a two-dimensional random walk model using simulation-based approach. The two-dimensional region in R^2 is a circular region of radius 100 units (1 unit can be 1 cm or 1 meter, or 1 km). We would refer our two dimensional circular space as a disc, d(0,R). A node or nodes within a circular

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region d(0,R) at time t, undertakes a random walk whose next position at the xed discrete time t+1 unit time' is modeled as follows: (a) Step size is a discrete random variable. You can assume that step size is between {0,0.5,1}. (b) Orientation is a discrete random variable between [02]. For example - a node at the center of a 100-unit radius circle will take a random step of size r between {0,0.5,1} and a direction with angle . To begin with, you may nd it easier to assume that all step sizes and angles are equally likely.

Over the next course of time slots the node will traverse a random path based on the random walk model described above. Of course, at some point in time, it is quite likely that after many units of time, the node might try to leave the 100-unit circular region. Its re-entry model, to ensure that the node does not escape the test region, is left for the students to be worked-out. As an example, once the node hits the boundary you can ensure that its bounces o the circumference back into the region. Whatever model of node re-entry you choose, it should be based on logic, explanation and some literature review. You would be asked for its explanation and justication.