Online Scheduling of Bounded Length Jobs to Maximize Throughput

TL;DR

This paper analyzes the online scheduling problem for jobs with deadlines and weights, providing bounds on the competitive ratio for jobs with fixed or bounded processing times, relevant to network packet transmission.

Contribution

It establishes new bounds on the competitive ratio for online scheduling with preemptions, specifically for jobs with fixed or bounded processing times.

Findings

Competitive ratio between 2.598 and 5 for fixed processing time k.

Competitive ratio is Theta(k/log k) when processing times are at most k.

Results improve understanding of online scheduling efficiency bounds.

Abstract

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).