Abstract
In early queueing models the characteristics of the arrival and service time distributions are constant over time. This chapter shows how a Markov Modulated Queueing System can be used to model queueing systems with the latter dependence structure. It describes how the Batch Markovian Arrival Process (BMAP) can be used to model queueing systems with correlation between the interarrival and service time of a customer. The chapter illustrates the modelling technique with a number of examples. It examines the potential of the modelling technique to obtain performance measures and insights for queueing systems with dependence between interarrival and service times. The chapter considers queueing models in which various dependence structures occur simultaneously. It focuses on modelling correlation between interarrival and service times of customers with the use of the BMAP. The chapter utilizes the BMAP for modelling a number of variants of the collector model.
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