中等工件的重尾极限与比较调度
Heavy-Tailed Limits for Medium Size Jobs and Comparison Scheduling
摘要：
我们研究了处理器共享（PS），前台后台处理器共享（FBPS）和最短剩余处理时间优先（SRPT）调度纪律的条件逗留时间分布的事件中，到达平稳的客户的作业大小小于正好k>=0的前m>=k到达。然后，在前一个事件的条件下，这个新到达的客户的逗留时间分布表现为渐近相同，就好像客户被隔离地服务于PS/FBPS的速率为（1-ρ）/（k+1）的服务器，以及SRPT的速率为（1-ρ）的服务器，其中ρ是业务强度。因此，引入的概念的条件限制，使我们能够区分的渐近性能的研究，通过显示SRPT表现出相当好的渐近行为相对较小的工作比PS/FBPS。受上述结果的启发，我们提出了一个近似的SRPT纪律的基础上，一种新的自适应作业分组机制，使用相对大小比较新到达的工作，前m到达。具体地说，如果新到达的作业小于前m个作业中的k个且大于前m个作业中的m-k个，则将其路由到类k中。然后，使用静态优先级调度的类较小的作业具有较高的优先级。该机制的良好性能，即使是少量的类m+1，证明了使用渐近分析下的重尾作业要求。我们还讨论了改进的比较分组机制，提高了工作分类的准确性，在一个小的额外的复杂性为代价。
英文摘要：
We study the conditional sojourn time distributions of processor sharing (PS), foreground background processor sharing (FBPS) and shortest remaining processing time first (SRPT) scheduling disciplines on an event where the job size of a customer arriving in stationarity is smaller than exactly k>=0 out of the preceding m>=k arrivals. Then, conditioning on the preceding event, the sojourn time distribution of this newly arriving customer behaves asymptotically the same as if the customer were served in isolation with a server of rate (1-ρ)/(k+1) for PS/FBPS, and (1-ρ) for SRPT, respectively, where ρis the traffic intensity. Hence, the introduced notion of conditional limits allows us to distinguish the asymptotic performance of the studied schedulers by showing that SRPT exhibits considerably better asymptotic behavior for relatively smaller jobs than PS/FBPS. Inspired by the preceding results, we propose an approximation to the SRPT discipline based on a novel adaptive job grouping mechanism that uses relative size comparison of a newly arriving job to the preceding m arrivals. Specifically, if the newly arriving job is smaller than k and larger than m-k of the previous m jobs, it is routed into class k. Then, the classes of smaller jobs are served with higher priorities using the static priority scheduling. The good performance of this mechanism, even for a small number of classes m+1, is demonstrated using the asymptotic queueing analysis under the heavy-tailed job requirements. We also discuss refinements of the comparison grouping mechanism that improve the accuracy of job classification at the expense of a small additional complexity.
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。
