Minimizing Maximum Response Time and Delay Factor in Broadcast Scheduling

TL;DR

This paper develops and analyzes online algorithms for broadcast scheduling, focusing on minimizing maximum response time and delay factor, providing competitive guarantees and extending results to weighted metrics.

Contribution

It proves FIFO is 2-competitive for varied page sizes and introduces an improved online algorithm for delay-factor minimization with better speed-competitiveness tradeoffs.

Findings

FIFO is 2-competitive for different-sized pages

New algorithm achieves O(1/ε^2)-competitiveness with near speed 1+ε or 2+ε

Greedy LWF-like algorithm is not constant-competitive for delay factor

Abstract

We consider online algorithms for pull-based broadcast scheduling. In this setting there are n pages of information at a server and requests for pages arrive online. When the server serves (broadcasts) a page p, all outstanding requests for that page are satisfied. We study two related metrics, namely maximum response time (waiting time) and maximum delay-factor and their weighted versions. We obtain the following results in the worst-case online competitive model. - We show that FIFO (first-in first-out) is 2-competitive even when the page sizes are different. Previously this was known only for unit-sized pages [10] via a delicate argument. Our proof differs from [10] and is perhaps more intuitive. - We give an online algorithm for maximum delay-factor that is O(1/eps^2)-competitive with (1+\eps)-speed for unit-sized pages and with (2+\eps)-speed for different sized pages. This improves on the algorithm in [12] which required (2+\eps)-speed and (4+\eps)-speed respectively. In addition we show that the algorithm and analysis can be extended to obtain the same results for maximum weighted response time and delay factor. - We show that a natural greedy algorithm modeled after LWF (Longest-Wait-First) is not O(1)-competitive for maximum delay factor with any constant speed even in the setting of standard scheduling with unit-sized jobs. This complements our upper bound and demonstrates the importance of the tradeoff made in our algorithm.