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Improving routing decisions in parallel non-observable queues

机译:改善并行不可观察队列中的路由决策

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We revisit the well-known problem of scheduling in N = 2 non-observable parallel single-server queues with one dispatcher having no queue to store the incoming jobs. The dispatcher does not observe the current states of the queues and servers and the sizes of the incoming jobs. The only available information to it is the job size distribution, job's inter-arrival time distribution and server's speeds. For this problem setting it is known that if the dispatcher can memorize the sequence of its previous decisions, then a deterministic policy is better than the random choice policy with respect to the job's mean waiting and mean sojourn time. In this paper we address the following question: can the deterministic policy be improved if the dispatcher, in addition to the decisions made, can memorize also the times between the decisions? We describe the new policy and numerically show that it is almost always possible to do better with it than with the deterministic policy. Two algorithms for choosing decisions under the new policy are given. Both are based on the Lindley recursion and are approximate in nature, because utilize the discretization of the underlying distributions. Our findings show that the relative gain of the new policy may reach , when minimizing job's mean sojourn time, and more than for the job's mean waiting time.
机译:我们重新审视了N> = 2个不可观察的并行单服务器队列中的调度问题,其中一个调度程序没有队列来存储传入的作业。调度程序不会观察队列和服务器的当前状态以及传入作业的大小。唯一可用的信息是作业大小分布,作业到达时间的分布和服务器的速度。对于此问题设置,已知的是,如果调度员可以记住其先前决策的顺序,那么就作业的平均等待时间和平均逗留时间而言,确定性策略要比随机选择策略好。在本文中,我们解决以下问题:如果调度员除了做出决策之外,还可以记住决策之间的时间,可以改善确定性策略吗?我们描述了新策略,并从数字上显示出,与确定性策略相比,几乎总是可以做得更好。给出了两种在新策略下选择决策的算法。两者都基于Lindley递归并且本质上是近似的,因为利用了基础分布的离散化。我们的研究结果表明,在使工作的平均逗留时间最小化的同时,新政策的相对收益可能达到,并且比工作的平均等待时间还多。

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