We consider a variant of the classic real-time scheduling problem, which has natural applications in cloud computing. The input consists of a set of jobs, and an integer parameter k ≥ 1. Each job is associated with a processing time, a release time, a due-date and a positive weight. The goal is to feasibly schedule a subset of the jobs of maximum total weight on a single machine, such that each of the jobs is preempted at most k times. Our theoretical results for the real-time k-bounded preemptive scheduling problem include hardness proofs, as well as algorithms for subclasses of instances, for which we derive constant-ratio performance guarantees. We bridge the gap between theory and practice through a comprehensive experimental study, in which we also test the performance of several heuristics for general instances on multiple parallel machines. We use in the experiments a linear programming relaxation to upper bound the optimal solution for a given instance. Our results show that while k-bounded preemptive scheduling is hard to solve already on highly restricted instances, simple priority-based heuristics yield almost optimal schedules for realistic inputs and arbitrary values of k.

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.