分布式自私负载均衡
Distributed Selfish Load Balancing
摘要：
假设一组$m$任务将在一组$n$资源之间尽可能平等地共享。一个博弈论的机制来找到一个合适的分配是将每个任务与一个“自私的代理”相关联，并要求每个代理选择一个资源，资源的成本是选择它的代理的数量。代理将被期望从过载迁移到欠载资源，直到分配变得平衡。最近的工作研究了如何在分布式环境中，代理人自私地迁移，没有任何集中控制的情况下，这可以发生的问题。在本文中，我们讨论了一个自然的协议的代理，结合了以下可取的功能：它可以实现在一个强分布式设置，不使用中央控制，并具有良好的收敛性能。对于$m\gg n$，系统在预期时间$O(\log\log m)$内变得近似平衡（$ε$ -纳什均衡）。我们使用鞅技术，该过程收敛到一个完美的平衡分配在预期的时间$O(\log\log m+n^4)$。我们也给出了收敛时间的一个下界$Ω(\max\{\log\log m,n\})$。
英文摘要：
Suppose that a set of $m$ tasks are to be shared as equally as possible amongst a set of $n$ resources. A game-theoretic mechanism to find a suitable allocation is to associate each task with a ``selfish agent'', and require each agent to select a resource, with the cost of a resource being the number of agents to select it. Agents would then be expected to migrate from overloaded to underloaded resources, until the allocation becomes balanced. Recent work has studied the question of how this can take place within a distributed setting in which agents migrate selfishly without any centralized control. In this paper we discuss a natural protocol for the agents which combines the following desirable features: It can be implemented in a strongly distributed setting, uses no central control, and has good convergence properties. For $m\gg n$, the system becomes approximately balanced (an $ε$-Nash equilibrium) in expected time $O(\log\log m)$. We show using a martingale technique that the process converges to a perfectly balanced allocation in expected time $O(\log\log m+n^4)$. We also give a lower bound of $Ω(\max\{\log\log m,n\})$ for the convergence time.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
