Retrial queue of BMAP/PH/N type with customers balking, impatience and non-persistence

Abstract

We consider a multi-server retrial queueing system with the Batch Markovian Arrival Process and phase type service time distribution. Such a quite general queueing system suits for modeling, e.g., modern wireless communication networks. We assume that arriving customers, which do not succeed to start the service immediately upon arrival due to the lack of available servers, may leave the system forever (balk) or join the orbit for further retrials. Customers in the orbit are impatient (they may leave the system forever after exponentially distributed duration of the stay in the orbit) and non-persistent (they may leave the system forever after any unsuccessful attempt to reach the service). Approach by V. Ramaswami and D. Lucantoni for description of several independent Markov processes in parallel that allows to compute the stationary distribution of the system for large number of servers is used along with the results for multi-dimensional asymptotically quasi-Toeplitz Markov chains for computation of steady state distribution of the system states and some its performance measures.