一种基于微分对策的渐进风险敏感控制
An escape time criterion for queueing networks: Asymptotic risk-sensitive control via differential games
摘要：
考虑随机网络的风险敏感控制问题。在控制这样的网络时，如果希望调节大缓冲区和缓冲区溢出的发生，则逃逸时间标准可以是有用的。本文提出了一种风险敏感的逃逸时间准则，与普通逃逸时间准则相比，该准则对短时间间隔内发生的退出惩罚更重。在大缓冲区限制下研究了风险敏感问题的性质，并将其与具有约束动力学的确定性微分对策的值联系起来。我们证明了游戏有价值，价值是（粘度）解决方案的偏微分方程。对于一个简单的网络，计算值，证明了该方法的适用性。
英文摘要：
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 which 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.
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