ASYMPTOTICALLY OPTIMAL CONTROL FOR A MULTICLASS QUEUEING MODEL IN THE MODERATE DEVIATION HEAVY TRAFFIC REGIME

• 成果类型: Article
• 署名作者: Atar, Rami; Cohen, Asaf
• 署名单位: Technion Israel Institute of Technology; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1269
• 发表日期: 2017
• 页码: 2862-2906
• 关键词: RISK-SENSITIVE CONTROL; differential-games; stochastic-control; networks; criteria; systems

摘要

A multi-class single-server queueing model with finite buffers, in which scheduling and admission of customers are subject to control, is studied in the moderate deviation heavy traffic regime. A risk-sensitive cost set over a finite time horizon [0, T] is considered. The main result is the asymptotic optimality of a control policy derived via an underlying differential game. The result is the first to address a queueing control problem at the moderate deviation regime that goes beyond models having the so-called pathwise minimality property. Moreover, despite the well-known fact that an optimal control over a finite time interval is generically of a nonstationary feedback type, the proposed policy forms a stationary feedback, provided T is sufficiently large.