Diffusion Limits for Shortest Remaining Processing Time Queues
Diffusion Limits for Shortest Remaining Processing Time Queues
复制标题
最短剩余处理时间队列的扩散限制
DOI：
10.1214/10-ssy016
复制
发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Amber L. Puha
中科院分区：
文献类型：
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作者：
H. C. Gromoll;Łukasz Kruk;Amber L. Puha
我们提出了一个重流量分析的单服务器队列更新到达和一般分布的i.i.d.。服务时间，在此期间服务器采用最短剩余处理时间（SRPT）策略。在典型的交通拥挤假设下，我们证明了一个测度值状态描述子的扩散极限定理，由此我们得出了一个类似的队长过程的定理。这些结果使我们能够对SRPT的队长最优性做出一些观察。特别是，他们提供了最尖锐的说明队列长度最优性和服务质量之间的众所周知的紧张局势，这一政策。
We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaining Processing Time (SRPT) policy. Under typical heavy traffic assumptions, we prove a diffusion limit theorem for a measure-valued state descriptor, from which we conclude a similar theorem for the queue length process. These results allow us to make some observations on the queue length optimality of SRPT. In particular, they provide the sharpest illustration of the well-known tension between queue length optimality and quality of service for this policy.