Mathematical Sciences: Research in Large Deviations, Queueing Networks, and Statistical Mechanics

在最近的工作中，布朗大学的Paul Dupuis和这位研究者提出了一种新的、广泛适用的方法来研究大偏差理论。在这种方法中，大偏差理论的许多方面被简化为概率测度的弱收敛理论。本研究讨论了这种弱收敛方法在一些重要问题上的新应用。该方法还引起了几个目前正在研究的计算问题。应用领域包括一般类别的排队网络和统计力学中的几个模型。大偏差理论是概率论研究的一个重要领域，在统计学、统计力学和排队论等许多领域都有应用。在最近的工作中，布朗大学的Paul Dupuis和这位研究者提出了一种新的、广泛适用的方法来研究大偏差理论。这种方法可以为大偏差现象提供新的见解，并允许研究人员通过计算确定理论的准确性。一个主要的应用领域将是排队系统，它出现在计算机网络的建模中。

In recent work a new and widely applicable approach to the theory of large deviations has been developed by Paul Dupuis of Brown University and this investigator. In this approach many aspects of the theory of large deviations are reduced to the theory of weak convergence of probability measures. This research treats new applications of this weak convergence approach to a number of important problems. The method also gives rise to several computational questions that are currently under investigation. Areas of application include a general class of queuing networks and several models in statistical mechanics. The theory of large deviations is an important area of probabilistic research having applications to a number of areas including statistics, statistical mechanics, and queuing theory. In recent work a new and widely applicable approach to the theory of large deviations has been developed by Paul Dupuis of Brown University and this investigator. This approach may give new insight into large deviation phenomena and allow researchers to determine computationally the accuracy of the theory. A main area of application of will be to queuing systems, which arise in the modeling of computer networks.