ERGODIC CONTROL OF MULTI-CLASS M/M/N plus M QUEUES IN THE HALFIN-WHITT REGIME

• 成果类型: Article
• 署名作者: Arapstathis, Art; Biswas, Anup; Pang, Guodong
• 署名单位: University of Texas System; University of Texas Austin; Pennsylvania Commonwealth System of Higher Education (PCSHE); Pennsylvania State University; Pennsylvania State University - University Park
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/14-AAP1081
• 发表日期: 2015
• 页码: 3511-3570
• 关键词: steady-state approximations; heavy-traffic limits; convex delay costs; Asymptotic Optimality; scheduling control; queuing-systems; Servers; EQUATIONS

摘要

We study a dynamic scheduling problem for a multi-class queueing network with a large pool of statistically identical servers. The arrival processes are Poisson, and service times and patience times are assumed to be exponentially distributed and class dependent. The optimization criterion is the expected long time average (ergodic) of a general (nonlinear) running cost function of the queue lengths. We consider this control problem in the Halfin-Whitt (QED) regime, that is, the number of servers n and the total offered load r scale like n approximate to r + (rho) over cap root r for some constant (rho) over cap. This problem was proposed in [Ann. Appl. Probab. 14 (2004) 1084-1134, Section 5.2]. The optimal solution of this control problem can be approximated by that of the corresponding ergodic diffusion control problem in the limit. We introduce a broad class of ergodic control problems for controlled diffusions, which includes a large class of queueing models in the diffusion approximation, and establish a complete characterization of optimality via the study of the associated HJB equation. We also prove the asymptotic convergence of the values for the multi-class queueing control problem to the value of the associated ergodic diffusion control problem. The proof relies on an approximation method by spatial truncation for the ergodic control of diffusion processes, where the Markov policies follow a fixed priority policy outside a fixed compact set.