An analytic model of a wireless mobile system with two different types of calls

Motivated from analytic models of wireless mobile system where there are new calls and handoff calls in each cell, we consider a general model with two different types of calls in this paper. The key difference here from the existing wireless models are that (1) the different types of calls possess different call holding time and different cell residence time and (2) one type of calls has the priority over another type of calls from the viewpoint of reservation and an available buffer. More detailed differences between the existing models and the proposed model in novelty are stated. For the proposed model, the state process governing the system is verified to be a quasi-birth-and-death process and the transition rate matrix of this process is explicitly derived. Furthermore, the closed formulae of the blocking probabilities for each types of calls are obtained, the blocking periods for each types of calls are verified to be phase type distributions and the corresponding distributions are explicitly derived.