Semi-Markov processes (SMPs) provide a rich framework for many real-world problems. However, due to difficulty implementing practical solutions they are rarely used with their full capability. The theory of SMPs is quite mature but was mainly developed at a time when computational resources were not widely available. With the exception of some of the simplest cases, solutions to SMPs are inherently numerical, and SMPs have been underutilized by practitioners because of difficulty implementing the theory in applications. This paper demonstrates the theory and computational methods needed to implement SMP models in practical settings. Methods are illustrated with an application modeling the movement of coronary patients in a hospital. Our aim is to allow practitioners to use richer SMP models without being burdened with the rigorous mathematical theory.
翻译：半马尔科夫进程(SMPs)为许多现实世界问题提供了一个丰富的框架。然而,由于难以实施实际解决方案,它们很少能完全使用。SMPs理论相当成熟,但主要是在计算资源不普遍的情况下开发的。除了一些最简单的案例外,SMPs的解决方案本质上是数字性的,而SMPs由于在应用中难以应用该理论,从业人员对SMPs的利用不足。本文件展示了在实际环境中实施SMP模型所需的理论和计算方法。方法通过在医院对冠状病人的移动进行应用模型示范来说明。我们的目标是允许开业者使用更丰富的SMP模型,而无需严格的数学理论负担。
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