Journal
STOCHASTIC MODELS
Volume 28, Issue 1, Pages 29-48Publisher
TAYLOR & FRANCIS INC
DOI: 10.1080/15326349.2011.614478
Keywords
LDQBD process; Retrial queue; Unreliable server
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Funding
- U.S. Air Force Office of Scientific Research [FA9550-08-1-0004]
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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.
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