The Influence Mobility Model: A Novel
Hierarchical Mobility Modeling Framework
Muhammad U. Ilyas and Hayder Radha
Michigan State University

Motivation
 Many mobility models used for design and testing of ad-hoc networks are random mobility models.
 Group mobility models bring some structure to completely random entity mobility models.
 Today’s mobility models seem to ignore one important characteristic of mobile nodes, i.e. different classes of nodes influence each other.
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ECE: Michigan State University

Previous Work
Based on the works of…
 Chalee Asavathiratham’s work on the “Influence
Model” presented in his doctoral dissertation.
 Jin Tiang et al. work on “Graph-based mobility models”.
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ECE: Michigan State University

Feature Wishlist for the
“Ideal” Mobility Model
 Task based movement
 Path selection
 Node classification
 Class transition
 Dependence/ Influence


(

)



 Scale invariance

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Current Work: Scope
 Obtain a graph-based representation of the simulated scenario based on paths on geographical map.
– Step 1: Determine the different types of nodes in the simulated scenario.
– Step 2: Build a graph-based transportation network
(transnet) for each node type/ mode of transportation.
– Step 3: Combine/ connect transnets.
 Determine network influence matrix D .
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ECE: Michigan State University

Graph-based Representation of Simulation Plane





Determine number of node classes.
Cut up the map of the area being simulated into sites (vertices) in which mobility of nodes belonging to the same class is described by the same set of parameters.
Determine paths between sites
(edges) and obtain a transportation subnet.
Repeat for all node classes.
Interconnect vertices of different transportation subnets where nodes change over from one subnet to another.
Output: A set of interconnected transportation subnets.
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ECE: Michigan State University

Graph-based Representation of Simulation Plane
G



G
G
11 m 1
G
1 m
G mm




G: Connectivity Matrix
•Consists of submatrices G ij
•Basic elements of G are 1s and 0s
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Graph-based Representation of Simulation Plane
 This form of representation of the simulation area by means of the connectivity matrix G restricts the movement of nodes.
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ECE: Michigan State University

Markov Chains vs.
Influence Model
 Similarities
– Both Markov Chains (MC) and the Influence Model
(IM) can be defined by stochastic matrices and be graphically represented as weighted di-graphs.
 Differences
– A Markov Chain describes the state of a system and the transition probabilities to other states conditional on the current state.
– The Influence Model describes the states of a number of systems equal to the number of vertices in the graph.
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ECE: Michigan State University

Markov Chains vs.
Influence Model
 Differences (Cont’d):
– In MC the edge weights on outgoing edges represent the transition probabilities.
– In the IM the edge weights on incoming edges represent the magnitude of the influence from other nodes.
– MC and the IM differ in their evolution equations.
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ECE: Michigan State University

0.3
0.3
0.2
A
0.7
0.8
0.5
0.1
C
B
0.2
0.1
Markov Chains vs.
Influence Model
A
B
C
A B C




0.3
0.7
0.1 0.2
0.1
0.2
0.8
0.5
0.1




0.1
0.2
A
0.6
0.7
0.5
0.1
C
B
0.4
0.1
A
B
C
0.1
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A B C




0.3
0.2
0.5
0.6
0.1
0.4
0.1 0.7
0.1





[
  
Binary Influence Model
 Evolution Equations for Binary Influence Model
 D network influence matrix (nxn)
 r[k+1] probability vector (nx1)
 s[k] status vector (nx1)
 Bernoulli() coin flipping function
[
[ 1]
 
( [

1])
W ireless A nd V id e o Communication s ( WAVES ) Lab
ECE: Michigan State University

Binary Influence Model
 The Binary Influence Model (BIM) restricts the states to be either 0 or 1.
 We are using the BIM in the Influence
Mobility Model to model states of sites as either free/ accessible or congested/ inaccessible.
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Example: Pedestrian Crossing
5
11
6
3/4
12
7
13 14
8 9 10
 Note: We used a special form of the Binary
Influence Model, the “
Evil Rain Model
” for
this particular example.
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ECE: Michigan State University

Example: Pedestrian Crossing
6
Average number of congested sites vs. time
Average number of congested pedetrian sites
Average number of congested car sites
5
4
3
2
1
0
0 10 20 30 40 50
Time
60 70 80 90 100
W ireless A nd V id e o Communication s ( WAVES ) Lab
ECE: Michigan State University

Example: Pedestrian Crossing
6
Average number of congested sites vs. time
Average number of congested pedetrian sites
Average number of congested car sites
5
4
3
2
1
0
0 10 20 30 40 50
Time
60 70 80 90 100
W ireless A nd V id e o Communication s ( WAVES ) Lab
ECE: Michigan State University

Future Work
 Replacing the Binary Influence Model with the General Influence Model.
 Associating costs with the links on the connectivity matrix and allocating limited budgets to individual nodes.
 A routing algorithm that routes nodes through the transnets within budget constraints.
W ireless A nd V id e o Communication s ( WAVES ) Lab
ECE: Michigan State University

Q&A

Evil Rain Model
D e
 



1
0
0
1
0
0 e e D
1 2



 e

1

[ ]

0

 
D
1
0
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ECE: Michigan State University

Example 2: Intra-state Travel
C1 11/12
3/4 C2
5/6
7/8
9/10
C3
13/14
C4
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Time