Pattern Time Distributions and Their Applications

点击翻译按钮获取中文摘要

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.