Exponential supermartingales for evaluating end-to-end backlog bounds

Abstract

A common problem arising in network performance analysis with the stochastic network calculus is the evaluation of ( min , +) convolutions. This paper presents a method to solve this problem by applying a maximal inequality to a suitable constructed supermartingale. For a network with D/M input, end-to-end backlog bounds obtained with this method improve existing results at low utilizations. For the same network, it is shown that at utilizations smaller than a certain threshold, fluid-flow models may lead to inaccurate approximations of packetized models.