Stationary distribution of the two-phase queue with intermediate buffer

Abstract

We consider a tandem queueing system consisting of two phases and having an intermediate buffer. The first phase is represented by the BMAP/G/X queue. After service at the first phase a customer proceeds to the second phase which is described by a multi-server queue with a finite buffer. A customer leaves the system forever or waits service at the second phase in the buffer if it completes the service at the first phase and meets the buffer being full. The waiting period is accompanied by blocking the first phase server operation. The stationary distribution of the system states at an arbitrary time is derived. The dependence of the system performance measures on the correlation in the input flow and buffer capacity is numerically illustrated.