Statistical Analysis of Delay Bound Violations at an Earliest Deadline First (EDF) Scheduler

In this paper, we develop an analytical framework for providing statistical delay guarantees in an Earliest Deadline First (EDF) scheduler which multiplexes traf-c from multiple markovian sources with heterogeneous delay requirements. Our framework permits the computation of steady-state delay bound violation probabilities (i.e., the fraction of traac that does not meet its delay bounds) at the EDF scheduler, and can be therefore used to characterize the schedulable region of EDF in a statistical setting. Our method employs results from the theory of large deviations and the theory of eeective bandwidths, and demonstrates that eeective bandwidths at both innnite and nite time scales have to be considered in the analysis of delays at the EDF scheduler (this is in contrast to the analysis of packet losses at a multiplexor, where only the eeective bandwidth at innnite time scales is relevant). Our framework is of general use, and suitable to handle a broad range of markovian sources. As illustrating examples, we apply our method to two simple models, poisson and markovian on-oo uid traac, and compare the analytical results with simulations, showing that the analysis is quite accurate. The framework presented in this paper can serve as the basis for the design of a Call Admission Control (CAC) mechanism which provides statistical guarantees on traac transfer delays. Such a statistical CAC approach can ooer dramatic advantages in network utilization over CAC frameworks based on deterministic delay bounds.