Performance of the (BMAP1, BMAP2)/(PH1, PH2)/N retrial queueing system with finite buffer

This paper consider the (BMAP1, BMAP2)/(PH1, PH2)/N retrial queue with finite-position buffer. The behavior of the system is described in terms of continuous time multi-dimensional Markov chain. Arriving type I calls find all servers busy and join the buffer, if the positions of the buffer are insufficient, they can go to orbit. Arriving type II calls find all servers busy and join the orbit directly. Each server can provide two types heterogeneous services with Phase-type (PH) time distribution to every arriving call (including types I and II calls), arriving calls have an option to choose either type of services. The model is quite general enough to cover most of the systems in communication networks. We derive the ergodicity condition, the stationary distribution and the main performance characteristics of the system. The effects of various parameters on the system performance measures are illustrated numerically.