Retrial queueing models in discrete time: a short survey of some late arrival models

Abstract

This paper presents an overview of one-server queueing models with retrials in discrete-time. In all these models the number of primary customers arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each customer requires from the server a generally distributed number of slots for his service, and the service times of the different customers are independent. Only models with delayed access are considered, and the so-called late arrival setup is chosen. For all the models the steady-state behavior is studied through the generating function of the number of customers in the orbit. From the generating function several performance measures are deduced, like the average orbit size and the mean busy period.