A discrete single server queue with Markovian arrivals and phase type group services

Attahiru Sule Alfa, K. Laurie Dolhun and S. Chakravarthy

International Journal of Stochastic Analysis, 1995, vol. 8, 1-26

Abstract:

We consider a single-server discrete queueing system in which arrivals occur according to a Markovian arrival process. Service is provided in groups of size no more than M customers. The service times are assumed to follow a discrete phase type distribution, whose representation may depend on the group size. Under a probabilistic service rule, which depends on the number of customers waiting in the queue, this system is studied as a Markov process. This type of queueing system is encountered in the operations of an automatic storage retrieval system. The steady-state probability vector is shown to be of (modified) matrix-geometric type. Efficient algorithmic procedures for the computation of the rate matrix, steady-state probability vector, and some important system performance measures are developed. The steady-state waiting time distribution is derived explicitly. Some numerical examples are presented.

Date: 1995
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnijsa:614742

DOI: 10.1155/S1048953395000153

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