Channel holding time in mobile cellular networks with generalized Coxian distributed cell dwell time

In this paper, probability distributions of new and handoff call channel holding times in mobile cellular networks are derived under the assumption that cell dwell time has generalized Coxian distribution. It is shown that when cell dwell time has a generalized Coxian distribution, the resulting residual cell dwell time has generalized Coxian distribution as well. Furthermore, both new and handoff call channel holding times have generalized Coxian distributions of the same order (number of stages and number of phases within the stages). Additionally, it is demonstrated that the phases on each stage of the hyper-generalized Coxian distributed channel holding times have the same mean permanence time. Therefore, the global channel holding time has also generalized Coxian distribution of the same order (number of stages and number of phases within the stages) of those of the new and handoff call channel holding times. This result permits to simplify teletraffic analysis of cellular networks as a single state variable can be used to keep track of all the types of calls (new and handed off) in a phase (of any stage) with both the same mean permanence time and order within the stages. Mathematical expressions to calculate the parameters of the resulting distributions in terms of the parameters of the distributions of both cell dwell time and unencumbered service time are given. The results obtained in this work are relevant because they allow one to develop analytically and computationally tractable general teletraffic models for performance evaluation of mobile wireless networks under more realistic assumptions.