A Discrete-Time retrial queueing system with service upgrade

Abstract

We study the Markov chain underlying the considered queueing system obtaining the gen- erating function of the number of customers in the orbit and in the system as well as the stationary distribution of the time that a customer spends in the server. We derive the stochastic decomposition law and as an application we give bounds for the proximity between the steady-state distributions for our queueing system and its corresponding standard system.