A Differential Game 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: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2016.0780
• 发表日期: 2016
• 页码: 1354-1380
• 关键词: RISK-SENSITIVE CONTROL

摘要

We study a differential game that governs the moderate-deviation heavy-traffic asymptotics of a multiclass single-server queueing control problem with a risk-sensitive cost. We consider a cost set on a finite but sufficiently large time horizon, and show that this formulation leads to stationary feedback policies for the game. Several aspects of the game are explored, including its characterization via a (one-dimensional) free boundary problem, the semi-explicit solution of an optimal strategy, and the specification of a saddle point. We emphasize the analogy to the well-known Harrison-Taksar free boundary problem which plays a similar role in the diffusion-scale heavy-traffic literature.