并行机下独立任务调度的无秩序代价分析  

Price of anarchy analysis for scheduling selfish tasks on parallel machines

作　　者：王长军[1] 贾永基[1] 徐琪[1] 王晓锋[1] 

机构地区：[1]东华大学旭日工商管理学院,上海200051

出　　处：《管理科学学报》2010年第5期44-50,81,共8页Journal of Management Sciences in China

基　　金：国家自然科学基金资助项目(70772073;60874076);上海市自然科学基金资助项目(07ZR14003)

摘　　要：每个任务都具有异构的正规或非正规目标,系统也具有独立的全局目标.由于任务的自利性,无序竞争常导致系统全局目标的恶化,造成无秩序代价.为此,采用非合作博弈建立同速并行处理机下该问题的模型,定义Nash均衡调度,证明其存在性,定量分析不同情况(系统目标分别为最小化完工时间之和与最小化最大完成时间之和;任务目标分别为正规型与任意型)下Nash均衡调度的无秩序代价,显得必要而完备.研究发现,当系统目标为最小化完成时间之和或者独立任务具有非正规型性能指标时,无秩序代价会恶化.Consider the problem of scheduling selfish tasks （or agents ） --whose objective is the minimization of their heterogeneous regular or non-regular objectives - on identical parallel machines in order to minimize a global objective. Because of tasks＇ selfishness, anarchistic competition without mechanism or global coordinator would deteriorate the global performance, and then, price of anarchy. Hence, corresponding noncooperative game is introduced to model the case of identical parallel machine and an equilibrium result named Nash equilibrium schedule is given. The existence of Nash equilibrium schedule is proved and the tight price of anarchy in the different situations （the system＇ s performance objective is selected as minimization of total completion time or minimization of makespan ; and the task＇ s is regular or arbitrary. ） are analyzed quantitatively. The results show the price of anarchy may be extremely poor when the system＇ s performance objective is to minimize the total completion time or the independent task＇ s is non-regular.

关 键 词：无秩序代价 调度 排序模型 博弈理论 

分 类 号：TP29[自动化与计算机技术—检测技术与自动化装置]