Online Scheduling of Bounded Length Jobs to Maximize Throughput

We consider an online scheduling problem, motivated by the issues present at the joints of networks using ATM and TCP/IP. Namely, IP packets have to broken down to small ATM cells and sent out before their deadlines, but cells corresponding to different packets can be interwoven. More formally, we consider the online scheduling problem with preemptions, where each job j is revealed at release time r_j, has processing time p_j, deadline d_j and weight w_j. A preempted job can be resumed at any time. The goal is to maximize the total weight of all jobs completed on time. Our main result are as follows: we prove that if all jobs have processing time exactly k, the deterministic competitive ratio is between 2.598 and 5, and when the processing times are at most k, the deterministic competitive ratio is Theta(k/log k)

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/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.Comment: 16 pages, 2 figure

Longest Wait First for Broadcast Scheduling

We consider online algorithms for broadcast scheduling. In the pull-based broadcast model there are $n$ unit-sized pages of information at a server and requests arrive online for pages. When the server transmits a page $p$, all outstanding requests for that page are satisfied. The longest-wait-first} (LWF) algorithm is a natural algorithm that has been shown to have good empirical performance. In this paper we make two main contributions to the analysis of LWF and broadcast scheduling. \begin{itemize} \item We give an intuitive and easy to understand analysis of LWF which shows that it is O(1/\eps^2)-competitive for average flow-time with (4+\eps) speed. Using a more involved analysis, we show that LWF is O(1/\eps^3)-competitive for average flow-time with $(3.4+\epsilon)$ speed. \item We show that a natural extension of LWF is O(1)-speed O(1)-competitive for more general objective functions such as average delay-factor and $L_k$ norms of delay-factor (for fixed $k$). \end{itemize

Online Scheduling to Minimize the Maximum Delay Factor

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

The 9th Workshop on Models and Algorithms for Planning and Scheduling Problems

This volume contains extended abstracts of papers presented at the 9th Worksho