Probabilistic Version Of Random-Walk

There are two types of mobility models. One is Indoor Mobility Model and the other is Outdoor Mobility Model. It is further classified into various types-

Indoor Mobility Model
• Random-Walk
• Random Way-Point
• Random Direction

Outdoor Mobility Model
• Gauss Markov
• Probabilistic version of Random-Walk

In this topic, we will learn about the Outdoor Mobility Model’s Probabilistic version of Random-Walk. Random-Walk was basically the model of Indoor Mobility Model but in this one probabilistic matrix is added making it the part of the Outdoor Mobility Model’s Probabilistic version of Random-Walk. It utilizes a probability matrix to determine the position of a particular mobile node in next step.

This version has three states-
• State 0: current
• State 1: previous
• State 2: next

Probabilistic version of Random-Walk

Following the diagram, suppose (0) is a node at X’=X. Now, if we go to previous state that is at (1) at X’=X-1 or to next state i.e, at (2) at X’=X+1, they has probability to go to next or previous state. 0 here defines the current location. We can go to next state with 0.5 probability or go back to previous state with 0.5 probability. Same work for Y node too.

Now, working on its matrix by following the probabilistic matrix given above.

• Looking at (0, 0), there is no probability so it value remains 0.
• For (0, 1), it is 0.5
• For (0, 2), it is 0.5
• For (1, 0), it is 0.3
• For (1, 1), it is 0.7 (It is a loop)
• For (1, 2), it is 0 (As it cannot go from previous to next state)
• For (2, 0), it is 0.3
• For (2, 1), it is 0 (As it cannot go from next to previous state)
• For (2, 2), it is  0.7 (It is a loop)

The new matrix is:

What it means ?
Whether it is node X or node Y, the same probability matrix works on both. At a time, they can only work on three states i.e, previous, current or next.