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.