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所在平台: Coursera |
课程主页: https://www.coursera.org/learn/quantitative-formal-modeling-1
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课程名称：定量形式建模与最坏情况性能分析 课程概述：欢迎参加定量形式建模与最坏情况性能分析课程。在本课程中，您将学习如何以理论计算机科学中流行的方式建模和解决性能问题，并训练您的抽象思维能力。完成本课程后，您将学会从标记的生产和消费角度思考系统行为，并能够用前缀序和计数函数的数学形式化这种思维。您将学习到彼得里网（Petri-nets）、定时和标记消费/生产系统的调度，以及对于一种特殊类别的彼得里网（称为单速数据流图），您将学会如何对基本性能指标（如吞吐量、延迟和缓冲）进行最坏情况分析。 免责声明：虽然课程中有大量小示例，但起初并未讨论许多工业规模的系统。其原因有二：首先，我并不打算教授您达到工业水平的性能分析技能，而是希望您能够一般性地、抽象地思考建模和性能分析，正是这种能力在未来面对任何性能分析问题时最为重要。其次，尽管数据流技术在工业中具有应用，但单速数据流这一子类过于限制，无法在大型建模示例中实际使用。然而，其他数据流技术的分析原则均基于单速数据流。因此，本课程是任何相关高级课程的良好基础。 课程大纲： 第一部分：将系统建模为标记消费/生产系统 在本模块中，您将学习绘制标记消费/生产系统的模型，并能够以非正式的方式与他人进行交流。您将能够绘制自己的模型，并用通用术语解释它们，同时了解标准彼得里网的消费/生产系统解释。 第二部分：语法与语义 本模块将进一步训练您的抽象思维能力。您将学会将任何动态系统的行为形式化为前缀序，并将消费/生产系统的解释形式化为该前缀序上的计数函数。您会了解彼得里网解释对这些计数函数施加的限制，以及如何利用这些限制来证明彼得里网解释的属性。 第三部分：性能分析 在本模块中，您将学习如何利用单速数据流图的结构对性能指标（如吞吐量、延迟和缓冲）进行最坏情况分析。您将学会计算数据流图的最大周期平均值，构建其周期调度，优化调度以分析延迟，并确定保持最坏情况分析有效的缓冲区大小。 第四部分：最后一个示例 在最后一周中，我们将讨论一个示例，总结到目前为止所学的知识，并提供一些额外的阅读材料，以激发进一步探索的兴趣。
Part: 1
Title:Modeling systems as token consumption/production systems
Description:In this module/week you will learn to draw a model of a token consumption/production system, and communicate your interpretation of this model with others in an informal manner. At the end of this model, you will be able to draw your own models, and explain your interpretation of them in general terms. Also, you will know about the standard Petri-net interpretation of consumption/production systems, and will be able to point out particular patterns in Petri-net models. Finally, you will be able to refine a consumption/production model into a model that contains sufficient information to allow worst-case performance analysis. This is all tested using a peer-reviewed assignment.
Part: 2
Title:Syntax and semantics
Description:In this module/week, you will be really training your abstract thinking skills. After finishing this module, you will have learned how to formalize the behavior of any dynamical system as a prefix order, and how to formalize the interpretation of a consumption/production system as a counting function on such a prefix order. You understand how the Petri-net interpretation puts certain restrictions on these counting functions, and how you can exploit those restrictions to prove properties about Petri-net interpretations, without knowing the actual interpretation itself. At the end of the module, you will practice the formalization of performance metrics as logical properties of counting functions, by recognizing right and wrong examples of formalization.
Part: 3
Title:Performance analysis
Description:In this module/week you will learn to exploit the structure of single-rate dataflow graphs to perform worst-case analysis of performance metrics like throughput, latency and buffering. After this week, you know how to calculate the maximum cycle mean of a dataflow graph, how to construct a periodic schedule for it, how to optimize this schedule for latency analysis, and how to determine the size of buffers with back-pressure such that the worst-case analysis remains valid. If you understood the material of the previous module/week, the proofs presented in this week will give you a deeper understanding of the mathematical underpinning of these methods.
Part: 4
Title:One final example
Description:In this last week, we just discuss one more example, following the outline of the peer-reviewed assignment of the first module/week. It's just a little summary, combining everything we have learned so far, and there is some additional reading material to trigger an appetite for further discovery.
Welcome to Quantitative Formal Modeling and Worst-Case Performance Analysis. In this course, you will learn about modeling and solving performance problems in a fashion popular in theoretical computer science, and generally train your abstract thinking skills. After finishing this course, you have learned to think about the behavior of systems in terms of token production and consumption, and you are able to formalize this thinking mathematically in terms of prefix orders and counting functions. You have learned about Petri-nets, about timing, and about scheduling of token consumption/production systems, and for the special class of Petri-nets known as single-rate dataflow graphs, you will know how to perform a worst-case analysis of basic performance metrics, like throughput, latency and buffering. Disclaimer: As you will notice, there is an abundance of small examples in this course, but at first sight there are not many industrial size systems being discussed. The reason for this is two-fold. Firstly, it is not my intention to teach you performance analysis skills up to the level of what you will need in industry. Rather, I would like to teach you to think about modeling and performance analysis in general and abstract terms, because that is what you will need to do whenever you encounter any performance analysis problem in the future. After all, abstract thinking is the most revered skill required for any academic-level job in any engineering discipline, and if you are able to phrase your problems mathematically, it will become easier for you to spot mistakes, to communicate your ideas with others, and you have already made a big step towards actually solving the problem. Secondly, although dataflow techniques are applicable and being used in industry, the subclass of single-rate dataflow is too restrictive to be of practical use in large modeling examples. The analysis principles of other dataflow techniques, however, are all based on single-rate dataflow. So this course is a good primer for any more advanced course on the topic. This course is part of the university course on Quantitative Evaluation of Embedded Systems (QEES) as given in the Embedded Systems master curriculum of the EIT-Digital university, and of the Dutch 3TU consortium consisting of TU/e (Eindhoven), TUD (Delft) and UT (Twente). The course material is exactly the same as the first three weeks of QEES, but the examination of QEES is at a slightly higher level of difficulty, which cannot (yet) be obtained in an online course.
