The Steady-State Behaviour of a Stochastic Clearing System with Bounded Waiting Times

Abstract

The stochastic clearing system considered in this paper is characterized by an uncontrollable Poisson input process and bounded customers' wating times. We assume that all the quantity currently present in the system is instantaneously removed whenever there are at least M items in the queue, or ev0ery t time units since the first arrival after the last clearing, whichever occurs first. The objective is to study the steady-state behaviour of this system. Knowledge of this steady-state behaviour can be used for the evaluation of the system performance as a function of the system's parameters. We present explicit expressions for the queue length and waiting time distribution, the average queue length, and the average waiting time under steady-state conditions. This work is related to dispatching in transportation systems with stationary Poisson arrivals.