Analysis of Retrial Queueing System with Heterogeneous Servers and Phase Type Distribution of Service Times

A multi-server retrial queueing system is analysed. Customer arrival to the system is described by a Markovian arrival process. Servers of the system are heterogeneous. The service times have a phase-type distribution with different irreducible representations. The dynamics of the system states is described by a multidimensional Markov chain. The generator of this Markov chain is derived. Ergodicity condition is presented. The expressions for computation of some performance characteristics of the system are derived.