Representations of phase type distributions and their applications in stochastic modelling

相型分布的表示及其在随机建模中的应用

• 批准号: 203546-2007
• 负责人: He, QiMing
• 金额: $ 1.35万
• 依托单位: Dalhousie University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2008
• 资助国家: 加拿大
• 起止时间: 2008-01-01 至 2009-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=392856
• 关键词: Representations; phase; type; distributions; their

Performance analysis and optimal design of stochastic systems whose state space has a large number of states can be challenging problems. This is known as the "curse of dimensionality" problem common to queueing models, inventory models, and supply chains. The main issue at stake is computational efficiency. A number of approaches such as the state space reduction, approximation, and decomposition have been introduced to solve the problems. However, there is no universally effective method. Thus, there is a need to look for new solution methods. Following the state space reduction approach, we propose to study PH-representations of phase-type (PH) distributions and to develop efficient algorithms for computing minimal, simple, or specially structured PH-representations for PH-distributions.

状态空间具有大量状态的随机系统的性能分析和优化设计可能是具有挑战性的问题。这被称为排队模型、库存模型和供应链中常见的“维数灾难”问题。主要问题是计算效率。人们引入了状态空间缩减、近似和分解等多种方法来解决这些问题。 然而，没有普遍有效的方法。因此，需要寻找新的解决方法。遵循状态空间缩减方法，我们建议研究相型 (PH) 分布的 PH 表示，并开发有效的算法来计算 PH 分布的最小、简单或特殊结构的 PH 表示。