Approximations of general discrete time queues by discrete time queues with arrivals modulated by finite chains

Sharma, Vinod (1997) Approximations of general discrete time queues by discrete time queues with arrivals modulated by finite chains. In: Advances in Applied Probability, 29 (4). pp. 1039-1059.

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Abstract

Recently, Asmussen and Koole showed that any discrete or continuous time marked point process can be approximated by a sequence of arrival streams modulated by finite state continuous time Markov chains. If the original process is customer (time) stationary then so are the approximating processes. Also, the moments in the stationary case converge. For discrete marked point processes we construct a sequence of discrete processes modulated by discrete time finite state Markov chains. All the above features of approximating sequences of Asmussen and Koole continue to hold. For discrete arrival sequences (to a queue) which are modulated by a countable state Markov chain we form a different sequence of approximating arrival streams by which, unlike in the Asmussen and Koole case, even the stationary moments of waiting times can be approximated. Explicit constructions for the output process of a queue and the total input process of a discrete time Jackson network with these characteristics are obtained.

Item Type:	Journal Article
Publication:	Advances in Applied Probability
Publisher:	Applied Probability Trust
Additional Information:	Copyright of this article belongs to Applied Probability Trust.
Keywords:	Marked Point Processes;Discrete Time Queues;Approximations of Point Processes;Convergence of Stationary Moments;
Department/Centre:	Division of Electrical Sciences > Electrical Engineering
Date Deposited:	17 May 2007
Last Modified:	19 Sep 2010 04:35
URI:	http://eprints.iisc.ac.in/id/eprint/9778

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