Mathematical Sciences: Asymptotic and Singular Pertubation Techniques with Applications

本研究将继续应用渐近 方法，以帮助在不同类型的性能评估 例如，大型网络，交互式网络， 计算机系统和通信网络。 这些渐近 方法允许人们估计性能标准，即使当 没有精确解，近似解 它们提供的数据往往非常准确， 简单情况下的精确解和数值模拟。 大多数人不喜欢排队等候。 以更一般的 从某种意义上说，这种“等待问题”经常发生在计算机中， 通信系统。 例如，当你做一个长 电话公司的计算机可能不得不把 如果有大量呼叫， 正在进行中 取决于如何 有效的电话系统能够优先考虑您的电话， 您可能无法完成通话，或者您可能会听到 消息通知您再试一次。 类似的问题出现时， 计算机相互“交谈”：如果数据的传输不 那么数据的传输要么减慢， 或完全停止。 通过这项研究，校长 研究者将使用近似技术提供 估计各种计算机和通信的等待时间 系统.

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.