Pattern Time Distributions and Their Applications

这项研究项目致力于在各种涉及偶然性的模型中，寻找有效的通用技术来确定预期时间，直到罕见事件发生。因为直到这些事件发生的时间的概率分布通常具有很大的方差，直接的模拟通常不是有效的；因为状态描述通常是多维的，所以标准的马尔可夫方法通常也不能实现。利用更新理论的思想，以及新开发的减少方差的模拟技术，在以前的拨款资助的研究中，开发了有效的方法来寻找观察随机数据时罕见模式发生的预期时间。在前人研究的基础上，本项目建议考虑更一般随机过程的罕见事件，例如多服务台排队系统的工作量超过其承载能力的预期时间。此外，当局亦会研究防止系统变得过于挤迫的方法，有时会阻止新来港人士加入该系统。这方面的例子是排队模型，在排队模型中，潜在的到达首先呈现给看门人，该看门人必须决定是否允许该到达加入系统，通常具有关于系统中当前客户数量的有限信息。还将确定用于研究特定类别可靠性模型的小系统故障概率的有效模拟程序。灾难性的事件，如生产过程中断、核电站脱机或电信系统因超载而崩溃，往往是罕见的事件。如果成功，这项研究将大大有助于使工业用户能够有效地确定在目前的运营政策下发生此类事件的时间的概率分布。此外，还将确定防止此类系统崩溃的更有效的运营政策。

This research project is concerned with finding efficient general techniques for determining the expected time until a rare event occurs in a variety of models involving chance. Because the probability distributions of the times until such events occur usually have large variances, straightforward simulations are typically not efficient; because the state description is usually multidimensional, standard Markov methods also typically cannot be implemented. Using ideas from renewal theory, along with newly developed variance reducing simulation techniques, efficient ways of finding the expected time for a rare pattern to occur when observing random data were developed in previous grant supported research. Building on these previous studies, this project proposes to consider rare events of more general stochastic processes, such as the expected time until the workload of a multiple server queuing system exceeds its carrying capacity. In addition, methods to keep a system from becoming too congested by sometimes blocking new arrivals from joining the system will also be studied. Examples of this are queuing models in which a potential arrival first presents itself to a gatekeeper who must decide, usually with limited information about the number of customers presently in the system, whether to allow that arrival to join the system. Efficient simulation procedures for studying small system failure probabilities for specific classes of reliability models will also be determined. Catastrophic events such as when a production process breaks down, or a nuclear power plant goes off-line, or a telecommunication system crashes because of overload, tend to be rare events. If successful this research will go a long way towards enabling industrial users to efficiently determine the probability distribution of the time until such events occur under present operating policies. In addition, more efficient operating policies that keep such systems from crashing will be determined.