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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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
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Abstract	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.
AbstractList	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.
Author	Cordeiro, James D. Kharoufeh, Jeffrey P.
Author_xml	– sequence: 1 givenname: James D. surname: Cordeiro fullname: Cordeiro, James D. organization: Department of Mathematics and Statistics , Air Force Institute of Technology – sequence: 2 givenname: Jeffrey P. surname: Kharoufeh fullname: Kharoufeh, Jeffrey P. email: jkharouf@pitt.edu organization: Department of Industrial Engineering , University of Pittsburgh
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Keywords	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
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SubjectTerms	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
Title	The Unreliable M/M/1 Retrial Queue in a Random Environment
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