Title: A single-server Poisson queueing system with delayed-service

Authors: Aliakbar Montazer Haghighi, Dimitar P. Mishev, Stefanka S. Chukova

Addresses: Department of Mathematics, Prairie View A&M University, PO Box 519 – MS2225, Prairie View, TX 77446-0519, USA. ' Department of Mathematics, Prairie View A&M University, PO Box 519 – MS2225, Prairie View, TX 77446-0519, USA. ' School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, Wellington, New Zealand

Abstract: In this paper, we investigate busy period and queue length (steady-state and transient) of a single-server Poisson queue with delayed-service, to set the tone for more complicated models that will appear later. We will analyse this model by considering M/G/1 as well as the use of differential difference equations approximating a non-Markovian system. We obtain the distribution of the length of a busy period, steady-state mean and distribution of the queue length, Laplace transform of the probability of the system being empty and Laplace transform of the generating function of the distribution of the transient queue length.

Keywords: delayed service; non-Markovian; Poisson queues; queueing systems; single server; busy period; queue length.

DOI: 10.1504/IJOR.2008.018999

International Journal of Operational Research, 2008 Vol.3 No.4, pp.363 - 383

Published online: 27 Jun 2008 *

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