Brownian Control Problems for a Multiclass M/M/1 Queueing Problem with Model Uncertainty

• 成果类型: Article
• 署名作者: Cohen, Asaf
• 署名单位: University of Haifa
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.2018.0944
• 发表日期: 2019
• 页码: 739-766
• 关键词: controlled stochastic networks; optimality; queues

摘要

We consider a multidimentional Brownian control problem (BCP) with model uncertainty that formally emerges from a multiclass M/M/1 queueing control problem under heavy traffic with model uncertainty. The BCP is formulated as a multidimensional stochastic differential game with two players: a minimizer who has an equivalent role to the decision maker in the queueing control problem and a maximizer whose role is to set up the uncertainty of the model. The dynamics are driven by a Brownian motion. We show that a state-space collapse properly holds. That is, the multidimensional BCP can be reduced to a one-dimensional BCP with model uncertainty that also takes the form of a two-player stochastic differential game. Then, the value function of both games is characterized as the unique solution to a free-boundary problem from which we extract equilibria for both games. Finally, we analyze the dependence of the value function and the equilibria on the ambiguity parameters.