Scheduling jobs with stochastic holding costs

Lee, Dabeen and Vojnovic, Milan ORCID: 0000-0003-1382-022X (2021) Scheduling jobs with stochastic holding costs. In: Ranzato, Marc'Aurelio, Beygelzimer, Alina, Dauphin, Yann, Liang, Percy S. and Wortman Vaughan, Jenn, (eds.) Advances in Neural Information Processing Systems 34. Advances in Neural Information Processing Systems. Neural Information Processing Systems Foundation, pp. 19375-19384. ISBN 9781713845393

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Abstract

This paper proposes a learning and scheduling algorithm to minimize the expected cumulative holding cost incurred by jobs, where statistical parameters defining their individual holding costs are unknown a priori. In each time slot, the server can process a job while receiving the realized random holding costs of the jobs remaining in the system. Our algorithm is a learning-based variant of the cμ rule for scheduling: it starts with a preemption period of fixed length which serves as a learning phase, and after accumulating enough data about individual jobs, it switches to nonpreemptive scheduling mode. The algorithm is designed to handle instances with large or small gaps in jobs' parameters and achieves near-optimal performance guarantees. The performance of our algorithm is captured by its regret, where the benchmark is the minimum possible cost attained when the statistical parameters of jobs are fully known. We prove upper bounds on the regret of our algorithm, and we derive a regret lower bound that is almost matching the proposed upper bounds. Our numerical results demonstrate the effectiveness of our algorithm and show that our theoretical regret analysis is nearly tight.

Item Type:	Book Section
Additional Information:	© 2021 Neural information processing systems foundation. All rights reserved.
Divisions:	Statistics
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Date Deposited:	30 Jun 2022 09:24
Last Modified:	20 Dec 2024 00:19
URI:	http://eprints.lse.ac.uk/id/eprint/115465

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