The discrete-time MAP/PH/1 queue with multiple working vacations

Goswami, C. and Selvaraju, N. (2010) The discrete-time MAP/PH/1 queue with multiple working vacations. Applied Mathematical Modelling, 34(4), pp. 931-946. (doi: 10.1016/j.apm.2009.07.021)

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Abstract

We consider a discrete-time single-server queueing model where arrivals are governed by a discrete Markovian arrival process (DMAP), which captures both burstiness and correlation in the interarrival times, and the service times and the vacation duration times are assumed to have a general phase-type distributions. The vacation policy is that of a working vacation policy where the server serves the customers at a lower rate during the vacation period as compared to the rate during the normal busy period. Various performance measures of this queueing system like the stationary queue length distribution, waiting time distribution and the distribution of regular busy period are derived. Through numerical experiments, certain insights are presented based on a comparison of the considered model with an equivalent model with independent arrivals, and the effect of the parameters on the performance measures of this model are analyzed.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Goswami, Dr Cosmika
Authors: Goswami, C., and Selvaraju, N.
College/School:College of Medical Veterinary and Life Sciences > Institute of Infection Immunity and Inflammation
Journal Name:Applied Mathematical Modelling
Publisher:Elsevier
ISSN:0307-904X
ISSN (Online):1872-8480
Published Online:08 August 2009

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