Representations of phase type distributions and their applications in stochastic modelling

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是一个具有挑战性的问题。这就是排队模型、库存模型和供应链中常见的“维度诅咒”问题。关键的问题是计算效率。引入了状态空间约简、近似和分解等方法来解决这些问题。然而，并没有普遍有效的方法。因此，有必要寻找新的解决方法。根据状态空间约简方法，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。

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.