IMSE 865 ADV SIM
Dr. Easton PROJECT 1
Derek Christensen
The goal of this project is to create three simulation models using Python and a generic random number generator.
Part A
Design a dam for the Army Corp of Engineers that would only fail once every 100 years. The model should be run for 100 years for 30 replications. The lake height is measured once each day and the normal height is 1108͛ above sea level.
Assumptions
20% chance of precipitation each day
If there is precipitation, the type is:
o 75% Shower
o 20% Rain
o 5% Downpour
Amount of precipitation per type:
o Shower: Uniform Distribution [0.05͟, 0. 60͟]
o Rain: Uniform Distribution [0.40͟, 1.20͟]
o Downpour: Uniform Distribution [1.00͟, 5.00͟]
Amount the lake loses each day:
o If lake height is 5͛ or more above normal, then it loses ½͟
o Otherwise, ¼͟
Amount the lake gains each day of precipitation, based on the amount of precipitation:
o < 0.40͟: Gain = Precipitaion
o >= 0.40͟ and <= 1.00͟: Gain = 2 * Precipitation
o > 1.00͟: Gain = 5* Precipitaion
Technical Report
The model was written in Python 2.7 with one library imported (Random). Since the goal is to build a dam that will fail once every 100 years, we must predict what the second highest point would be on average over the 30 replications and build to that height, so we will keep track of the maximum height in each of the 30 one-hundred year replications (maxmax) in an array and also, the 2nd highest height reached in an array as well (max2nd). Randomness will be determined using the random.randint(lv, uv) function from the Random library, where lv and uv are the lower and upper bounds (inclusively) on the range from which we need a random integer picked.
The main part of the code is two nested For loops. The outer loop is iterated 30 times to generate the 30 replications and the inner loop is iterated 36,500 times to generate the 100 years needed.
Part B
This simulation will simulate a simplified baseball game (hits and outs only) and compare a contact hitter (Gwynn) and a homerun hitter (McGwire) by using Gwynn as all 9 batters for one team and McGwire as all nine batters for the other team and see which one scores the most runs on average over 100 games.
A third team is also to be compared which with the first two batters being Gwynn, the middle four being McGwire and the last 3 being Gwynn.
Assumptions
McGwire Career Stats
o Single .1269
o Double .0407
o Triple .0010
o Home Run .0942
o The remainder are outs.
Gwynn’s Career Stats
o Single .2024
o Double .0585
o Triple .0145
o Home Run .0628
o The remainder are outs.
Part C
This project will simulate an M/M/1 queue from scratch using Python, for 160 hours.
Assumptions
Arrival Distribution: Exponential 4/hr
Service Distribution: Exponential 5/hr
NB: U(0,1) Distribution can be converted into an Exponential Distribution with a rate of lambda as follows: -ln(u)/lambda