Sharp Bounds in Stochastic Network Calculus

TL;DR

This paper improves stochastic network calculus bounds for bursty Markov-Modulated On-Off traffic by deriving martingale-based bounds that are significantly tighter and more accurate for various scheduling policies, addressing previous looseness issues.

Contribution

It introduces a general martingale-based sample-path bound for SNC that enhances per-flow performance bounds across multiple scheduling disciplines.

Findings

Martingale bounds exhibit exponential decay with the number of flows.

Numerical results show high accuracy of bounds for FIFO, SP, and EDF.

GPS scheduling bounds are improved but still somewhat loose, indicating room for further refinement.

Abstract

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 \textit{per-flow} analysis is typically proclaimed as a highlight of SNC, the bounds can unfortunately indeed 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, EDF, and GPS scheduling. The obtained (Martingale) bounds gain an exponential decay factor of ${\mathcal{O}}(e^{-\alpha n})$ in the number of flows $n$. Moreover, numerical comparisons against simulations show that the Martingale bounds are remarkably accurate for FIFO, SP, and EDF scheduling; for GPS scheduling, although the Martingale bounds substantially improve the Standard bounds, they are numerically loose, demanding for improvements in the core SNC analysis of GPS.