Abstract We study the Task Assignment based on Guessing Size (TAGS) policy in a parallel and homogeneous server system. The policy parameters are the number of servers h and a set of cutoffs s 1 s 2 , l d o t s , s h − 1 . In this policy, all the incoming jobs are routed to the first server and jobs are run up to s 1 time units. If they complete they leave the system, but jobs that do not complete after s 1 time units are killed and moved to the end of the queue of the second server, where service starts from scratch. Likewise, jobs that are executed in server i and complete service before s i units of time, leave the system, whereas jobs that do not complete are killed and routed to the next server. We first study the stability of such system and provide a precise utilization threshold for the existence of stable parameters for a given job size distribution. We compute the threshold for several families of distributions and provide bounds for others. We show that TAGS is most stable for bounded Pareto distributions with parameter α = 1 . Besides, we provide tight bounds on the performance of the TAGS policy where the cutoffs are chosen to minimize average waiting time in the asymptotic regime where the largest job size tends to infinity for the Bounded Pareto distribution and the system load smaller than one. In this case, we show that the performance ratio between TAGS and a version called SITA which does require knowledge of job size is at most 2. We then consider more broadly the same asymptotic regime and consider a bound on the average waiting time for any distribution. This is compatible with having a conservative policy which will work well for any job size distribution. We show rather tight upper and lower bounds which again match those of SITA up to a factor of 2. These bounds are considerably lower than the corresponding bounds of competing policies such as Random or Least Work Remaining. We also show that for all these policies the bounded Pareto distribution with α = 1 is close to being the worst possible among all distributions with the same job size range. We show using the stability results that in the same regime, if we increase the load the gap between SITA and TAGS grows dramatically and eventually, the TAGS system cannot be stabilized. The conclusion from all our analysis is that TAGS is best used as a conservative policy with minimal requirements on small systems with relatively low utilization and where the range of job sizes is large.

中文翻译：

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基于猜测大小策略的任务分配分析

摘要 我们研究了在并行和同类服务器系统中基于猜测大小 (TAGS) 策略的任务分配。策略参数是服务器的数量 h 和一组截止值 s 1 s 2 , ldots , sh − 1 。在此策略中，所有传入作业都路由到第一台服务器，并且作业最多运行 s 1 个时间单位。如果它们完成，它们就会离开系统，但是在 s 1 个时间单位后没有完成的作业将被杀死并移动到第二个服务器的队列末尾，服务从头开始。同样，在服务器 i 中执行并在 si 单位时间之前完成服务的作业离开系统，而未完成的作业将被终止并路由到下一个服务器。我们首先研究此类系统的稳定性，并为给定作业规模分布的稳定参数的存在提供精确的利用率阈值。我们计算了几个分布族的阈值，并为其他分布族提供了界限。我们表明 TAGS 对于参数 α = 1 的有界帕累托分布最稳定。此外，我们对 TAGS 策略的性能提供了严格的限制，其中选择截止点以最小化渐近机制中的平均等待时间，在该渐近机制中，对于有界帕累托分布和系统负载小于 1，最大作业规模趋于无穷大。在这种情况下，我们表明 TAGS 与确实需要作业规模知识的名为 SITA 的版本之间的性能比最多为 2。然后，我们更广泛地考虑相同的渐近机制，并考虑任何分布的平均等待时间的界限。这与具有适用于任何工作规模分布的保守政策兼容。我们展示了相当严格的上限和下限，它们再次与 SITA 的上限和下限相匹配，最高可达 2 倍。这些上限远低于竞争策略（如随机或最少剩余工作量）的相应边界。我们还表明，对于所有这些策略，α = 1 的有界帕累托分布接近于具有相同工作规模范围的所有分布中最差的可能。我们使用稳定性结果表明，在相同的情况下，如果我们增加负载，SITA 和 TAGS 之间的差距会急剧增加，最终，TAGS 系统无法稳定。