Diffusion Models for Performance Analysis of Large-Scale Service Systems

随机处理网络已被用于模拟大规模的服务系统，包括客户联络中心和医院运营。由于随机处理网络的复杂性，通常很难或不可能及时计算其性能指标。扩散模型为各类随机处理网络提供了有效的近似。如果成功，该研究将有助于创建新的分析工具，以实现客户联络中心的准确人员配置和优质客户服务。 它也将有助于创建分析工具，为医院住院流程管理。研究将建立稳态扩散近似的收敛速度。 所建立的收敛速度保证了具有给定系统参数的随机处理网络的稳态扩散近似的准确性，这些参数不一定会达到任何极限。 PI计划完全开发一个基于Stein方法的框架，以证明收敛速度。 该框架目前有四个组成部分：泊松方程和梯度界，发电机耦合，状态空间崩溃，和矩界。该框架，可能增加其他关键组件，将通过两类随机处理网络的开发和演示：多个池的多服务器系统和网络的单服务器队列。

Stochastic processing networks have been used to model large-scale service systems including customer contact centers and hospital operations. Due to the complexity of a stochastic processing network, it is often difficult or impossible to compute its performance measures in a timely manner. Diffusion models offer efficient approximations for various classes of stochastic processing networks. If successful, the research will contribute to the creation of new analytical tools for accurate staffing and quality customer service at customer contact centers. It will also contribute to the creation of analytical tools for hospital inpatient flow management.The research will establish convergence rates of steady-state diffusion approximations. The established convergence rates guarantee the accuracy of the steady-state diffusion approximation of a stochastic processing network with given system parameters, which are not necessarily going to any limit. The PI plans to fully develop a framework that is based on Stein's method to prove the convergence rates. The framework currently has four components: Poisson equations and gradient bounds, generator coupling, state space collapse, and moment bounds. The framework, with possible addition of other key components, will be developed and demonstrated through two classes of stochastic processing networks: multiple pools of many-server systems and networks of single-server queues.