Steady-state analysis of a multiclass MAP/PH/c queue with acyclic PH retrials

A multi-class c-server retrial queueing system in which customers arrive according to a class-dependent Markovian arrival process (MAP) is considered. Service and retrial times follow class-dependent phase-type (PH) distributions with the further assumption that PH distributions of retrial times are acyclic. A necessary and sufficient condition for ergodicity is obtained from criteria based on drifts. The infinite state space of the model is truncated with an appropriately chosen Lyapunov function. The truncated model is described as a multi-dimensional Markov chain and a Kronecker representation of its generator matrix is numerically analyzed.