Real-time queueing network theory

Abstract

This paper presents real-time queueing network theory, the extension of real-time queueing theory introduced by J.P. Lehoczky (1996) to Jackson queueing networks. This theory describes the behavior of standard Jackson queueing networks when the tasks have end-to-end deadlines. This theory is focused on describing the instantaneous multidimensional profiles of the lead-times of all the tasks in all the nodes of the network. The earliest end-to-end deadline first policy is used at all nodes in the network, although the theory permits other scheduling policies and different policies at different nodes. The real-time network problem is formulated in general, but it is analyzed under heavy traffic conditions where the traffic intensity at each node approaches 1. In this case, the multivariate queue length process converges to a Brownian network, a multivariate Brownian motion constrained to the first orthant. The conditional multivariate lead-time profiles at each of the nodes given the queue lengths converge to a deterministic profile. This characterization is borne out by simulation, and is used to design and evaluate queue control policies to reduce task lateness.