Mathematical Sciences: Presidential Young Investigator

排队模型出现在计算机性能评估、通信网络和运输调度等多种应用中。排队系统可以用随机过程来描述，因为顾客到达的时间可以看作是随机变量。本课题旨在研究近似随机模型的扩散方程。特别地，一种射线技术获得近似解的多维扩散方程和类似的技术适用于原始离散模型将被开发。

Queueing models arise in diverse applications such as computer performance evaluation, communications networks and transportation scheduling. Queueing systems can be described by stochastic processes since customers' arrival times can be viewed as random variables. This project is to pursue the study of diffusion equations which approximate the stochastic model. In particular, a ray technique for obtaining approximate solutions to multi-dimensional diffusion equation and a similar technique applicable to the original discrete model will be developed.