Theory and application of Markov modelling

在过去，我一直积极参与随机建模及其在计算机性能评估、呼叫中心和通信方面的应用。我主要研究确定性方法，也就是不依赖于随机数的方法。这迫使我使用马尔可夫系统，也就是说，未来只取决于当前状态的系统。我在这个领域的主要贡献之一是随机化方法，也称为均匀化。这种方法已经被其他人在处理广义随机petri网和类似产品的各种软件产品中实现，例如Möbius。另一种方法，即所谓的GTH （Grassmann/Taksar/Heyman）方法也被广泛使用。我们现在建议将我们的方法应用于几个应用领域，包括卫生应用。我已经用这个方法澄清了一些关于初始化偏差的问题。此外，还将研究有关模拟运行长度的一些问题。在这项研究中，我们依赖于我们之前发明的确定性方法来寻找马尔可夫事件系统的时间平均值的均值和方差。我也在研究将任意离散事件系统转换成马尔可夫链的方法。

In the past, I have been actively involved in stochastic modeling and its applications to computer performance evaluation, call centers and communication. I worked mainly with deterministic methods, that is, methods that do not rely on random numbers. This has forced me to use Markovian systems, that is, systems where the future only depends on the present state. One of my main contributions in this area has been the randomization method, also called uniformization. This method has been implemented by others in various software products dealing with generalized stochastic Petri-nets and similar products, such as Möbius. Another method, the so-called GTH (Grassmann/Taksar/Heyman) method is also widely used. We now propose to apply our methods in several application areas, including health applications. I have already applied this method to clarify some issues regarding the initialization bias. Also, a number of problems regarding the simulation run length will be investigated. In this research, we relied on deterministic methods we invented earlier to find means and variances of time averages for Markovian event systems. I am also working on methods to convert arbitrary discrete event systems into Markov chains.