A decomposable random walk model for mobility in wireless communications

In this paper we develop models to represent the time until boundary crossing and associated statistics in cellular wireless networks. We propose modeling the terminal movements within a cell by a discrete two-dimensional random walk process. We note that in such an environment mobile units tend to move in roughly a straight line, with occasional backtracking, for a significant period of time before changing direction. We determine the time until crossing an exit point from a circular cell by choosing a random direction from the starting point to an exit point. The user would actually be moving in fluctuating directions until reaching this exit point. Subsequently, we calculate the expected time to reach the exit point as a function of the constant speed of travel and the propensity to change direction en route. The model is rather general and has the potential to be used for highly irregular cell shapes when boundary crossing is not distance-based but determined by propagation attenuation-based criterion.