A stochastic model to capture space and time dynamics in wireless communication systems

We construct a version of the recently developed Poisson-Arrival-Location Model (PALM) to study communicating mobiles on a highway, giving the distribution of calls in progress and handoffs as a function of time and space. In a PALM arrivals generated by a nonhomogeneous Poisson process move independently through a general state space according to a location stochastic process. If, as an approximation, we ignore capacity constraints, then we can use this model to describe the performance of wireless communication systems. Our basic model here is for traffic on a one-way, single-lane, semi-infinite highway, with movement specified by a deterministic location function. For the highway PALM considered here, key quantities are the call density, the handoff rate, the call-origination-rate density and the call-termination-rate density, which themselves are simply related by two fundamental conservation equations. We show that the basic highway PALM can be applied, together with independent superposition, to treat more complicated models. Our analysis provides connections between teletraffic theory and highway traffic theory.