Analysis of retrial queue with heterogeneous servers and markovian arrival process

Multi-server retrial queueing system with heterogeneous servers is analyzed. Customers arrive to the system according to the Markovian arrival process. Arriving primary customers and customers retrying from orbit occupy available server with the highest service rate, if any. Otherwise, the customers move to the orbit having an infinite capacity. Service times have exponential distribution. The total retrial rate infinitely increases when the number of customers in orbit increases. Behavior of the system is described by multi-dimensional continuous-time Markov chain which belongs to the class of asymptotically quasi-Toeplitz Markov chains. This allows to derive simple and transparent ergodicity condition and compute the stationary distribution of the chain. Presented numerical results illustrate the dynamics of some performance indicators of the system when the average arrival rate increases and the importance of account of correlation in the arrival process. © The Editor(s) (if applicable) and The Author(s), under exclusive licence to Springer Nature Singapore Pte Ltd. 2020.