Simulation Modules

# Simulation Modules - SYSC4005-5001 simulation project You...

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SYSC4005-5001 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. inter-arrival 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 inter-arrival 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 modulo-1 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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each 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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Simulation Modules - SYSC4005-5001 simulation project You...

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