State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
State Space Collapse in Many-Server Diffusion Limits of Parallel Server Systems
复制标题
并行服务器系统多服务器扩散限制中的状态空间崩溃
DOI：
10.1287/moor.1110.0494
复制
发表时间：
2011
期刊：
影响因子：
--
通讯作者：
Tolga Tezcan
中科院分区：
文献类型：
--
作者：
J. Dai;Tolga Tezcan
我们考虑一类排队系统，由并行的服务器池和多个客户类别组成。假设客户服务时间呈指数分布。我们研究了这些排队系统在大流量情况下的渐近行为，这种情况被称为 Halfin-Whitt 多服务器渐近情况。我们的主要贡献是为并行服务器系统建立状态空间崩溃结果的通用框架。在我们的工作中，状态空间崩溃是指跟踪每个类别中等待服务的客户数量以及各个服务器池正在服务的每个类别中的客户数量的进程维数的减少。我们定义并引入了“状态空间崩溃”函数，它控制状态空间崩溃的确切细节。我们表明，如果相应的确定性流体动力学模型满足类似的状态空间崩溃条件，则状态空间崩溃结果在多服务器繁重流量中成立。与多类排队网络的单服务器大流量设置不同，我们的流体动力学模型不同于多服务器队列的标准流体模型。我们的方法在精神上类似于 Bramson [Bramson, M. 1998。状态空间崩溃及其应用于多类排队网络的大流量限制。排队系统30 89--148.]，重点关注单服务器大流量状态。我们通过在静态缓冲区优先策略和文献中提出的阈值策略下建立 V 模型系统的多服务器扩散限制的状态空间崩溃结果来说明我们的结果的应用。
We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin-Whitt many-server asymptotic regime. Our main contribution is a general framework for establishing state space collapse results in this regime for parallel server systems. In our work, state space collapse refers to a decrease in the dimension of the processes tracking the number of customers in each class waiting for service and the number of customers in each class being served by various server pools. We define and introduce a “state space collapse” function, which governs the exact details of the state space collapse. We show that a state space collapse result holds in many-server heavy traffic if a corresponding deterministic hydrodynamic model satisfies a similar state space collapse condition. Unlike the single-server heavy traffic setting for multiclass queueing network, our hydrodynamic model is different from the standard fluid model for many-server queues. Our methodology is similar in spirit to that in Bramson [Bramson, M. 1998. State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems30 89--148.], which focuses on the single-server heavy traffic regime. We illustrate the applications of our results by establishing state space collapse results in many-server diffusion limits for V-model systems under static-buffer-priority policy and the threshold policy proposed in the literature.