Diffusion Models for Performance Analysis of Large-Scale Service Systems

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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.