A BMAP|PH|1 queue with feedback operating in a random environment

Feedback queues play an important role in real-life service systems, where customers may require repeated services. In this paper, we consider a feedback queue with batch Markovian arrivals and phase type services. We further assume that both the arrival process and service times are influenced by an external finite state Markovian environment. The stationary state distributions of the queue and the sojourn time are calculated and numerical examples are presented.