
 Power Consumption
 Signal Power (Transmission Range)
 Mobility Pattern
 And so on
How Many Mobility Model are inspected?
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Entity Mobility Models
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Random Walk Mobility Model
Random Waypoint Mobility Model
Random Direction Mobility Model
A Boundless Simulation Area Mobility Model
Gauss-Markov Mobility Model
A Probability Version of the Random Walk
Mobility Model
City Section Mobility Model
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Group Mobility Models
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Exponential Correlated Random Mobility Model
Column Mobility Model
Nomadic Community Mobility Model
Pursue Mobility Model
Reference Point Group Mobility Model
Random Walk
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Parameters:

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Speed =
[Speed_MIN,Speed_MA
X]
Angle = [0,2π]
Traversal Time (t) or
Traversal Distance (d)
Random Waypoint
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Parameters

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Speed =
[Speed_MIN,Speed_MA
X]
Destination =
[Random_X,Random_Y]
Pause Time >= 0
Random Direction
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Parameters:
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Speed =
[Speed_MIN,Speed_MA
X]
Direction = [0,π] (Initial
[0,2π])
Pause Time
Go straight with
selected direction until
bump to the boundary
then pause to select
another direction
Boundless Simulation Area

Parameters:
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v(t+△t) =
min{max[v(t)+△v,0], Vmax}
θ(t+△t) = θ(t) + △θ
x(t+△t) = x(t) + v(t) *
cosθ(t)
y(t+△t) = y(t) + v(t) *
cosθ(t)
△v = [-Amax*△t , Amax*△t]
△θ = [-α*△t , α*△t]
Gauss-Markov
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Parameters:
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sn  sn1  (1   )s  (1   2 )sn1
d n  d n1  (1   )d  (1   2 )d n1
When approach the
edge, d value will
change to prevent the
node stocking at the
edge
Probability Version of Random Walk
City Section
Group Mobility
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Exponential Correlated Random Mobility Model
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Column Mobility Model
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Nomadic Community Mobility Model
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Given a reference grid, each node has a reference point on the
reference grid
Each node can move freely around its reference point (Ex:
Random Walk)
Similar to Column Mobility Model, but all nodes of a group share
a reference point
Pursue Mobility Model
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new_pos = old_pos + acceleration(target-old_pos) +
random_vector
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Reference Point Group
Mobility Model
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Group movements are
based on the path traveled
by a logical center for the
group
GM: Group Motion Vector
RM: Random Motion
Vector
Random motion of
individual node is
implemented by Random
Waypoint without Pause
Simulation Parameters
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Simulation Package: ns-2
50 Mobile Nodes
100m Transmission Range
Simulation Time from 0s ~ 2010s
 Results is collected from 1010s
Routing Protocol: Dynamic Source Routing (DSR)
Each mobility model has 10 different runs and show with 95%
confidence interval
Simulated Model
 Random Walk
 Random Waypoint
 Random Direction
 RPGM
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100% Intergroup communication
50% Intergroup communication, 50% Intragroup communication
What results do different mobility models
bring?
Observation of Different Mobility Models
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The performance of an ad hoc network protocol can
vary significantly with different mobility models
The performance of an ad hoc network protocol can
vary significantly when the same mobility model is
used with different parameters
Data traffic pattern will affect the simulation results
Selecting the most suitable mobility model fitting to
the proposed protocol
Considerations when Applying Each
Mobility Model
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Random Walk
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Random Waypoint
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Most realistic mobility model
Probabilistic Random Walk
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Although moving without boundary, the radio propagation and neighboring
condition are unrealistic
Gauss-Markov
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Unrealistic model
Pause time before reaching the edge  Similar to Random Walk
Boundless Simulation
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Scenarios such as conference or museum
Random Direction
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Small input parameter: Stable and static networks
Large input parameter: Similar to Random Waypoint
Choosing appropriate parameters to fit real world is difficult
City Section
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For some protocol designed for city walk
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Exponential Correlated Random Mobility Model
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Column, Nomadic Community, Pursue Mobility
Models
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Theoretically describe all other mobility models, but
selecting appropriate parameter is impossible
Above three mobility models can be modeled by RPGM
with different parameters
RPGM Model
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Generic method for group mobility
Assigned an entity mobility model to handle groups and
individual node
Random Waypoint Considered Harmful

