状态依赖有限处理器共享队列的近似与最优控制
Approximations and Optimal Control for State-dependent Limited Processor Sharing Queues
AI总结：
本文研究了服务速率依赖于占用服务器作业数的处理器共享服务器的近似与控制，提出基于重交通扩散分析的近优控制策略，通过构造状态依赖的处理器共享服务器序列获得漂移函数，并通过数值算法解决动态并发限制控制问题。
摘要：
本文研究了服务速率依赖于占用服务器作业数的处理器共享服务器的近似与控制，提出基于重交通扩散分析的近优控制策略，通过构造状态依赖的处理器共享服务器序列获得漂移函数，并通过数值算法解决动态并发限制控制问题。我们扩展研究到动态调整并发限制的控制策略，提供了两种新颖的数值算法来解决相关的扩散控制问题。我们的算法可以视为“平均成本”迭代：第一个算法使用二分查找平均成本，可以在时间$O\left( \log^2 \frac{1}ε \right)$内找到一个$ε$-最优策略；第二个算法使用牛顿-拉夫森方法求根，需要$O\left( \log \frac{1}ε \log\log \frac{1}ε\right)$时间。数值实验展示了我们近似在选择最优或近优静态和动态并发控制启发式方法方面的准确性。
英文摘要：
The paper studies approximations and control of a processor sharing (PS) server where the service rate depends on the number of jobs occupying the server. The control of such a system is implemented by imposing a limit on the number of jobs that can share the server concurrently, with the rest of the jobs waiting in a first-in-first-out (FIFO) buffer. A desirable control scheme should strike the right balance between efficiency (operating at a high service rate) and parallelism (preventing small jobs from getting stuck behind large ones). We employ the framework of heavy-traffic diffusion analysis to devise near optimal control heuristics for such a queueing system. However, while the literature on diffusion control of state-dependent queueing systems begins with a sequence of systems and an exogenously defined drift function, we begin with a finite discrete PS server and propose an axiomatic recipe to explicitly construct a sequence of state-dependent PS servers which then yields a drift function. We establish diffusion approximations and use them to obtain insightful and closed-form approximations for the original system under a static concurrency limit control policy. We extend our study to control policies that dynamically adjust the concurrency limit. We provide two novel numerical algorithms to solve the associated diffusion control problem. Our algorithms can be viewed as "average cost" iteration: The first algorithm uses binary-search on the average cost and can find an $ε$-optimal policy in time $O\left( \log^2 \frac{1}ε \right)$; the second algorithm uses the Newton-Raphson method for root-finding and requires $O\left( \log \frac{1}ε \log\log \frac{1}ε\right)$ time. Numerical experiments demonstrate the accuracy of our approximation for choosing optimal or near-optimal static and dynamic concurrency control heuristics.
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。
