A conservation law for a wide class of queueing disciplines

Abstract

Abstract A large class of queueing disciplines is defined for Poisson arrival statistics. For this class, a Conservation Law is proven which constrains the allowed variation in the average waiting times. Specifically, defining ρ p as the product of the average arrival rate and the average service time for customers from the p th priority group (where the priority system is any queue discipline included in the defined class) and W p as their average waiting time (in queue), the Conservation Law states that Σ ρ p W p is invariant over the set of queue disciplines in the class.