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The Influence Mobility Model: A Novel Hierarchical Mobility Modeling Framework

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.

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The Influence Mobility Model: A Novel Hierarchical Mobility Modeling Framework

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

  2. 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.

  3. 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”.

  4. Feature Wishlist for the “Ideal” Mobility Model • Task based movement • Path selection • Node classification • Class transition • Dependence/ Influence • Scale invariance   ()    

  5. 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.

  6. 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.

  7. Graph-based Representation of Simulation Plane • G: Connectivity Matrix • Consists of submatrices Gij • Basic elements of G are 1s and 0s

  8. 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.

  9. 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.

  10. 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.

  11. Markov Chains vs. Influence Model 0.2 0.3 0.1 A B 0.7 0.8 0.5 0.1 0.2 C 0.1 0.2 0.3 0.1 A B 0.6 0.7 0.5 0.1 0.4 C 0.1

  12. 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

  13. 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.

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

  15. Example: Pedestrian Crossing

  16. Example: Pedestrian Crossing

  17. 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.

  18. Thank You Q&A

  19. Evil Rain Model

  20. Example 2: Intra-state Travel Link Number Time

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