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Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes

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Artalejo, Jesús R. and Chakravarthy, S. R. (2006) Algorithmic analysis of the maximum level length in general-block two-dimensional Markov processes. Mathematical Problems In Engineering, 2006 (2). pp. 1-15. ISSN 1024-123X

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Official URL: http://www.hindawi.com/journals/mpe/2006/053570/abs/


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Abstract

Two-dimensional continuous-time Markov chains (CTMCs) are useful tools for studying stochastic models such as queueing, inventory, and production systems. Of particular interest in this paper is the distribution of the maximal level visited in a busy period because this descriptor provides an excellent measure of the system congestion. We present an algorithmic analysis for the computation of its distribution which is valid for Markov chains with general-block structure. For a multiserver batch arrival queue with retrials and negative arrivals, we exploit the underlying internal block structure and present numerical examples that reveal some interesting facts of the system.


Item Type:Article
Additional Information:

J. R. Artalejo thanks the support received from the Research Project MTM 2005-01248. The research was conducted while S. R. Chakravarthy was visiting the Complutense University of Madrid, Madrid, Spain, and would like to thank the hospitality of the Department of Statistics and Operations Research.

Uncontrolled Keywords:Networks; Queues
Subjects:Sciences > Mathematics > Operations research
ID Code:15564
Deposited On:11 Jun 2012 07:42
Last Modified:03 Aug 2018 11:03

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