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 perfor- mance 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.