Mathematical Sciences: Asymptotic and Singular Pertubation Techniques with Applications

这项研究将继续应用渐近方法来帮助评估不同类型的排队系统的性能，如大型排队网络、交互计算机系统和通信网络。这些渐近方法使人们即使在没有精确解的情况下也可以估计性能标准，并且与更简单情况和数值模拟的精确解相比，它们提供的近似解通常是非常准确的。大多数人不喜欢排队等候。在更广泛的意义上，这样的“等待问题”经常发生在计算机和通信系统中。例如，当您拨打长途电话时，如果在您通话时有大量呼叫正在进行，电话公司的计算机可能不得不将您的呼叫放入等待队列中。根据电话系统确定呼叫优先级的效率，您可能会完成呼叫，也可能会听到录音留言通知您重试。当计算机相互“对话”时，也会出现类似的问题：如果数据的排队不正确，那么数据的传输要么减慢，要么完全停止。在这项研究中，首席研究人员将使用近似技术来估计各种计算机和通信系统中的等待时间。

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.