PCS networks with correlated arrival process and retrial phenomenon

In this paper, the arrival of new calls and handoff calls to a personal communications services (PCS) network is modeled by a Markov arrival process (MAP) in which we allow correlation of the interarrival times among new calls, among handoff calls, as well as between these two kinds of calls. A new call will retry again if the first attempt is blocked. The PCS network consists of homogeneous cells and each cell consists of a finite number of channels. Under the general conditions that all random variables involved have general phase type (PH) distribution, we develop the explicit expression of the infinitesimal generator matrix of the Markov chain governing the network and find its complexity. This has been a difficult matrix to obtain, judging from the works in the literature. It is very complex to develop and has not been previously obtained by other researchers. Some methods to find the stationary probability of the network are discussed. Particularly, we introduce an effective method, from which we can obtain the new call blocking probability and the handoff call failure probability. Also, the busy period of the orbit is introduced. This is an interesting measure from the viewpoint of network provider; its distribution and expectation are then obtained. The results presented in this paper can be used to provide some guidelines to performance evaluation for PCS network design.