AN M/M/1 QUEUE IN RANDOM ENVIRONMENT WITH DISASTERS

Noam Paz () and Uri Yechiali ()
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Noam Paz: Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel
Uri Yechiali: Department of Statistics and Operations Research, School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel;

Asia-Pacific Journal of Operational Research (APJOR), 2014, vol. 31, issue 03, 1-12

Abstract: We study a M/M/1 queue in a multi-phase random environment, where the system occasionally suffers a disastrous failure, causing all present jobs to be lost. The system then moves to a repair phase. As soon as the system is repaired, it moves to phase i with probability qi ≥ 0. We use two methods of analysis to study the probabilistic behavior of the system in steady state: (i) via probability generating functions, and (ii) via matrix geometric approach. Due to the special structure of the Markov process describing the disaster model, both methods lead to explicit results, which are related to each other. We derive various performance measures such as mean queue sizes, mean waiting times, and fraction of lost customers. Two special cases are further discussed.

Keywords: M/M/1 queue; random environment; disasters; lost customers; generating functions; matrix geometric (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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DOI: 10.1142/S021759591450016X

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