Analysis of a Retrial Queue with Limited Processor Sharing Operating in the Random Environment

Queueing system with limited processor sharing, which operates in the Markovian random environment, is considered. Parameters of the system (pattern of the arrival rate, capacity of the server, i.e., the number of customers than can share the server simultaneously, the service intensity, the impatience rate, etc.) depend on the state of the random environment. Customers arriving when the server capacity is exhausted join orbit and retry for service later. The stationary distribution of the system states (including the number of customers in orbit and in service) is computed and expressions for the key performance measures of the system are derived. Numerical example illustrates possibility of optimal adjustment of the server capacity to the state of the random environment.