Resumen
A single-server retrial queueing model with the batch Markovian arrival process and phase-type service time distribution is analyzed. The system has R operation modes which are switched by a Markovian random environment. The multi-dimensional Markov chain describing the behavior of the system is investigated by means of continuous time asymptotically quasi-toeplitz Markov chains. It allows to obtain a constructive form ergodicity condition and elaborate stable algorithms for calculating the stationary distribution. Main performance measures are computed. Numerical illustrations are presented.