Lectures on
Probability and Stochastic Processes IX

Indian Statistical Institute, Kolkata
December 12 - 16, 2014

Renewal Reward Type Approach to Brownian Motion in Poisson Voronoi Cells

Debayan Das

Here a Brownian Motion with restarts, occurring in one dimensional Poisson-Voronoi cells is considered. The process restarts from a given distribution whenever it crosses one such cell. The motivation is to model and analyze interactions between movement of one typical mobile user in one dimension and the coverage areas of the base stations. The base stations are located according to a Poisson Process and Voronoi cells are formed accordingly. The main goal is to obtain the limiting behavior of some performance measures.