Delay bounds on a queueing system with consistent priorities

A discrete-time queueing system operating under a two-level, consistent priority service policy is studied. The consistency of the policy guarantees that no low priority customer will be served before a previously (or simultaneously) arrived high priority one. Unlike the well known head of the line priority policy (which is consistent), the considered policy provides for limited service to low priority customers, even in the presence of high priority ones. The proposed policy may be viewed as a consistent version of the straightforward gated/limited service priority policy. It may also be viewed as a compromise between the head of the line priority policy and the straightforward gated/limited priority service policy. The customer service time is assumed to be deterministic and equal to one time unit, which makes the queueing model applicable to a packet communication network environment; potential relevant applications are presented. Based on renewal arguments, the theory of infinite dimensional linear equations and a work-conservation law, a general methodology is developed for the derivation of arbitrarily tight bounds on the induced mean packet delay