The BMAP/G/1→⋅/PH/1/M tandem queue with feedback and losses

Tandem queues are good mathematical models of communication systems and networks, so their investigation is important for theory and applications. In this paper, exact analytical analysis of the tandem queue of the BMAP/G/1→⋅/PH/1/M type with customers loss in case when the intermediate buffer is full and with possible feedback is implemented. Possible correlation in the input stream is taken into account by of assuming the Batch Markovian Arrival Process (BMAP). Stability condition for the tandem is derived. Stationary distribution of the system states is derived. Loss probability is calculated. Dependence of the system performance measures on correlation in the input flow, buffer capacity, and feedback probability is numerically illustrated.