Performance Evaluation of Wireless Cellular Networks with Mixed Channel Holding Times

In most analytical models for wireless cellular networks, the channel holding times for both new and handoff calls are usually assumed to be independent and identically distributed. However, simulation study and field data show that this assumption is invalid. In this paper, we present a new general analytical model in wireless cellular networks where channel holding times for new and handoff calls are distinctly distributed with different average values. For our proposed model, we first derive the explicit matrix product-form solution of the stationary probability for number of new and handoff calls in the system. We then show that the expression of the stationary probability for total number of calls in the system possesses a scalar product-form solution if and only if the expected channel holding times for both new and handoff calls are the same. Moreover, we derive analytical results for the blocking probabilities of new and handoff calls. Finally, we compare our new theoretical results with the corresponding simulation results and two already existing approximations. Through this comparison study, we show that our analytical results are indeed the same as the simulation results and that there are certainly significant estimation errors for the existing approximations.