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ISE 4100: Stochastic Modeling and Poisson DistributionAutumn 2014

HW #4(ARENA Simulation and Input Analysis)

Due: Oct. 28, 2014, Tuesday.

Notes:

KSZ: Simulation with Arena, 6th edition by Kelton et al.

BCNN: Jerry Banks, John S. Carson II, Barry L. Nelson, and David M. Nicol,Discrete-Event System Simulation, 5th edition, Prentice Hall, 2010.

ARENA Simulation:

Upload your .doe files by 3:55pm on due date to the Homework #4 Drop-box folder on Carmen. For other parts of these problems, please write themdown along with your other answers and return in class.

1. (16pts)

(a) (KSZ) Chapter 5, Exercise 5-5. Prepare a summary table. Please upload your.doe file for this problem and return your summary results and interpretations inclass.

(b) (KSZ) Chapter 5, Exercise 5-6. Prepare a summary table and compare it to theresult of Exercise 5-6. Write brief comments. Please upload your .doe file for thisproblem and return your summary results and interpretations in class.

2. (24pts)

(a) (KSZ) Chapter 5, Exercise 5-13. Prepare a summary table. Please upload your.doe file for this problem and return your summary results and interpretations inclass.

(b) (KSZ) Chapter 5, Exercise 5-14. Prepare a summary table and compare it to theresult of Exercise 5-13. Write brief comments. Please upload your .doe file forthis problem and return your summary results and interpretations in class.

(c) (KSZ) Chapter 5, Exercise 5-15. Prepare a summary table and compare it to theresult of Exercise 5-14. Write brief comments. Please upload your .doe file forthis problem and return your summary results and interpretations in class.

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ARENA Input Analyzer:

3. (16pts)(World Cup Soccer Goals)[Chu]The aim of this question to use the Input Analyzer to determine an appropriate dis-

tribution for a real-world dataset. The dataset is uploaded on Carmen. It containsinformation about the 232 soccer games played from the 1990 World Cup, held in Italy,to the 2002 World Cup, held jointly by South Korea and Japan. There were 535 goalsscored during this period. The dataset contains this information two ways. First, itlooks at the number of goals scored per game. Second, it looks at the inter-goal times.The inter-goal times, i.e., the time between goals are calculated by appending eachgame. The below figure shows how the inter-goal times were obtained.

Figure 1: Illustration of how the inter-goal times were obtained. The *s denote when a goalwas scored during a game, and the games are appended to calculate inter-goal times of goalsfrom different games.

Analyze the following experiments from the soccer game by using the ARENA InputAnalyzer.

(a) Run the ARENA Input Analyzer with the inter-goal times data (use Inter-Goal

Times sheet). Which distribution is the best fitted one? Why? Explain.

(b) Run the ARENA Input Analyzer with the number of goals per game data (useNumber of Goals in each Game sheet). List all the statistically acceptabledistributions. Which distribution would you pick? Why? Explain.

Probability Plots in Microsoft Excel:

4. (14pts) For this problem, use the data given in hw4probplots.xlx. Upload yourExcel sheet on Carmen. Return your summary results and interpretationsin class.

(a) Suppose the data follows a Normal Distribution. Estimate the parameters of thisdistribution using the provided data.

(b) Suppose the data follows a Gamma Distribution. Estimate the parameters ofthis distribution using the provided data. Use the parameters of the Gammadistribution given in BCNN.

Hint: You can see Example 9.15 in BCNN on how to estimate the parameters ofa gamma distribution.

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(c) Create a Q-Q plot and a P-P plot using the normal distribution. Does normaldistribution provide a good fit? Comment on the plots.

(d) Create a Q-Q plot and a P-P plot using the gamma distribution. Comment onthe plots. Does gamma distribution provide a good fit? How does it compare tothe normal probability plots?

Hint: Be CAREFUL!The Gamma distributions representation (and parameters)in the book might be different than the Gamma distributions representation (andparameters) in Excel. Dont forget to make the necessary changes to use theGamma distribution functions (GAMMADIST, GAMMAINV) in Excel to createthe plots!

Goodness-of-Fit Tests:

5. (15pts) (BCNN) Chapter 9- EXERCISE 14. (NEW: Do NOT turn this in on Oct. 28,2014, Tuesday! This question on K-S test is NO LONGER part of HW4)

6. (15pts) (BCNN) Chapter 9- EXERCISE 16.

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