On a single-server queue with fixed accumulation level, state dependent service, and semi-Markov modulated input flow

The authors study the queueing process in a single-server queueing system with state dependent service and with the input modulated by a semi-Markov process embedded in the queueing process. It is also assumed that the server capacity is r≥1 and that any service act will not begin until the queue accumulates at least r units. In this model, therefore, idle periods also depend upon the queue length.