Waiting characteristics of queueing system Geo/Geo/1/∞ with negative claims and a bunker for superseded claims in discrete time

Abstract

A discrete time single-line queueing system with independent geometric streams of regular and negative claims, infinite buffer, and geometric service is considered. A negative claim pushes a regular claim out of the buffer queue and moves it to a bunker of infinite capacity. If the buffer is empty, a negative claim leaves the system without any effect. After servicing a claim, the system receives the next claim from the buffer, if it is not empty, or from the bunker. We obtain relations for stationary waiting and sojourn time distributions of the regular claim.