Delay Bounds for Multiclass FIFO

TL;DR

This paper derives delay bounds for multiclass FIFO scheduling in deterministic and stochastic settings, filling a gap in existing research and providing explicit bounds with practical examples and simulations.

Contribution

It introduces the first comprehensive delay bounds for multiclass FIFO in deterministic and stochastic models, extending known results from single-class FIFO.

Findings

Delay bounds for multiclass D/D/1, GI/GI/1, and G/G/1 systems.

Explicit bounds demonstrated through examples and compared with simulations.

Provides theoretical guarantees for delay performance in multiclass FIFO scheduling.

Abstract

FIFO is perhaps the simplest scheduling discipline. For single-class FIFO, its delay guarantee performance has been extensively studied: The well-known results include a stochastic delay bound for $GI/GI/1$ by Kingman and a deterministic delay bound for $D/D/1$ by Cruz. However, for multiclass FIFO, few such results are available. To fill the gap, we prove delay bounds for multiclass FIFO in this work, considering both deterministic and stochastic cases. Specifically, delay bounds are presented for multiclass D/D/1, GI/GI/1 and G/G/1. In addition, examples are provided for several basic settings to demonstrate the obtained bounds in more explicit forms, which are also compared with simulation results.