SYSC40055001 simulation project
You will need to develop the simulation modules in part b) of this document. You will
need to learn about traffic generation before developing the modules. This is done in the
following part.
a) Traffic generation
We will need traffic generators for the arrival processes and the service time
distributions. As such we will always assume Poisson arrivals (i.e. interarrival times are
exponentially distributed random variables with parameter
λ)
and service times will be
assumed to be exponential random variables with parameter
µ
. Hence, you will need to
build a traffic routine that generates exponentially distributed random variates! This can
be used for generating the arrival events and service completion events.
We will need to see the effect of the correlation in the interarrival times on the
simulation output. Hence, your generator should be able to generate random variables
with adjustable autocorrelation. I would recommend to read the “Paper on
Transform
Expand Sample (TES)” that is posted on the web site in the project area. I will summarize
the paper in the next section. The methodology outlined in the paper will be used to
generate correlated exponentially distributed random variables.
a1) Summary of the TES modeling methodology
This methodology will enable you to generate random variables with adjustable
correlation. It is based on the following steps:
1.
Create a series of
random numbers U
n
that are uniformly distributed in [0,1) and
are correlated. This can be done recursively as follows:
U
n+1
=< U
n
+ V
n+1
>, n=0,1,2,….
.
Where the initial condition U
0
is a random number in [0,1) and <.> denotes the
modulo1 operation as described in the paper. V
n
is a series of independent and
identically distributed random variables. We will generate these variables using the
uniform distribution f
V
(v) shown below:
You should generate the series V
n
. Furthermore, you should read and understand
from the paper that the numbers U
n
will be uniformly distributed in [0,1) and they are
furthermore correlated. In particular the correlation increases when the a
,b
come close to
v
a
b
.5
.5
1/(a+b)
f
V
(v)
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View Full Documenteach other! Furthermore, when a=b=0.5 (i.e. V
n
are uniform in [0.5,0.5) then the
numbers
U
n
become independent and uniformly distributed in [0,1). Hence, the
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 Spring '10
 LAMBADARIS
 Probability theory, Exponential distribution, Cumulative distribution function

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