The BMAP/SM/1 retrial queue with controllable operation modes

We deal with a single-server retrial queueing system having two modes of operation. Under the fixed mode, the system operates as a normal system with a batch Markovian arrival process (BMAP), semi-Markovian (SM) service process and a constant total retrial rate. Different modes are distinguished by characteristics of the input, service and retrial rate. The mode of operation can be switched at the service completion epochs depending on the queue-length. The strategy of control belongs to the class of hysteretic strategies. We calculate a stationary distribution of numbers of calls in the orbit at service completion epochs. We also discuss the problem of optimizing the strategy of control.