The Unreliable M/M/1 Retrial Queue in a Random Environment

We examine an M/M/1 retrial queue with an unreliable server whose arrival, service, failure, repair, and retrial rates are all modulated by an exogenous random environment. Provided are conditions for stability, the (approximate) orbit size distribution, and mean queueing performance measures which...

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Bibliographic Details
Published in:Stochastic models Vol. 28; no. 1; pp. 29 - 48
Main Authors: Cordeiro, James D., Kharoufeh, Jeffrey P.
Format: Journal Article
Language:English
Published: Philadelphia, PA Taylor & Francis Group 01.01.2012
Taylor & Francis
Taylor & Francis Ltd
Subjects:
Distribution theory
Exact sciences and technology
LDQBD process
Mathematics
Operations research
Probability and statistics
Probability theory and stochastic processes
Retrial queue
Sciences and techniques of general use
Special processes (renewal theory, markov renewal processes, semi-markov processes, statistical mechanics type models, applications)
Stochastic analysis
Stochastic processes
Studies
Unreliable server
Stochastic model
Probability theory
Retrial queue
LDQBD process
Failure rate
Mean estimation
Steady state
Statistical method
90B22
Unreliable server
Analytical method
Distribution function
Environment
Matrix method
60K25
Queue
Numerical stability
ISSN:1532-6349, 1532-4214
Online Access:Get full text
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Summary:We examine an M/M/1 retrial queue with an unreliable server whose arrival, service, failure, repair, and retrial rates are all modulated by an exogenous random environment. Provided are conditions for stability, the (approximate) orbit size distribution, and mean queueing performance measures which are obtained via matrix-analytic methods. Additionally, we consider the problem of choosing arrival and service rates for each environment state with the objective of minimizing the steady state mean time spent in orbit by an arbitrary customer, subject to cost and revenue constraints. Two numerical examples illustrate the main results.
Bibliography:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:1532-6349
1532-4214
DOI:10.1080/15326349.2011.614478