On the optimality of threshold control in queues with model uncertainty
On the optimality of threshold control in queues with model uncertainty
复制标题
模型不确定性队列阈值控制的最优性
DOI：
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发表时间：
2010
期刊：
影响因子：
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通讯作者：
J. Shanthikumar
中科院分区：
文献类型：
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作者：
A. Jain;Andrew E. B. Lim;J. Shanthikumar
我们考虑一个单阶段排队系统，其中到达和离开由具有随机强度的点过程建模。到达会产生成本，而离开会产生收入。其目标是通过控制强度受容量限制和持有成本的利润最大化。当到达和离开过程的随机模型是完全已知的，那么阈值策略是已知的最优。很多时候，由于缺乏足够的校准数据或不准确的假设，到达和离开过程不能准确地建模和控制。证明了在极大极小鲁棒模型下，当过程中的不确定性由相对熵表征时，阈值策略是最优的。我们的模型概括了相对熵的标准概念，以解释到达和离开过程中不同程度的模型不确定性。我们还研究了不确定性水平对最优阈值控制的影响。
We consider a single-stage queuing system where arrivals and departures are modeled by point processes with stochastic intensities. An arrival incurs a cost, while a departure earns a revenue. The objective is to maximize the profit by controlling the intensities subject to capacity limits and holding costs. When the stochastic model for arrival and departure processes are completely known, then a threshold policy is known to be optimal. Many times arrival and departure processes can not be accurately modeled and controlled due to lack of sufficient calibration data or inaccurate assumptions. We prove that a threshold policy is optimal under a max–min robust model when the uncertainty in the processes is characterized by relative entropy. Our model generalizes the standard notion of relative entropy to account for different levels of model uncertainty in arrival and departure processes. We also study the impact of uncertainty levels on the optimal threshold control.