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.

Price of anarchy of a scheduling game with hybrid coordination mechanisms

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.