Online Scheduling to Minimize the Maximum Delay Factor

TL;DR

This paper studies online scheduling algorithms for minimizing maximum delay factor in unicast and broadcast models, providing new algorithms with competitive ratios and proving lower bounds on achievable performance.

Contribution

It introduces new online algorithms for delay factor minimization in both unicast and broadcast models, with competitive ratios and speed augmentations, and establishes lower bounds on performance.

Findings

Algorithms achieve near-optimal competitive ratios with speed augmentation.

Lower bounds show the difficulty of delay factor scheduling even with unit-time requests.

Different algorithms are designed for arbitrary and similar-sized pages in broadcast models.

Abstract

In this paper two scheduling models are addressed. First is the standard model (unicast) where requests (or jobs) are independent. The other is the broadcast model where broadcasting a page can satisfy multiple outstanding requests for that page. We consider online scheduling of requests when they have deadlines. Unlike previous models, which mainly consider the objective of maximizing throughput while respecting deadlines, here we focus on scheduling all the given requests with the goal of minimizing the maximum {\em delay factor}.We prove strong lower bounds on the achievable competitive ratios for delay factor scheduling even with unit-time requests.For the unicast model we give algorithms that are $(1 + \eps)$-speed $O({1 \over \eps})$-competitive in both the single machine and multiple machine settings. In the broadcast model we give an algorithm for similar-sized pages that is $(2+ \eps)$-speed $O({1 \over \eps^2})$-competitive. For arbitrary page sizes we give an algorithm that is $(4+\eps)$-speed $O({1 \over \eps^2})$-competitive.