Sharp per-flow delay bounds for bursty arrivals: The case of FIFO, SP, and EDF scheduling

The practicality of the stochastic network calculus (SNC) is often questioned on grounds of potential looseness of its performance bounds. In this paper, it is uncovered that for bursty arrival processes (specifically Markov-Modulated On-Off (MMOO)), whose amenability to per-flow analysis is typically proclaimed as a highlight of SNC, the bounds can unfortunately be very loose (e.g., by several orders of magnitude off). In response to this uncovered weakness of SNC, the (Standard) per-flow bounds are herein improved by deriving a general sample-path bound, using martingale based techniques, which accommodates FIFO, SP, and EDF scheduling. The obtained (Martingale) bounds capture an extra exponential decay factor of O (e^-αn) in the number of flows n. Moreover, numerical comparisons against simulations show that the Martingale bounds are not only remarkably accurate, but they also improve the Standard SNC bounds by factors as large as 100 or even 1000.