论文标题
在延长的繁忙交通状态下的并行服务器系统：下限
Parallel server systems under an extended heavy traffic condition: A lower bound
论文作者
论文摘要
在扩散量表上研究并行服务器系统（PSS）的标准设置是基于沉重的交通状况（HTC），该设置假设基础静态分配线性程序（LP）至关重要，并且具有独特的解决方案。该解决方案确定了基本活动的图，该活动标识了运行的活动集（即类服务器对）。在本文中，我们探讨了扩展的HTC，其中LP仅被认为是至关重要的。由于允许多个解决方案，因此可以使用多组操作活动，称为模式。正式地，与模型关联的控制问题的缩放限制是由所谓的工作负载控制问题（WCP）给出的，其中与扩散过程相关的成本应通过在这些模式之间动态切换来最小化。我们的主要结果是WCP的值构成了与PSS模型相关的成本的渐近下限。
The standard setting for studying parallel server systems (PSS) at the diffusion scale is based on the heavy traffic condition (HTC), which assumes that the underlying static allocation linear program (LP) is critical and has a unique solution. This solution determines the graph of basic activities, which identifies the set of activities (i.e., class-server pairs) that are operational. In this paper we explore the extended HTC, where the LP is merely assumed to be critical. Because multiple solutions are allowed, multiple sets of operational activities, referred to as modes, are available. Formally, the scaling limit for the control problem associated with the model is given by a so called workload control problem (WCP) in which a cost associated with a diffusion process is to be minimized by dynamically switching between these modes. Our main result is that the WCP's value constitutes an asymptotic lower bound on the cost associated with the PSS model.