Yoon has published a paper indicating that
network average speed of RWP will decay to
zero in simulation
Setting the minimum speed larger than zero
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Besides speed decaying, the nodes with
RWP tend to cross the center of the area
(0, Ymax)
(X1 - 0) * (Ymax - Y1)
(Xmax, Ymax)
(Xmax - X1) * (Ymax - Y1)
First :
( X max  X 1 )( Ymax Y1 )
X max Ymax
Second :
(X1, Y1)
(X1 - 0) * (Y1 - 0)
Third :
(Xmax - X1) * (Y1 - 0)
( X 1  0 )( Y1  0 )
X max Ymax
Fourth :
(0, 0)
(Xmax, 0)
( X 1  0 )( Ymax Y1 )
X max Ymax
( X max  X 1 )(Y1  0 )
X max Ymax
If you can’t move quickly, please don’t go
too far
V2
Dshorter
V1
V4
V3
Dshorter
Vmin<V3,V4<Vlower<V1,V2<Vmax
If you are close to the wall, don’t be afraid
Start Position
Target Position
Fixed Lower Speed, Varied Shorter
Distance
Fixed Lower Speed, Varied Shorter Distance
12
Random Waypoint
Lower Speed, Shorter Distance (2, 400)
Lower Speed, Shorter Distance (2, 300)
Average Speed (m/s)
10
Lower Speed, Shorter Distance (2, 200)
Lower Speed, Shorter Distance (2, 100)
Lower Speed, Shorter Distance (2, 50)
8
6
4
2
0
0
5000
10000
20000
15000
Simulation Time (seconds)
25000
30000
35000
Varied Lower Speed, Fixed Shorter
Distance
Random Waypoint
Speed 1m/s
Speed 2m/s
Speed 3m/s
Speed 4m/s
Speed 5m/s
Speed 6m/s
Speed 7m/s
Varied Speed Fixed Distance(200m)
12
Average Speed (m/s)
10
8
6
4
2
0
0
5000
10000
15000
20000
25000
Simulation Time (seconds)
30000
35000
Ripple Mobility Model with LSSD
Ripple Mobility Model (Radius: 1000m, Lower Speed: 2m/s)
12
Average Speed (m/s)
10
Without LSSD
Shorter Distance
Shorter Distance
Shorter Distance
Shorter Distance
Shorter Distance
400m
300m
200m
100m
50m
8
6
4
2
0
0
5000
10000
15000
20000
Simulation Time (seconds)
25000
30000
35000
Ripple Mobility Model with LSSD and
Shorter Radius
Ripple Mobility Model (Radius: 500m, Lower Speed: 2m/s)
12
Average Speed (m/s)
10
Without LSSD
Shorter Distance
Shorter Distance
Shorter Distance
Shorter Distance
Shorter Distance
400m
300m
200m
100m
50m
8
6
4
2
0
0
5000
10000
15000
20000
Simulation Time (second)
25000
30000
35000
How does the speed distribute during the
simulation
The Number of Speed Generation
Random Waypoint
Lower Speed Shorter Distance (2, 50)
Lower Speed Shorter Distance (6, 50)
Ripple Mobility Model(2, 50)
4500
4000
Number of Events
3500
3000
2500
2000
1500
1000
500
0
0
2
4
6
8
10
12
Speed Distribution
14
16
18
20
That’s the Answer
The Duration of Speed
Random Waypoint
Lower Speed Shorter Distance (2, 50)
0.7
Lower Speed Shorter Distance (6, 50)
Ripple Mobility Model(2, 50)
0.6
Duration Ratio
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
12
10
Speed Distribution
14
16
18
20
Spatial Distribution Comparisons
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Cumulate the nodal appearance in the square of
100mx100m (Moving area is 1000mx1000m)
Conclusions
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The defects in RWP are explored by some
research and solutions are also proposed
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Decaying Average Speed
Unfair Moving Pattern
Most proposed solutions target to one of the
defects but not both
To generate different moving pattern within
the same speed range is a reasonable
requirement but it has not been brought up
Reference


