Tandem Queues with Correlated Arrivals and Their Application to System Structure Performance Evaluation

Abstract

Tandem queues are assumed to have several stations (stages, phases) in series. In such systems after receiving service in a certain station, a customer goes to the next station to get service. Tandem queues can be used for modeling real-life networks with a linear topology as well as for the validation of general decomposition algorithms in networks. Thus, tandem queueing systems have found much interest in the literature. Most of early papers on tandem queues are devoted to exponential queuing models. Over the last two decades efforts of many investigators in tandem queues were directed to weakening the distribution assumptions on the arrival pattern and service times. In particular, the arrival process should be able to capture correlation and explosive nature of real traffic in modern communication networks. As it was noted in Sect. 6.2, the correlation and the variability of inter-arrival times in input flows are taken into account via the consideration of a BMAP. In this section, we consider a number of two-station and multi-station tandem queues with BMAP, general or PH distribution of service times and different configuration of stations.