Coxian distribution modeling for the generalized and unified teletraffic analysis of mobile cellular networks

In this paper, the Coxian distribution model to characterize users' mobility (through cell dwell time) is proposed and its application for the teletraffic analysis of mobile cellular networks is presented. To the best authors' knowledge, Coxian distribution has not been previously considered in the literature to characterize users' mobility in cellular networks. The Coxian distribution includes as particular cases several relevant previously proposed models in the literature (i.e., hyper-exponential, Erlang, hypo-exponential, and hyper-Erlang). We demonstrate that, when the cell dwell time has a Coxian distribution, the residual cell dwell time can be represented by a Coxian model. More important, it is shown that the Coxian distribution assumption for the cell dwell time naturally leads to a joint representation of the cell dwell time and residual cell dwell time distributions by a Coxian distribution of the, so called, global cell dwell time. Consequently, our teletraffic model is made computationally tractable by keeping track in a single state variable all the calls (new and handed off) in a phase (of any stage) with both the same mean permanence time and order within the stages. Thus, the analytical model proposed in this paper provides a simple, general, unified, and versatile framework for the teletraffic analysis of mobile cellular networks.