Section 2.1: Lehmer Random Number Generators: Introduction
Section 2.1: Lehmer Random Number Generators:
Introduction
Discrete-Event Simulation: A First Course
c 2006 Pearson Ed., Inc.
Discrete-Event Simulation: A First Course
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Section 2.1: Lehmer Random Number Generators: Introduction
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Section 2.1: Lehmer Random Number Generators:
Introduction
ssq1 and sis1 require input data from an outside source
The usefulness of these programs is limited by amount of
available data
What if more data needed?
What if the model changed?
What if the input data set is small or unavailable?
A random number generator address all problems
It produces real values between 0.0 and 1.0
The output can be converted to random variate via
mathematical transformations
Discrete-Event Simulation: A First Course
Section 2.1: Lehmer Random Number Generators: Introduction
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Random Number Generators
Historically there are three types of generators
table look-up generators
hardware generators
algorithmic (software) generators
Algorithmic generators are widely accepted because they meet
all of the following criteria:
randomness - output passes all reasonable statistical tests of
randomness
controllability - able to reproduce output, if desired
portability - able to produce the same output on a wide variety
of computer systems
efficiency - fast, minimal computer resource requirements
documentation - theoretically analyzed and extensively tested
Discrete-Event Simulation: A First Course
Section 2.1: Lehmer Random Number Generators: Introduction
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Algorithmic Generators
An ideal random number generator produces output such that
each value in the interval 0.0 < u < 1.0 is equally likely to
occur
A good random number generator produces output that is
(almost) statistically indistinguishable from an ideal generator
We will construct a good random number generator satisfying
all our criteria
Discrete-Event Simulation: A First Course
Section 2.1: Lehmer Random Number Generators: Introduction
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Conceptual Model
Conceptual Model:
Choose a large positive integer m. This defines the set
Xm = {1, 2, . . . , m ? 1}
Fill a (conceptual) urn with the elements of Xm
Each time a random number u is needed, draw an integer x
at random from the urn and let u = x/m
Each draw simulates a sample of an independent identically
distributed sequence of Uniform(0, 1)
The possible values are 1/m, 2/m, . . . , (m ? 1)/m.
It is important that m be large so that the possible values are
densely distributed between 0.0 and 1.0
Discrete-Event Simulation: A First Course
Section 2.1: Lehmer Random Number Generators: Introduction
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