A decomposable random walk model for mobility in wireless communications

In this paper we develop models to represent the time until boundary crossi ng and associated statistics in cellular wireless networks. We propose mode ling the terminal movements within a cell by a discrete two-dimensional ran dom walk process. We note that in such an environment mobile units tend to move in roughly a straight line, with occasional backtracking, for a signif icant 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 movin g in fluctuating directions until reaching this exit point. Subsequently, w e 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. T he model is rather general and has the potential to be used for highly irre gular cell shapes when boundary crossing is not distance-based but determin ed by propagation attenuation-based criterion.