具有FIFO服务规则的Redundancy-d稳定域的一个下界
A Lower Bound on the stability region of Redundancy-d with FIFO service discipline
摘要：
Redundancy-d（R（d））是一种负载均衡方法，用于将传入的作业路由到K台服务器，每台服务器都有自己的队列。每个到达的作业被复制成2<=d<=K个任务，然后路由到随机均匀选择的d个服务器。当第一个任务完成服务时，剩余的d-1任务被取消，作业离开系统。尽管事实上，R（d）是已知的，在某些条件下，大大提高工作完成时间相比，根本不使用冗余，很少有人知道一个更基本的性能标准：什么是一组到达率下的R（d）排队系统与FIFO服务纪律是稳定的？在这种情况下，由于系统的冗余和取消的复杂动态，现有的结果是稀缺的，并限于非常特殊的情况下，联合服务时间分配的任务。在本文中，我们提供了一个非平凡的，封闭形式的下界的稳定区域R（d）的一般联合服务时间分布的任务有限的第一和第二时刻。本文考虑了一类具有伯努利到达的离散时间系统，并假设工件是按到达顺序加工的。我们使用的工作量过程和二次李雅普诺夫函数来表征的到达率的系统是稳定的。虽然模拟结果表明我们的界限并不严格，但它提供了一个易于检查的性能保证。
英文摘要：
Redundancy-d (R(d)) is a load balancing method used to route incoming jobs to K servers, each with its own queue. Every arriving job is replicated into 2<=d<=K tasks, which are then routed to d servers chosen uniformly at random. When the first task finishes service, the remaining d-1 tasks are cancelled and the job departs the system. Despite the fact that R(d) is known, under certain conditions, to substantially improve job completion times compared to not using redundancy at all, little is known on a more fundamental performance criterion: what is the set of arrival rates under which the R(d) queueing system with FIFO service discipline is stable? In this context, due to the complex dynamics of systems with redundancy and cancellations, existing results are scarce and are limited to very special cases with respect to the joint service time distribution of tasks. In this paper we provide a non-trivial, closed form lower bound on the stability region of R(d) for a general joint service time distribution of tasks with finite first and second moments. We consider a discrete time system with Bernoulli arrivals and assume that jobs are processed by their order of arrival. We use the workload processes and a quadratic Lyapunov function to characterize the set of arrival rates for which the system is stable. While simulation results indicate our bound is not tight, it provides an easy-to-check performance guarantee.
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。
