Analysis of the finite source MAP/PH/N retrial G-queue operating in a random environment

Finite source retrial G-queues are good mathematical models of communication systems and networks, so their investigation is important for theory and applications. In this paper, we analyze the MAP/PH/N retrial queue with finite number of sources and MAP arrivals of negative customers operating in a finite state Markovian random environment. The arrival of a negative customer with equal probability goes to any busy server to remove the customer being in service. The multi-dimensional Markov chain describing the behavior of the system is investigated. The algorithms for calculating the stationary state probabilities are elaborated. Main performance measures are obtained. Illustrative numerical examples are presented.