On a bivariate Markov process arising in the theory of single-server retrial queues

Abstract

The paper deals with a special bivariate Markov process which can be considered as the joint process of the channel (server) state and the number of customers in the orbit of a Markovian single server retrial system with state dependent intensities. Several retrial queues, analysed in the literature, are special cases in view of the versatility of the process. Necessary and sufficient conditions for the regularity, ergodicity and recurrence of the process are given. For the stationary distribution a product formula is derived. Further the busy period, the number of served customers and other related quantities are studied.