Performance Analysis of Mobile Cellular Networks with MMPP Call Arrival Patterns

Abstract

In this paper, the performance of mobile multi-cellular networks with Markov modulated Poisson process (MMPP) call arrivals is mathematically analyzed and numerically evaluated. In particular, new call requests in each cell are considered to follow independent two-state MMPP (MMPP-2). Three different analysis approaches are evaluated in this paper: based on bi-dimensional, tri-dimensional, and four-dimensional birth and death processes. In the bi-dimensional (tri-dimensional) {four-dimensional} queuing analysis, handoff call requests arriving to the reference cell are approximated by a Poisson process (MMPP-7) {MMPP-43}. Contrary to previously published related works, the parameters of the different MMPP used to approximately modelling handoff calls are iteratively calculated as function of the different system characteristics. In the four-dimensional queuing analysis, we propose to model the incoming handoff call requests to each cell with similar characteristics to the resulting process of the aggregation of the new and handoff call requests processes in the neighboring cells. In particular, the state transition rates of the MMPP are considered to be proportional to the aggregated rate of the call requests processes in the neighboring cells. The accuracy of the numerical results obtained with the proposed analytical approach is compared against those obtained by both a teletraffic analysis considering that handoff call requests follow a Poisson process and a discrete-event computer simulator. The effect of users' mobility factor and burstiness of new call arrivals on system performance are evaluated.