A conservation law for a wide class of queueing disciplines

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 ρp as the product of the average arrival rate and the average service time for customers from the pth priority group (where the priority system is any queue discipline included in the defined class) and Wp as their average waiting time (in queue), the Conservation Law states that Σ ρp Wp is invariant over the set of queue disciplines in the class.