Analysis of small cell networks with randomly wandering users

We develop a framework to model and study cellular networks with randomly wandering users. Our model captures user displacement resulting from random mobility patterns and arrival positions, which in turn influences the transmission rates. We model the user movements by a random walk with exponential wandering times. Each cell is composed of disjoint (transmission) rate regions and we model each rate region as an equivalent step in the random walk model. We further use spatial queuing theoretic tools to obtain explicit expressions for the expected service time (total time duration for which the user derives service from the cell), call busy and drop probabilities.We obtain approximate closed form expressions for optimal cell size (for some asymptotic speed cases and small cell radii) and validate them via numerical simulations. We show that the optimal cell size increases with the increase in the speed of the users or in the power budget and decreases with increase in path loss factor.