Modeling and Performance Evaluation with Computer Science Applications

1
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
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,