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Dr. I-Shyan Hwang Computer Science and Engineering Yuan-Ze University Sept. 14, 2005

Modeling and Performance Evaluation with Computer Science Applications – Probability, Markov Chains & Queuing Networks. Dr. I-Shyan Hwang Computer Science and Engineering Yuan-Ze University Sept. 14, 2005. Prelude.

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Dr. I-Shyan Hwang Computer Science and Engineering Yuan-Ze University Sept. 14, 2005

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  1. Modeling and PerformanceEvaluation with Computer Science Applications – Probability, Markov Chains & Queuing Networks Dr. I-Shyan Hwang Computer Science and Engineering Yuan-Ze University Sept. 14, 2005

  2. Prelude • As computer and communication systems become more complex, system designers are increasingly called upon to locate information bottlenecks or create optimal systems for specific needs. • Performance modeling techniques have become an important tool for this type of work – and indispensable to anyone dealing with questions of reliability, availability and quality in operations, communications, and manufacturing.

  3. Examples • Computer scientists and engineers need powerful techniques to analyze algorithms and computer systems. • Networking engineers and need methods to analyze the behavior of protocols, routing algorithm and congestion in networks. • Communication networks between nodes will meet diverse traffic and contention from many sources: Ethernet, radio, fibre-optic. • High performance computing, supported by VLSI technology, has led to the development of parallel computer architectures.

  4. Essential of Probability Theory • Dealing with averages of mass phenomena occurring sequentially or simultaneously: telephone calls, radar detection, quality control, birth and death rates, and queuing theory,…. • Three steps in the applications of probability 1. Observation. 2. Deduction. 3. Prediction.

  5. Markov Chains • Markov processes provide very flexible, powerful and efficient means for the description and analysis of dynamic system properties. • Markov processes constitute a special, perhaps the most important, sub-class of a stochastic processes – a generalization of the concept of random variables, which provides a relation between the elements of a possibly infinite family of random variables. • Markov processes constitute the fundamental theory underlying the concept of queueing systems.

  6. Queues • Queues of some sort are central in the majority of models on computer and other communication systems, which represent contention for a source. • Any queue consists of three components: an arrival process which determines when customers arrive at the queue and possibly what their characteristic are, a buffer or waiting room where customers wait to be served and a service time requirement for each customer at the server serving the queue. (queue length = waiting room + service time

  7. Analytical Model vs. Simulation • The established analytical model must be verified by simulation. • Most real-world systems are too complex to allow realistic models to be evaluated analytically, and these model must be studied by means of simulation. • In a simulation, we use a computer to evaluate a model numerically, and data are gathered to estimate the desired true characteristics of the model.

  8. Other possible methodologies • AI – Fuzzy, Neural, GA, …

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