A discrete-time queue with service time adjustments and general retrial times

Abstract

This paper examines a discrete-time retrial queueing system where incoming customers can either choose a last-come, first-served (LCFS) discipline or enter an orbit. It accounts for the possibility of varying service times, which follow an arbitrary distribution, and the retrial times are also governed by an arbitrary distribution. The underlying Markov chain of the system has been analyzed, leading to the derivation of the generating function for the number of customers in both the orbit and the overall system, along with their expected values. The paper also establishes the stochastic decomposition law and, as an application, provides bounds for the difference between the steady-state distributions of the system in question and its standard equivalent. Recursive formulas for determining the steady-state distribution of customers in the orbit and the system are presented. The paper derives the distribution of the time a customer spends at the server and, consequently, the distribution of service times subject to possible variations. A detailed analysis of the time a customer spends in the orbit is also conducted. Finally, numerical examples are included to demonstrate how key parameters impact various system characteristics, with the main contributions of the research summarized in the conclusion.