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高校应用数学学报
Applied Mathematics A Journal of Chinese Universities  2017, Vol. 32 Issue (4): 473-486    DOI:
    
Price of anarchy of a scheduling game with hybrid coordination mechanisms
WEI Qi1;2, JIANG Tian-ying1
1. School of Finance and Trade, Ningbo Dahongying University, Ningbo 315100, China;
2. Department of Mathematics, Shanghai University, Shanghai 200444, China
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Abstract  Scheduling game is a kind of special scheduling problem used in Internet and cloud computing. Different from the traditional scheduling problem, each job is controlled by a selfish agent and it is only interested in choosing one machine to minimize its own cost. A scheduling game with hybrid coordination mechanisms is considered. There are $n$ selfish jobs and $m$ unrelated machines. The machine can choose WSPT policy or PS policy, and the social cost is the total weighted completion times of all jobs. A linear programming relaxation for this problem is designed firstly. Then by discussing the relationship between the linear programming and its dual, the main conclusion is given: The mixed Price of Anarchy (MPoA) of this scheduling game is exactly 4.

Key words： scheduling game      price of anarchy      coordination mechanism      dual linear programming     
Received: 26 July 2016      Published: 01 December 2018
CLC:  O223  
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WEI Qi
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Cite this article:

WEI Qi, JIANG Tian-ying. Price of anarchy of a scheduling game with hybrid coordination mechanisms. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 473-486.

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http://www.zjujournals.com/amjcua/     OR     http://www.zjujournals.com/amjcua/Y2017/V32/I4/473


一个混合协调分配机制下自私调度问题的社会无序代价分析

自私调度问题是一类应用于互联网和云计算的特殊调度问题. 不同于传统调 度问题, 它的每个工件是一个自私的参与者, 可以自主地选择一台机器加工以谋求自 身加工费用最小化. 针对机器可以自由选择WSPT机制或PS机制的混合协调分配机 制自私调度问题, 通过设计一个该问题的松弛线性规划, 然后写出该线性规划的对偶 规划. 比较上述两个规划的最优目标值, 以及该自私调度问题的最优社会费用和混 合Nash均衡解的最差社会费用这四个数值, 分析出该自私调度问题的混合社会无序代价为4.

关键词： 自私调度,  社会无序代价,  协调分配机制,  对偶规划 
[1] YAN Yu-jie. Study for batch scheduling on single machine[J]. Applied Mathematics A Journal of Chinese Universities, 2017, 32(4): 462-472.