Mathematical Sciences: Asymptotic and Singular Pertubation Techniques with Applications

点击翻译按钮获取中文摘要

This research will continue the application of asymptotic methods to aid in the performance evaluation of different types of queueing systems, such as large queueing networks, interactive computer systems and communication networks. These asymptotic methods allow one to estimate performance criteria even when an exact solution is not available, and the approximate answers they provide are very often highly accurate when compared to exact solutions for simpler cases and numerical simulations. Most people do not enjoy waiting in line. In a more general sense, such "waiting problems" occur frequently in computer and communication systems. For example, when you make a long distance call the telephone company's computers may have to put your call into a waiting line if there is a large number of calls in progress at the time of your call. Depending upon how efficiently the phone system is able to prioritize your call you may be able to complete your call or you may hear a recorded message informing you to try again. Similar problems arise when computers "talk" to each other: if the queueing of data is not done properly then the transmission of data is either slowed down or stopped completely. With this research the principal investigator will use approximation techniques to provide estimates of waiting times in various computer and communication systems.