Retrial tandem queue with BMAP-input and semi-Markovian service process

We consider a tandem queueing system consisting of two stations. The input flow at the single-server first station is described by a BMAP (batch Markovian arrival process). If a customer from this flow meets the busy server, it goes to the orbit of infinite size and tries its luck later on in exponentially distributed random time. The service time distribution at the first station is assumed to be semi-Markovian. After service at the first station a customer proceeds to the second station which is described by a multi-server queue without a buffer. The service time by the server of the second station is exponentially distributed. We derive the condition for the stable operation of the system and determine the stationary distribution of the system states. Some key performance measures are calculated and illustrative numerical results are presented. © 2017, Springer International Publishing AG.