Coordination mechanism for selfish scheduling under a grade of service provision

doi:10.1016/j.ipl.2013.01.014

Information Processing Letters

Volume 113, Issue 8, 30 April 2013, Pages 251-254

https://doi.org/10.1016/j.ipl.2013.01.014 Get rights and content

Abstract

In this paper, we study the problem of selfish scheduling game under a grade of service provision, where all machines and all jobs are labeled with the different grade of service (GoS) levels such that a job J can be assigned to execute on machine M only when the GoS level of machine M is not higher than the GoS level of job J. We consider two coordination mechanisms for this selfish scheduling game: the makespan policy and the LG-LPT policy. For the first mechanism, we show that the price of anarchy is exactly $\frac{3}{2}$ for two machines and $Θ (\frac{\log m}{\log \log m})$ for m $(⩾ 3)$ machines, respectively. For the second mechanism, we point out that the price of anarchy is $\frac{5}{4}$ for two machines and $2 - \frac{1}{m - 1}$ for m $(⩾ 3)$ machines, respectively, and we finally analyze the convergence to a Nash equilibrium of the induced game.

Highlights

► We study two coordination mechanisms for the selfish scheduling game under a GoS provision: makespan policy and LG-LPT policy. ► For first mechanism, the POA is $\frac{3}{2}$ for two machines and $Θ (\frac{\log m}{\log \log m})$ for m $(> 3)$ machines, respectively. ► For second mechanism, the POA is $\frac{5}{4}$ for two machines and $2 - \frac{1}{m - 1}$ for m $(> 3)$ machines, respectively. ► We finally analyze the convergence of the second mechanism to a Nash equilibrium of the induced game.

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Cited by (6)

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In 2008, we published a survey paper on machine scheduling with processing set restrictions [Leung, J.Y.-T., Li, C.-L., 2008. Scheduling with processing set restrictions: a survey. Int. J. Prod. Econ. 116 (2), 251–262]. Since the appearance of that survey paper, there has been a significant increase in interest in this field. In this paper, we provide an expository update of this line of research. Our survey covers five types of processing set restrictions, namely inclusive processing sets, nested processing sets, interval processing sets, tree-hierarchical processing sets, and arbitrary processing sets, and it covers both offline and online problems. While our main focus is on scheduling models with a makespan objective, other performance criteria are also discussed.
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^☆: Supported by the National Natural Science Foundation of China [Nos. 10861012, 61063011], the Project of the First 100 High-level Overseas Talents of Yunnan Province IRTSTYN.

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Coordination mechanism for selfish scheduling under a grade of service provision☆

Abstract

Highlights

Annals of Discrete Mathematics

Computers and Operations Research

Theoretical Computer Science