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

The Influence Mobility Model: A Novel Hierarchical Mobility Modeling Framework

Muhammad U. Ilyas and Hayder Radha

Michigan State University

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LabLabECE: Michigan State UniversityECE: 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.



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”.



Feature Wishlist for the “Ideal” Mobility Model

Task based movement Path selection Node classification Class transition Dependence/ Influence

Scale invariance

()



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.



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.




11 1

1

m

m mm

G G

G

G G

G: Connectivity Matrix

•Consists of submatrices Gij

•Basic elements of G are 1s and 0s




This form of representation of the simulation area by means of the connectivity matrix G restricts the movement of nodes.



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.



Markov Chains vs.

Influence ModelDifferences (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.



Markov Chains vs.

Influence Model

\

0.3 0.2 0.5

0.7 0.1 0.2

0.1 0.8 0.1

From To A B C

A

B

C

A

C

B0.20.3

0.50.80.7

0.1

0.1

0.1 0.2

A

C

B0.20.3

0.50.70.6

0.1

0.1

0.1 0.4

\

0.3 0.2 0.5

0.6 0.1 0.4

0.1 0.7 0.1

By On A B C

A

B

C



Binary Influence Model

[ 1] [ ]r k D s k

[ 1] [ ]r k D s k [ 1] ( [ 1])s k Bernoulli r k

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



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.



Example: Pedestrian Crossing

8 10 9

11 12 13 14

5 7

3/4

6

Note: We used a special form of the Binary Influence Model, the “Evil Rain Model” for this particular example.




0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6Average number of congested sites vs. time

Time

Ave

rage

num

ber

of c

onge

sted

site

s

Average number of congested pedetrian sitesAverage number of congested car sites




0 10 20 30 40 50 60 70 80 90 1000

1

2

3

4

5

6Average number of congested sites vs. time

Time

Ave

rage

num

ber

of c

onge

sted

site

s

Average number of congested pedetrian sitesAverage number of congested car sites



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.

Thank You

Q&A



Evil Rain Model

1 2

1 0 0

0 1 0eD

e e D

1

[ ] 0

[ ]es k

s k

D 1

0



Example 2: Intra-state Travel

C1

C4

C2

C3

3/4 5/6

7/8 9/10

11/12

13/14

Link N

umber

Time

Documents

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