多类共享队列的渐近最优策略与状态空间崩溃
An asymptotically optimal policy and state-space collapse for the multi-class shared queue
摘要：
本文研究了具有有限共享缓冲区的多类G/G/1排队系统。有任务接纳和服务器调度控制，其目的是最大限度地减少成本，其中包括保持和拒绝组件。我们构造了一个策略，是在繁忙的交通限制渐近最优。该策略源于Harrison-Taksar（HT）自由边界问题的解，并由单个自由边界点表示。我们表明，HT问题的解决方案转化为长度的过程遵循一个特定的{ \it三角}形式。这种形式意味着与已知的$cμ$优先级规则不同的长度控制策略，并且具有新颖的结构。我们认为，我们利用的概率方法可以成功地应用于解决云计算中的调度和接纳问题。
英文摘要：
We consider a multi-class G/G/1 queue with a finite shared buffer. There is task admission and server scheduling control which aims to minimize the cost which consists of holding and rejection components. We construct a policy that is asymptotically optimal in the heavy traffic limit. The policy stems from solution to Harrison-Taksar (HT) free boundary problem and is expressed by a single free boundary point. We show that the HT problem solution translated into the queuelength processes follows a specific {\it triangular} form. This form implies the queuelength control policy which is different from the known $cμ$ priority rule and has a novel structure. We exemplify that the probabilistic methods we exploit can be successfully applied to solving scheduling and admission problems in cloud computing.
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