Abstract
We study a fundamental online job admission problem where jobs with deadlines arrive online over time at their release dates, and the task is to determine a preemptive single-server schedule which maximizes the number of jobs that complete on time. To circumvent known impossibility results, we make a standard slackness assumption by which the feasible time window for scheduling a job is at least 1+varepsilon times its processing time, for some varepsilon >0. We quantify the impact that different provider commitment requirements have on the performance of online algorithms. Our main contribution is one universal algorithmic framework for online job admission both with and without commitments. Without commitment, our algorithm with a competitive ratio of mathcal {O}(1/varepsilon ) is the best possible (deterministic) for this problem. For commitment models, we give the first non-trivial performance bounds. If the commitment decisions must be made before a job’s slack becomes less than a delta -fraction of its size, we prove a competitive ratio of mathcal {O}(varepsilon /((varepsilon -delta )delta ^2)), for 0<delta <varepsilon . When a provider must commit upon starting a job, our bound is mathcal {O}(1/varepsilon ^2). Finally, we observe that for scheduling with commitment the restriction to the “unweighted” throughput model is essential; if jobs have individual weights, we rule out competitive deterministic algorithms.
Highlights
Many modern computing environments involve a centralized system for managing the resource allocation for processing many different jobs
An extended abstract of this paper was published at the Conference on Integer Programming and Combinatorial Optimization (IPCO) 2019 [8]
We provide a strong lower bound for the preemptive version of the problem in the presence of weights
Summary
Many modern computing environments involve a centralized system for managing the resource allocation for processing many different jobs. Throughput is a “social welfare” objective that tries to maximize total utility To this end, a solution may abort jobs close to their deadlines in favor of many shorter and more urgent tasks [12]. As companies start to outsource mission critical processes to external clouds, they may require a certain provider-side guarantee, i.e., service providers have to commit to complete admitted jobs before they cannot be moved to other computing clusters anymore. Analytical tools, that usually work with copies of databases, depend on faultless data This means, once such a copy process started, its completion must be guaranteed. In this paper we quantify the impact that different job commitment requirements have on the performance of online algorithms. We parameterize our performance guarantees by the slackness of jobs
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have