End-to-End Delay Approximation in Cascades of Generalized Processor Sharing Schedulers

This paper proposes an analytical method to evaluate the delay violation probability of traffic flows with statistical quality-of-service (QoS) guarantees in a generalized processor sharing scheduler. The statistical QoS targets, for each service class, are expressed in terms of a delay threshold and delay violation probability. We study both the single node and the end- to-end paths comprising multiple schedulers. Moreover, we assume that traffic admits a linear variance envelope, therefore, we account for leaky-bucket-regulated traffic, for general Markov-modulated Poisson process sources and Markov-modulated fluid process sources and, more in general, to the wide class of sources for which the variance of the cumulative generated traffic can be upper bounded by a linear function of time. Under these assumptions, we are able to derive an approximation on delay distributions for each class of the GPS scheduler. Moreover, by exploiting a novel framework for the calculation of statistical end-to-end delay bounds (the bounded variance network calculus) we iterate our formulas, derived for the isolated node, to multi-node paths and, in turn, we provide analytical forms for the end-to-end delay. Numerical investigation shows that our approximations are very close to the simulated values.