Multi-server queueing system with a Batch Markovian Arrival Process and negative customers

A multi-server queueing system with a finite buffer, where a Batch Markovian Arrival Process (BMAP) arrives, is studied. The servicing time of a customer has a phase-type (PH) distribution. Customers are admitted to the system in accordance with the disciplines of partial admission, complete admission and complete rejection. Except standard (positive) customers, a MAP flow of negative customers arrives to the system. In a random way, a negative customer removes from the system one of the positive customers that are at the server. A stationary distribution of system state probabilities, the Laplace–Stieltjes transformation of the stationary distribution of waiting time, major characteristics of system performance are found. Numerical examples are given.