Multi-dimensional asymptotically quasi-Toeplitz Markov chains and their application in queueing theory
Multi-dimensional asymptotically quasi-Toeplitz Markov chains with discrete and continuous time are introduced. Ergodicity and non-ergodicity conditions are proven. Numerically stable algorithm to calculate the stationary distribution is presented. An application of such chains in retrial queueing models with Batch Markovian Arrival Process is briefly illustrated.
asymptotically quasi-toeplitz markov chain ergodicity stable algorithm retrial queue multi-dimensional markov chain censored markov chain