Scheduling jobs with dwindling resource requirements in clouds

We consider a job-scheduling problem arising on cloud systems and in broadcasting networks, where the goal is to optimally utilize a limited amount of a resource (e.g., cloud servers, bandwidth, or storage capacity) available along a given time interval. The resource is utilized by a set of weighted jobs. The processing of a job consists of several contiguous stages, each having a specific length and a specific resource-demand, such that the set of demands forms a decreasing sequence. Each job is associated with a release time and a deadline, defining the time interval in which it can be processed. Some notable applications for this scenario include progressive download, QuickStart and prefetching methods, hierarchical image reconstruction, and routine security and maintenance tasks. The goal is to find a feasible schedule of a maximum-weight subset of the jobs. In a feasible schedule, at any time, the total amount of resource allocated to the active jobs does not exceed the available amount of resource. Since this problem is NP-hard already for highly restricted inputs, we focus on obtaining approximation algorithms and heuristics and present a comparative study among them. Our main result, the first constant-factor approximation algorithm for the problem, generalizes the state of art for the fundamental problem of resource constrained real-time scheduling, to scenarios where jobs may have dwindling resource requirements. Our empirical study shows that this algorithm is in fact nearly optimal for realistic inputs.