Computational Methods in Markov Chains

马尔可夫链中的计算方法

• 批准号: 9413309
• 负责人: Carl Meyer
• 金额: $ 20.23万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-01 至 1999-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9413309&HistoricalAwards=false
• 关键词: Computational; Methods; Markov; Chains

This project emphasizes practical as well as theoretical aspects surrounding the application and implementation of algorithms for computing stationary probabilities of discrete Markov chains. Special attention is devoted to applications in which discrete models are used to understand and analyze the dynamics of large systems comprised of a collection of loosely coupled subsystems such as in the study of queuing models and networks, telecommunications, computer performance evaluation, stochastic automata networks, and economic modeling and forecasting. Algorithmic facets concern the development and analysis of parallel multilevel methods based on aggregation/disaggregation techniques---both direct and iterative--- and some of these techniques are applied to problems involving stochastic automata networks. An architectural aspect involves the identification of features of vector and parallel computers that are best suited for implementing Markov chain algorithms. Theoretical components involve studying properties of Markov chains. These ideas are then used to generate error analyses aimed at understanding the convergence and stability properties of multilevel aggregation/disaggregation algorithms.

该项目强调实用性， 围绕算法的应用和实现的理论方面 用于计算离散马尔可夫链的平稳概率。 特别 注意力集中在离散模型用于 理解和分析由一个 松散耦合的子系统的集合，例如在排队模型的研究中 网络、电信、计算机性能评估、 随机自动机网络，经济建模和预测。 数学方面涉及并行多级方法的发展和分析 基于聚合/分解技术-直接和 迭代-其中一些技术适用于涉及 随机自动机网络架构方面涉及标识 矢量和并行计算机的功能，最适合 实现马尔可夫链算法。 理论部分涉及研究 马尔可夫链的性质这些想法被用来 生成旨在理解收敛性和稳定性的误差分析 多级聚集/解聚算法的性质。