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和本研究员开发了一种新的和广泛适用的大偏差理论方法。 在这种方法中，大偏差理论的许多方面都归结为概率测度的弱收敛理论。 这项研究对待新的应用程序，这种弱收敛的方法，一些重要的问题。 该方法还产生了几个计算问题，目前正在调查中。 应用领域包括一般的排队网络和统计力学中的几个模型。 大偏差理论是概率研究的一个重要领域，它在统计学、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和本研究员开发了一种新的和广泛适用的大偏差理论方法。 这种方法可以提供新的见解大偏差现象，并允许研究人员计算确定的理论的准确性。 的一个主要应用领域将是排队系统，这是在计算机网络建模中出现的。

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.