Providing End-to-End Statistical Delay Guarantees in cascades of Earliest Deadline First schedulers

 This paper proposes an analytical method to evaluate the delay violation probability of traffic flows with statistical Quality-of-Service (QoS) guarantees in an Earliest Deadline First (EDF) scheduler. The statistical QoS targets for each service class are expressed in terms of a delay threshold and delay violation probability. We study both cases isolated nodes and 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 MarkovModulated 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 EDF 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. Index Terms  End-to-End delay, Markov Modulated Poisson Process, statistical guarantees, network calculus, Earliest Deadline First.