Tracy Camp, Jeff Boleng, and Vanessa
Davies, “A Survey of Mobility Models for Ad
Hoc Network Research”, Wireless
Communication and Mobile Computing
(WCMC) 2002
Guolong Lin, Guevara Noubir, and Rajmohan
Raharaman, “Mobility Models for Ad Hoc
Network Simulation”, INFOCOM 2004
First Model
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X1, X2,…, Xn as non-overlapping time periods
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During each time periods Xi, the node travels with
some random speed Vi for some random distance
Di
Xi=Di/Vi Xi+1=Di+1/Vi+1
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Xi+1=Di+1/Vi+1
{Xi} is a renewal process
This model is applied on the homogeneous
metric space
Analytical Results of First Model
E[ D] z 1
( z) 
  dFV ( x)
lim
F
V
E[ X ] 0 x
t 
t
E[V ]  

lim
t 
E[ D] 1
f V ( z)  E[ X ]  z fV ( z)
t
2
E[ D]  Rmax
3
E[V  ] 

0
E[ D]
f ( z )dz 
E[ X ]

V
2 Rmax
Vmax
E[ X ] 
 ln(
)
3(Vmax  Vmin )
Vmin
Vmax  Vmin
Vmax
ln(
)
Vmin

Residual distance γt is represented the remaining
distance in time period Xi contains t
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Xi = (t0, t1)   Di , 
t0
t0 t1
2

Di
2
Residual waiting time βt is represented the
remaining time in time period Xi contains t
z
1
lim Ft ( z ) 
  [1  FD ( x)]dx
t 
E[ D] 0
1
lim f ( z ) 
 [1  FD ( z )]
t 
E[ D]
t
x
1
G( x)  lim Pr{ t  x} 
  [1  Fx ( y)]dy
t 
E[ X ] 0
Second Model
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The initial Speed and Distance are derived
from the stable state of First Model
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The movement state of a node at time t∞ is
characterized by Vt, γt, βt
For X0,
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D0 is selected according to Fγ(z)
V0 is selected according to FV(z)
The remaining periods are chosen as the
same as the first model
Analytical Observation
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Second model has the following distribution

E[ D] x 1
Pr{Vt  x} 
  y dFv ( y )
E[ X ] 0
S
x

1
S
Pr{ t  x} 
  [1  FD ( y)]dy
E[ D] 0
If the following formula is satisfied,
fV ( y )  ky, y  [Vmin ,Vmax ], k 

2
Vmax
2
2
 Vmin
Speed distribution is uniformly distributed within [Vmin, Vmax]
Simulation Results in Boundless Area
(Rmax=1000m, (0,20))
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Original:
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Distance D is picked from
Speed V is picked
uniformly from [Vmin, Vmax]
r2
FD (r )  2
Rmax
Modified:
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3
r3
F (r ) 
(r  2 )
2 Rmax
3Rmax
D0 is picked from
Vo is picked uniformly
from [Vmin, Vmax]
r
F
(
r
)

Di is picked from
R
Vi is picked from F ( x)  VX
0
d
2

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D
V
2
max
2
 Vmin
2
2
max  Vmin
2
Speed Distribution Comparison between
Modified and Original in Boundless Area
Simulation Results in Bounded Area
(1500mx1500m, (0,20))
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Original:
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Destination is picked
uniformly within the
simulation region
Speed is picked uniformly
from (Vmin, Vmax)
Modified
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Destination is picked
uniformly within the
simulation region
First Speed is picked
uniformly from (Vmin, Vmax)
Following Speed is picked
according to F ( x)  X  V
2
V
2
min
2
min
2
Vmax
V
Speed Distribution Comparison between
Modified and Original in Bounded Area
Extended Version of First and Second
Model
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Pause Time Z is considered in the extended
model
Z is independent of D, V (hence X)
It generates the following time sequence
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X1, Z1, X2, Z2, X3, Z3,…, Xn, Zn,…
The sequence is not renewal process
If pair of X and Z is considered, then {Yi} is
renewal process

Y1(X1+Z1), Y2(X2+Z2), Y3(X3+Z3),…, Yn(Xn+Zn),…
Discussions and Conclusions
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Renewal theory is useful to analyze and solve the
problem of speed decay in the RWP model
Derive target speed steady state distribution from
the formula to simulate the different impact on
routing protocol
Do not need to discard the initial simulation data to
achieve steady state
How is the nodal distribution?
RWP in Bounded Area is not derived from analytical
work