Asymptotic Analysis of Queueing Systems under Uncertainty

排队论是研究排队问题的应用概率和运筹学的一个分支。这一领域的研究受到现实应用的启发，在现实应用中，可以根据预测的等待时间分配资源，例如在呼叫中心，医疗保健和云计算中。传统上，在受控随机问题中，假设底层随机模型的参数是已知的。在这个项目中，研究者将通过假设模型参数未知的更现实的情况来解释不确定性。该项目将产生易于实施和广泛适用于不确定性下的网络模型的策略，这将导致更好的性能和资源利用率。此外，该项目旨在为这些问题开发新的数学工具和技术。该项目中的模型源于现实世界的问题，其结果将影响应用概率和运筹学。本研究计画将支援弱势族群，并训练研究生与本科生。本研究计画是在交通繁忙且模型参数不确定的情况下，对受控行车系统进行渐近分析。两种类型的不确定性被认为是：贝叶斯和贝叶斯。在Boghtian的情况下，决策者认为最坏情况下的标准是最小化，考虑到一类模型。渐近分析是使用一个有限的随机博弈，其中所涉及的球员是决策者和对手的球员。在贝叶斯的情况下，决策者对模型的参数有一个先验的信念，通过观察系统不断更新。在这里，学习方面的优化问题是感兴趣的。勘探/开采性质表明与多武装土匪问题有关。研究目标是：（1）建立一个综合性的理论框架，将不确定性引入到扩散缩放的交通繁忙状态中，在捕获不确定性和鲁棒性之间进行平衡，并获得易于实施的政策;（2）考虑简单的政策，这些政策在没有不确定性的情况下是渐近最优的，并检查它们在不确定性下的性能;及（3）联合收割机以下研究方向：扩散理论，扩散近似，不确定性和学习，此外，该奖项反映了NSF的法定使命，并被认为是值得通过使用基金会的智力价值和更广泛的评估来支持的。影响审查标准。

Queueing theory is a branch of applied probability and operations research that studies waiting lines. The research in this field is well-motivated by real-life applications where resources can be allocated based on predicted waiting times, for example in call centers, health care, and cloud computing. Traditionally, in controlled queueing problems, it is assumed that the parameters of the underlying random models are known. In this project, the investigator will account for uncertainty by assuming the more realistic case where the parameters of the model are unknown. The project will generate policies that are easy to implement and broadly applicable for queueing network models under uncertainty, which will lead to better performance and resource utilization. Moreover, the project aims to develop new mathematical tools and techniques for these problems. The models in this project stem from real-world problems and the results will impact both applied probability and operations research. This research project will support under-represented minority groups and train both graduate and undergraduate students.This research project is on the asymptotic analysis of controlled queueing systems under heavy traffic with uncertainty about the parameters of the model. Two types of uncertainty are considered: Knightian and Bayesian. In the Knightian case, the decision-maker considers a worst-case criterion to be minimized by taking into account a class of models. The asymptotic analysis is performed using a limiting stochastic game, where the involved players are the decision-maker and an adversary player. In the Bayesian case, the decision-maker has a prior belief on the parameters of the model, which is continuously updated by observing the system. Here, the learning aspect of the optimization problems is of interest. The exploration/exploitation nature suggests a connection to multi-armed bandit problems. The research objectives are: (1) to develop a comprehensive theoretical framework that builds uncertainty about the queueing models into the diffusion scaling heavy traffic regime, balancing between capturing uncertainty and robustness, and attaining easy-to-implement policies; (2) to consider simple policies, which are known to be asymptotic optimal in the case without uncertainty, and to examine their performance under uncertainty; and (3) to combine the following streams of research: queueing theory, diffusion approximations, uncertainty, and learning, and moreover, to develop new mathematical results beyond what is known in each stream considered separately.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.