STEIN'S METHOD FOR STEADY-STATE DIFFUSION APPROXIMATIONS OF M/Ph/n plus M SYSTEMS

被引:44
作者
Braverman, Anton [1 ]
Dai, J. G. [1 ]
机构
[1] Cornell Univ, Sch Operat Res & Informat Engn, Ithaca, NY 14850 USA
基金
美国国家科学基金会;
关键词
Stein's method; diffusion approximation; steady-state; many servers; state space collapse; convergence rate; HEAVY-TRAFFIC LIMITS; SPACE COLLAPSE; ASYMPTOTIC OPTIMALITY; QUEUING-NETWORKS; QUEUES; STATIONARITY; THEOREMS; HALFIN;
D O I
10.1214/16-AAP1211
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We consider M/Ph/n + M queueing systems in steady state. We prove that the Wasserstein distance between the stationary distribution of the normalized system size process and that of a piecewise Ornstein Uhlenbeck (OU) process is bounded by C/root T., where the constant C is independent of the arrival rate A and the number of servers n as long as they are in the HalfinWhitt parameter regime. For each integer m > 0, we also establish a similar bound for the difference of the mth steady-state moments. For the proofs, we develop a modular framework that is based on Stein's method. The framework has three components: Poisson equation, generator coupling, and state space collapse. The framework, with further refinement, is likely applicable to steady-state diffusion approximations for other stochastic systems.
引用
收藏
页码:550 / 581
页数:32
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