A Discrete-Time Retrial Queueing System With Service Upgrade

This paper considers a discrete-time retrial queueing system with displacements. The arriving customers can opt to go directly to the server obtaining immediately its service or to join the orbit. In the first case, the displaced customer goes directly to the orbit. The arrivals follow a geometrical law and the service times are general. We study the Markov chain underlying the considered queueing system obtaining the generating 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.