Introduction to Discrete Event Systems, Second Edition
Introduction to Discrete Event Systems, Second Edition
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DOI：
10.1007/978-0-387-68612-7
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
C. Cassandras;S. Lafortune
中科院分区：
文献类型：
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作者：
C. Cassandras;S. Lafortune
在阅读了前面的所有章节之后，读者会很自然地得出这样的结论：DES本质上是复杂的，很难分析，不管采用什么样的建模框架。我们也很自然地想知道DES中是否有任何性质可以用来开发分析、设计和控制的数学技术。在第一章中，我们看到，具有事件驱动动力学的系统不能通过微分（或差分）方程建模，这使得我们没有足够的数学工具来分析它们的行为。在Chaps。2-5，我们开发了一些模型，定时和不定时。虽然这些模型确实增强了我们对DES的理解，并为我们的分析提供了坚实的基础，但我们不能不注意到，它们涉及到相当复杂的符号，有时甚至是复杂的定义。事实上，这些模型的复杂性是如此之大，以至于为了对随机DES进行任何可管理的分析，我们被迫在第二章中。7-9，处理特殊类的马尔可夫链。即使在这个类，简单的公式在封闭形式是很难得到的;在第一章。8，我们看到，在一些简单的稳态系统之外，分析变得非常复杂。这种复杂性导致离散事件模拟成为目前研究DES，特别是随机DES的唯一通用工具。但是，正如我们在Chapter中看到的那样。10、仿真有其自身的局限性。首先，它是基于统计实验的，而统计实验的有效性必须始终被检查;例如，我们看到，在寻求稳态性能指标的估计时，选择模拟运行的长度的问题远非简单。其次，即使有了新一代非常快的计算机，模拟仍然是一种缓慢而昂贵的方法，当然不适合实时应用。在系统的设计或控制中，人们面临的一个典型问题是确定性能如何作为某个参数θ的函数而受到影响。在没有J（θ）形式的解析表达式的情况下，其中J（θ）是性能度量，人们被迫重复模拟系统，对于每个感兴趣的θ值至少一次。很容易看出，对于θ实际上是一个参数向量，或者可能是一系列待探索的替代设计或控制策略的复杂系统，这是一个多么乏味的过程。
After going through all the previous chapters, it would be natural for readers to conclude that DES are inherently complex and hard to analyze, regardless of the modeling framework adopted. It would also be natural to wonder whether there are any properties at all in DES that we can exploit in our effort to develop mathematical techniques for analysis, design, and control.In Chap.1, we saw that systems with event-driven dynamics cannot be modeled through differential (or difference) equations, leaving us with inadequate mathematical tools to analyze their behavior. In Chaps. 2–5, we developed a number of models, both timed and untimed. Although these models certainly enhance our understanding of DES and give us solid foundations for analysis, one cannot help but notice that they involve rather elaborate notation and sometimes intricate definitions. In fact, the complexity of these models was such that in order to proceed with any manageable analysis of stochastic DES we were forced, in Chaps. 7–9, to work with the special class of Markov chains. Even within this class, simple formulae in closed form are hard to come by; in Chap. 8, we saw that outside some simple queueing systems at steady state, analysis becomes extremely complicated. This complexity has led to discrete-event simulation as the only universal tool at this point for studying DES, especially stochastic ones. However, as we saw in Chap. 10, simulation has its own limitations. First, it is based on statistical experiments whose validity must always be checked; we saw, for example, that the problem of selecting the length of simulation runs in seeking estimates of steady-state performance measures is far from simple. Second, even with a new generation of very fast computers, simulation remains a slow and costly approach, certainly not suited for real-time applications. A typical problem one faces in the design or control of a system is that of determining how performance is affected as a function of some parameter θ. In the absence of analytical expressions of the formJ(θ), whereJ(θ) is a performance measure, one is forced to simulate the system repeatedly, at least once for each value of θ of interest. It is easy to see how tedious a process this becomes for complex systems where θ is in fact a vector of parameters or perhaps a list of alternative designs or control policies to be explored.