THE UNRELIABLE M/M/1 RETRIAL QUEUE IN A RANDOM ENVIRONMENT

摘要

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, toe consider the problem of choosing arrival and service rales 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.