论文标题
在延长的交通状态下，简单并行服务器系统中开关控制策略的渐近最优性
Asymptotic optimality of switched control policies in a simple parallel server system under an extended heavy traffic condition
论文作者
论文摘要
本文研究了最近引入的扩展繁重的交通状况下的2级，2服务器并行服务器系统，该系统指出，基础的“静态分配”线性程序（LP）至关重要，但不需要它具有独特的解决方案。主要的结果是构建政策，该策略在预期的扩散式队列长度的预期折扣线性组合中，在[1]中实现了下限，因此在[1]中得到了构建，因此在渐近上是最佳的（AO）。 LP的每个极端点解决方案都决定了控制模式，即一组活动（类 - 服务器对）是运行的。 当有多个解决方案时，可以动态选择这些模式。结果表明，AO所需的模式数为一或两个。在后一种情况下，（归一化）工作负载域中有一个切换点，其特征是自由边界问题。 我们的策略是通过确定基本策略对并在此切换点之间切换来定义的。 他们提供了沉重的交通文献中的第一个例子，在AO策略下，通过扩散过程给出了弱限制，在这种扩散过程中，漂移和扩散系数都是不连续的。
This paper studies a 2-class, 2-server parallel server system under the recently introduced extended heavy traffic condition, which states that the underlying 'static allocation' linear program (LP) is critical, but does not require that it has a unique solution. The main result is the construction of policies that asymptotically achieve a lower bound, proved in [1], on an expected discounted linear combination of diffusion-scaled queue lengths, and are therefore asymptotically optimal (AO). Each extreme point solution to the LP determines a control mode, i.e., a set of activities (class--server pairs) that are operational. When there are multiple solutions, these modes can be selected dynamically. It is shown that the number of modes required for AO is either one or two. In the latter case there is a switching point in the (normalized) workload domain, characterized in terms of a free boundary problem. Our policies are defined by identifying pairs of elementary policies and switching between them at this switching point. They provide the first example in the heavy traffic literature where weak limits under an AO policy are given by a diffusion process where both the drift and diffusion coefficients are discontinuous.
