By Kardi Teknomo, PhD .

Monte Carlo Simulation Tutorial

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Monte Carlo Simulation based on Observational Data

This section of tutorial we will demonstrate how to generate random distribution and Monte Carlo Simulation based on the observation data.

Suppose we have a frequency relative based on observation of traffic in one leg of an intersection like this:



Frequency Relative


Go straight

500 vehicles/hour



Turn Left

200 vehicles/hour



Turn Right

300 vehicles/hour




1000 vehicles/hour


We want to generate random distribution based on the observation table above. Since random-distribution generation is inverse distribution, we can inverse the cumulative distribution above. The procedure is very simple: generate random number Monte Carlo Simulation Tutorial (that is according to standard uniform distribution) using computer, then

If Monte Carlo Simulation Tutorial , then generate "Go Straight"

If Monte Carlo Simulation Tutorial , then generate "Turn Left"

If Monte Carlo Simulation Tutorial , then generate "Turn Right"

Monte Carlo Simulation Tutorial

The observation distribution is generated using transformation of standard uniform distribution as shown in diagram above.

The MS excel worksheet for this example can be downloaded here

The results of this simple Monte Carlo simulation are some statistics and sampling distribution for each observation.

Monte Carlo Simulation Tutorial

Monte Carlo Simulation Tutorial

In the worksheet, 2000 data are generated for each experiment. One Monte Carlo Numerical experiment is a replication of the survey assuming that the observation sample is the correct representation of the data. You can make as many experiments as you like simply by pressing F9 continuously after you delete the STOP cell. To reset the counter, you may type any letter or number in that particular cell

Monte Carlo Simulation Tutorial

The worksheet is using iteration of Excel (no Macro inside). Before simulation, make sure that the iteration option ON and the calculation mode is set to Automatic. The maximum iteration is set to 1 (one) as shown in the figure below. That setting is in menu Tools-Options.

Monte Carlo Simulation Tutorial

The mean and variance of the results are computed using recursive average and recursive variance formula.

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This tutorial is copyrighted .

Preferable reference for this tutorial is

Teknomo, Kardi. Monte Carlo Simulation Tutorial. tutorial/Simulation