An escape-time criterion for queueing networks: Asymptotic risk-sensitive control via differential games

• 成果类型: Article
• 署名作者: Atar, R; Dupuis, P; Shwartz, A
• 署名单位: Technion Israel Institute of Technology; Brown University
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.28.4.801.20514
• 发表日期: 2003
• 页码: 801-835
• 关键词: robust; DYNAMICS

摘要

We consider the problem of risk-sensitive control of a stochastic network. In controlling such a network, an escape-time criterion can be useful if one wishes to regulate the occurrence of large buffers and buffer overflow. In this paper a risk-sensitive escape time criterion is formulated, which in comparison to the ordinary escape-time criteria penalizes exits that occur on short time intervals more heavily. The properties of the risk-sensitive problem are studied in the large buffer limit and related to the value of a deterministic differential game with constrained dynamics. We prove that the game has value and that the value is the (viscosity) solution of a PDE. For a simple network, the value is computed, demonstrating the applicability of the approach.