A Discrete-Time $$GI^{X}/Geo^{Y}/1$$ Queue with Early Arrival System

Abstract

A discrete-time batch service queue with batch renewal input and random serving capacity rule under the late arrival delayed access system, has recently appeared in the literature (Barbhuiya and Gupta in Queueing Syst 91(3):347–365, 2019b). In this paper, we consider the same model under the early arrival system, since it is more applicable in telecommunication systems where an arriving batch of packets needs to be transmitted in the same slot in which it has arrived. In doing so, we derive the steady-state queue length distributions at various epochs, and show that in limiting case the result gets converted to the continuous-time queue (Barbhuiya and Gupta in J Differ Equ Appl 25(2):1–10, 2019a). We discuss few numerical results as well.