Analysis of Pico cells with Randomly Walking Users

In this paper, we develop a framework to analyze pico cells with randomly walking users. We model the user movements by a random walk with exponential wandering times. We partition each pico cell into disjoint regions based on the transmission rates allocated and model each rate region as an equivalent step in the random walk model. We further use queuing theoretic tools to obtain explicit expressions for the expected service time, call busy and drop probabilities. We obtain approximate closed form expressions for optimal cell size for the case of non-elastic traffic (for some asymptotic cases) and show that these values closely match the cell sizes obtained via numerical simulations. We also obtain analysis of users moving at high speeds and in a fixed direction (ex., those traveling in a car) using the theory developed in this paper. We study the influence of system parameters like, the path loss factor, speed of user movement, power budget etc, on these optimizers. We show that the optimal cell size increases with the increase in the speed of the users, decreases with increase in path loss factor, increases with increase in power budget. Index Terms Pico cells; Cell dimensioning; Random walk;