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

prelude
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.
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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.
essential of probability theory
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.

markov chains
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.
queues
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

analytical model vs simulation
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.
other possible methodologies
Other possible methodologies
  • AI – Fuzzy, Neural, GA, …