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

Noam Paz · Uri Yechiali

43 citations0/0 files storedAsia Pacific Journal of Operational Research

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Advanced Queuing Theory Analysis Reliability and Maintenance Optimization Probability and Risk Models

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.

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References

1971Queuing Problems with Heterogeneous Arrivals and Service 2007Queues with system disasters and impatient customers when system is down 1990A Queue with Service Interruptions in an Alternating Random Environment 1992A Storage Model with a Two-State Random Environment 1973A Queuing-Type Birth-and-Death Process Defined on a Continuous-Time Markov Chain 2010Transient analysis of a queue with system disasters and customer impatience

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