Diffusion-Scale Tightness of Invariant Distributions of a Large-Scale Flexible Service System
Diffusion-Scale Tightness of Invariant Distributions of a Large-Scale Flexible Service System
复制标题
大规模柔性服务系统不变分布的扩散尺度紧度
DOI：
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发表时间：
2013
影响因子：
1.2
通讯作者：
Alexander Stolyar
中科院分区：
文献类型：
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作者：
Alexander Stolyar
考虑了一个具有多个客户类别和多个服务器池的大规模服务系统，其平均服务时间同时依赖于客户类别和服务器池。允许的活动（路由选择）形成一棵树（在图中，顶点既是客户类又是服务器池）。我们研究了系统在Stolyar和Yudoya（2012）引入的叶子活动优先（leaf activity priority，ESTA）策略下的行为。渐近制度被认为是，在每个池中的客户的到达率和服务器的数量趋于∞成比例的缩放参数r，而整个系统的负载仍然严格的亚临界。我们证明了扩散标度（以平衡点为中心，缩小r −1/2）不变分布的紧密性。由此得到一个极限互换的结果：扩散标度不变分布的极限等于极限扩散过程的不变分布。
A large-scale service system with multiple customer classes and multiple server pools is considered, with the mean service time depending both on the customer class and server pool. The allowed activities (routeing choices) form a tree (in the graph with vertices being both customer classes and server pools). We study the behavior of the system under a leaf activity priority (LAP) policy, introduced by Stolyar and Yudovina (2012). An asymptotic regime is considered, where the arrival rate of customers and number of servers in each pool tend to ∞ in proportion to a scaling parameter r, while the overall system load remains strictly subcritical. We prove tightness of diffusion-scaled (centered at the equilibrium point and scaled down by r −1/2) invariant distributions. As a consequence, we obtain a limit interchange result: the limit of diffusion-scaled invariant distributions is equal to the invariant distribution of the limiting diffusion process.