Version 1
: Received: 3 March 2023 / Approved: 6 March 2023 / Online: 6 March 2023 (13:00:04 CET)
How to cite:
Li, Z.; Cheng, C. The Expected Competitive Ratio on a Kind of Stochastic-Online Followtime Scheduling with Machine Subject to an Uncertain Breakdown. Preprints2023, 2023030103. https://doi.org/10.20944/preprints202303.0103.v1
Li, Z.; Cheng, C. The Expected Competitive Ratio on a Kind of Stochastic-Online Followtime Scheduling with Machine Subject to an Uncertain Breakdown. Preprints 2023, 2023030103. https://doi.org/10.20944/preprints202303.0103.v1
Li, Z.; Cheng, C. The Expected Competitive Ratio on a Kind of Stochastic-Online Followtime Scheduling with Machine Subject to an Uncertain Breakdown. Preprints2023, 2023030103. https://doi.org/10.20944/preprints202303.0103.v1
APA Style
Li, Z., & Cheng, C. (2023). The Expected Competitive Ratio on a Kind of Stochastic-Online Followtime Scheduling with Machine Subject to an Uncertain Breakdown. Preprints. https://doi.org/10.20944/preprints202303.0103.v1
Chicago/Turabian Style
Li, Z. and Congdian Cheng. 2023 "The Expected Competitive Ratio on a Kind of Stochastic-Online Followtime Scheduling with Machine Subject to an Uncertain Breakdown" Preprints. https://doi.org/10.20944/preprints202303.0103.v1
Abstract
We consider the problem of scheduling tasks on a single machine subject to an uncertain breakdown to minimize the flowtime. Assume the machine is unavailable during the breakdown; the starting time of the breakdown is a random variable s with distribution function D(s) and the terminating time of the breakdown has no any other information; jobs are non-resumable. Under the assumptions, starting from the perspective of statistical optimization, we first define the expected competitive ratio of an algorithm to find the optimized solution with the considered problem. Further, we propose and prove a certain result on the expected competitive ratio of the SPT rule. In particular, we show that under a quite loose condition the expected competitive ratio of the SPT rule is no more than 5/4. Meanwhile, we also make some discussions about our studies. What we have done will rich and improve the studying results on the area of scheduling to minimize flowtime and advance the development of online optimization and statistical optimization.
Keywords
single machine; single breakdown; schedule; flowtime; stochastic optimization; online optimization
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
