Network Calculus Delay Bounds in Queueing Networks with Exact Solutions

摘要

The purpose of this paper is to shed light on the accuracy of probabilistic delay bounds obtained with network calculus. In particular, by comparing calculus bounds with exact results in a series of M/M/1 queues with cross traffic, we show that reasonably accurate bounds are achieved when the percentage of cross traffic is low. We use recent results in network calculus and, in addition, propose novel bounds based on Doob's maximal inequality for supermartingales. In the case of single M/M/1 and M/D/1 queues, our results improve existing bounds by Ω(log(1-ρ)~(-1)/1-ρ) when the utilization factor ρ converges to one.