CS457 - System Performance Evaluation - Winter 2010


Public Service Announcements

  1. Mid-term Examination: February 23rd, 16.30 at 18.00 in PHY145.
  2. Assignment 3.

Lecture 19 - A Final Simulation Example

Processor Sharing

Time-slicing model: pre-emptive multi-tasking

For example, three classes of jobs

  1. Jobs with active I/O: long think times, very little processing
  2. Interactive jobs without active I/O: substantial processing that will stop and start at widely spaced times
  3. Batch jobs: which go on for very long times.

Single server, three queues, needs a scheduling algorithm (discipline)

Important state

Initialization

Arrival

Departure

Start-service

Something is unrealistic about this model. What is it?

Something is unintuitive about this model. What is it?

This is always the case.


Random Variables

The mathematical foundation for random number is the random variable, which is a variable that has different values on different occasions.

  1. A probability distribution determines what values a random variable gets, and how often
  2. Discrete versus continuous random variables
  3. We usually assume that the random variables we want are independent and identically distributed (iid or IID).
  4. Most random variables we use have underlying distributions that are non-negative.
  5. Random variables are normally written as capitals.

Random variable concepts

  1. Cumulative distribution function (cdf or CDF):
  2. Probability density function (pdf or PDF):
  3. Probability mass function (pmf or PMF):

In discrete event simulation we model quantities like interarrival time or service time as IID random variables.

As a result we need to generate random variables from random number generators.

Random variables with arbitrary distributions

A random variable is uniquely defined by its CDF, F(x).

Examples of Discrete Distributions

  1. Bernoulli
  2. Discrete uniform
  3. Geometric Discrete
  4. Binomial

Poisson


Return to: