Scheduling jobs with multiple non-uniform tasks

Abstract

This paper considers the problem of maximizing the throughput of jobs wherein each job consists of multiple tasks. Consider a system offering a uniform capacity of a resource (say unit bandwidth). We are given a set of jobs, each consisting of a sequence of at most r tasks. Each task is associated with a window (specified by a release time and a deadline) within which it can be scheduled; each task also has a processing time and a bandwidth requirement. Each job has a profit associated with it. A feasible solution must choose a subset of jobs and schedule all the tasks for these jobs such that at any point of time, the total bandwidth requirement does not exceed the capacity of the resource; furthermore, the schedule must obey the precedence constraints (tasks of a job must be scheduled in order of the input sequence). The goal is to compute the feasible solution having maximum profit. Prior work has studied the problem without the notion of windows; furthermore, the algorithms presented therein require that the bandwidths of all the tasks of a job are uniform. Under these two restrictions, O(r)-approximation algorithms are known. Our main result presents an O(r)-approximation algorithm for the general case wherein tasks can have windows and bandwidths of tasks within the same job may be non-uniform. © 2013 Springer-Verlag.