Mathematical Sciences: Presidential Young Investigator

排队模型广泛应用于计算机性能评价、通信网络和交通调度等领域。排队系统可以用随机过程来描述，因为顾客的到达时间可以看作是随机变量。本课题致力于研究近似于随机模型的扩散方程。特别是，将开发一种用于获得多维扩散方程的近似解的射线技术和适用于原始离散模型的类似技术。

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.