Delay analysis of a queue with general service demands and correlated service capacities

We present the study of a non-classical discrete-time queueing model in which the customers each request a variable amount of service, called their “service demand”, from a server which is able to execute a variable amount of work, called its “service capacity”, during each time slot. We assume that the numbers of arrivals in consecutive time slots and the service demands of consecutive customers form two independent and identically distributed sequences. However, we allow the service capacities in consecutive time slots to be correlated according to a discrete-batch Markovian process. We study this model analytically and obtain an expression for the probability generating function of the delay of an arbitrary customer in steady state. The results are illustrated with several numerical examples.

ISBN:9783319937366

Publication year:2018

Accessibility:Closed