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.
Wireless And Video Communications (WAVES) Lab
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”.
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
Feature Wishlist for the
“Ideal” Mobility Model
 Task based movement
 Path selection
 Node classification
 Class transition
 Dependence/ Influence

 ()



 Scale invariance

Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
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.
Wireless And Video Communications (WAVES) Lab
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.
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
Graph-based Representation
of Simulation Plane
 G11
G  
Gm1
G1m 


Gmm 
G: Connectivity Matrix
•Consists of submatrices Gij
•Basic elements of G are 1s and 0s
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
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.
Wireless And Video Communications (WAVES) Lab
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.
Wireless And Video Communications (WAVES) Lab
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.
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
Markov Chains
vs.
Influence Model
0.2
0.3
A
0.1
0.70.8
0.5
0.1
B
From \ To
A B C
0.2
A
 0.3 0.2 0.5 
 0.7 0.1 0.2 


 0.1 0.8 0.1
B
C
C
0.1
0.2
0.3
A
0.1
0.60.7
0.5
C
0.1
B
By \ On
A B C
0.4
A
 0.3 0.2 0.5 
 0.6 0.1 0.4 


 0.1 0.7 0.1
B
C
0.1
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
r[k  1]  D  s[k ]
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
r[k  1]  D  s[k ]
s[k  1]  Bernoulli(r[k  1])
Wireless And Video Communications (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.
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
Example: Pedestrian Crossing
5
6
11
3/4
8
9
7
12
13
14
10
 Note: We used a special form of the Binary
Influence Model, the “Evil Rain Model” for
this particular example.
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
Example: Pedestrian Crossing
Average number of congested sites vs. time
6
Average number of congested pedetrian sites
Average number of congested car sites
Average number of congested sites
5
4
3
2
1
0
0
10
20
30
40
50
Time
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
60
70
80
90
100
Example: Pedestrian Crossing
Average number of congested sites vs. time
6
Average number of congested pedetrian sites
Average number of congested car sites
Average number of congested sites
5
4
3
2
1
0
0
10
20
30
40
50
Time
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
60
70
80
90
100
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.
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
Thank You
Q&A
Evil Rain Model
1 0
De   0 1
e1 e2
0
 1 


0  se [k ]   0 
 s[k ]
D 
D
1
0
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University
Example 2: Intra-state Travel
11/12
C3
3/4
C2
5/6
7/8
9/10
C4
13/14
Link Number
C1
Time
Wireless And Video Communications (WAVES) Lab
ECE: Michigan State University