Minimizing maximum response time and delay factor in broadcast scheduling

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/ε ²)-competitive with (1+ε)-speed for unit-sized pages and with (2+ε)-speed for different sized pages. This improves on the algorithm in [13] which required (2+ε)-speed and (4+ε)-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.