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Algorithmic analysis of the BMAP/D/k system in discrete time

Part of: Operations research and management science Computer system organization Special processes

Published online by Cambridge University Press:  01 July 2016

Attahiru Sule Alfa
Attahiru Sule Alfa*
Affiliation:
University of Manitoba
*
∗ Postal address: Department of Electrical and Computer Engineering, 15 Gillson Street, Winnipeg, Manitoba R3T 5V6, Canada. Email address: alfa@ee.umanitoba.ca
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Abstract

We exploit the structural properties of the BMAP/D/k system to carry out its algorithmic analysis. Specifically, we use these properties to develop algorithms for studying the distributions of waiting times in discrete time and the busy period. One of the structural properties used results from considering the system as having customers assigned in a cyclic order—which does not change the waiting-time distribution—and then studying only one arbitrary server. The busy period is defined as the busy period of an arbitrary single server based on this cyclic assignment of customers to servers. Finally, we study the marginal distribution of the joint queue length and phase of customer arrival. The structural property used for studying the queue length is based on the observation of the system every interval that is the length of one customer service time.

Keywords

Discrete timedeterministic servicemultiserverwaiting timebusy periodmarginal queue lengthbatch Markovian arrival processmatrix-analytic method

MSC classification

Primary: 60K25: Queueing theory
Secondary: 68M20: Performance evaluation; queueing; scheduling 90B22: Queues and service
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 35 , Issue 4 , December 2003 , pp. 1131 - 1152
Copyright
Copyright © Applied Probability Trust 2003 

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