Pattern Time Distributions and Their Applications

模式时间分布及其应用

• 批准号: 9901053
• 负责人: Sheldon Ross
• 金额: $ 26.03万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1999
• 资助国家: 美国
• 起止时间: 1999-06-15 至 2004-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9901053&HistoricalAwards=false
• 关键词: Pattern; Time; Distributions; Their; Applications

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.

这个研究项目关注的是寻找有效的通用技术，用于确定在各种涉及机会的模型中直到罕见事件发生的预期时间。 由于直到此类事件发生的时间的概率分布通常具有较大的方差，因此直接模拟通常效率不高;由于状态描述通常是多维的，因此标准马尔可夫方法通常也无法实现。 利用更新理论的思想，沿着与新开发的方差减少模拟技术，有效的方法，发现一个罕见的模式发生时，观察随机数据的预期时间在以前的补助金支持的研究。 基于这些以前的研究，本项目建议考虑更一般的随机过程的罕见事件，如多服务器排队系统的工作量超过其承载能力的预期时间。 此外，当局亦会研究一些方法，以避免系统变得过于挤塞，例如有时会阻止新来港人士加入系统。 这方面的例子是排队模型，其中一个潜在的到来首先提出自己的看门人必须决定，通常与有限的信息，目前在系统中的客户数量，是否允许该到达加入系统。 有效的模拟程序，研究小系统的故障概率为特定类别的可靠性模型也将被确定。 灾难性事件，如生产过程发生故障，或核电厂离线，或电信系统因过载而崩溃，往往是罕见的事件。 如果成功的话，这项研究将大大有助于使工业用户有效地确定时间的概率分布，直到这些事件发生在目前的经营政策。此外，还将确定更有效的操作政策，防止此类系统崩溃。