Final Exam

Information

The final exam will be in class on Thursday, April 28 starting at 5:30 pm. You may bring:

• One sheet of notes (8.5" x 11", you may use both sides)
• One non-programmable calculator

You will be provided any statistical tables you may need (e.g. for looking up critical values for Kolmogorov-Smirnov or Chi-Squared, or for looking up the area under a standard normal curve):

• Chi-Squared Table
• Standard Normal Table
• Kolmogorov-Smirnov Table
• Student's T Table
• Queueing Model Equations
• Probability Distribution Equations

Practice Questions

Practice questions are available via the Review page. You may also find it helpful to review the examples done in lecture (available in the lecture slides).

Material to Review

The final exam covers the following topics:

• Everything from the midterm
• Introduction to Simulating Discrete Events (slides)
• Queueing Models (slides)
  • Calculate long-run averages, server utilization
  • Little's Equation
  • System Stability
  • Steady State and Transient State
• Input Modeling (slides)
  • Parameter Estimation using the Maximum Likelihood Estimate
  • Goodness-of-fit tests
  • Covariance and Correlation
  • Multivariate input models
  • Time-series input models
• Verification & Validation (slides)
  • Steps to verify model correctness
  • Steps to verify model is accurate representation of real system
  • Comparing model output to data collected from real system
• Output Analysis (slides)
  • Confidence intervals
  • Comparing Alternative Designs
  • Correlated Sampling
  • Independent Sampling
  • Determining Steady State
• Monte Carlo Simulations (slides)
  • Monte Carlo Integration
  • Sampling techniques
  • Bayesian Networks

Survey Results

Of those who completed the survey, 75% wanted a lecture-style review, although one was also ok with question & answer.

Questions/Comments about final exam or review session:

• Will the exam be approximately the same length as the midterm?
  • Yes. You will have more time, but the exam should be about the same length.
• I would be fine with a combination of lecture-style and question/answer for the review session.

The requested topics are shown below (ordered by how strongly requested, shown in parentheses), with the specific questions asked:

1. Queueing Theory (8)
   • Markov processes
   • I think a review of what all the notation stands for and how to calculate it would be helpful.
   • I think what I find difficult about this topic is the many variable names and notation.  Although the actual server/queue problems covered in lecture are fairly simple, knowing which set of variables/equations goes with the specific problem can be confusing.
2. Input Modeling (6)
   • I would like to review MLE and/or Goodness of Fit tests; I don't have any particular questions, I would just like to review any examples of how to do them.
   • Time Series
3. Output Analysis (5)
   • Confidence Intervals
4. Verification & Validation (3)
   • I think it would be helpful to go over additional questions similar to the long-response question from the quiz two weeks ago (the question that asked use to explain what was good/bad about an experimental design in terms of verification and validation). Since this type of question ties together input modeling, verification/validation of that model, and analysis of the output, I think it would be beneficial to revisit a similar-style question prior to the final exam.
5. Material from the first half of the semester (2)
   • If the final is cumulative, then I would like a quick review on how to figure out which distribution to apply to a given situation.
   • Some of the random variate generation methods we discussed are still slightly confusing to me, including the polar coordinate and "special properties" methods. I understand them on a conceptual level, but I would find it challenging to actually use them with a given set of parameters/equations.
6. Monte Carlo Simulations (0)

Review Session

1. See questions 5-8 for Lecture 9 on the reviews page. Identify the kind of Queueing Model and solve the first two.
2. Compute the maximum likelihood estimate for the Normal distribution.
3. See question 5 for Lecture 10 on the reviews page.
4. An international news website records the time between hits for news stories. They have observed that hits seem to arrive in bursts. Given the time between hits below (in ms), show whether or not hits arrive in bursts. How would you generate random variates for hits to news stories?

   4.473
   3.892
   3.386
   2.946
   2.706
   2.568
   2.234
   1.943
   1.691
   1.471
   1.28
   1.113
   0.969
   0.843
   0.733
   0.638
   0.555
   0.834
   0.948
   0.825
   0.718
   2.536
   3.375
   3.879
   4.762
   4.143
   3.605
   3.136
   2.728
   3.88
   3.375

5. See Lecture 13's first question on the review page.
6. Are there any problems with the situation described below? Do you agree or disagree with the recommendation made to the board of directors? Explain your answer.

   A library is considering offering a new service to handicapped and elderly patrons: employees to find books requested by these patrons in the library and bring them to the patrons. The board of directors wants to know whether this service is going to be used and whethr to hire one or two employees for this service (if it will be used). You have been hired to help them answer these questions. To determine how many will use this service, you observe the number of patrons who go to the reference librarian and ask for help finding books. To determine how long it will take to locate a book, you record the average time it takes a patron to find a book. You create a model of the library, including how patrons use the library, and implement it in your programming language of choice. You do a series of runs to obtain a baseline -- how the library currently works. You then modify the model to include the service they're considering with one employee and do a series of runs. You add a second employee to the service and do another series of runs. For each version of the model, you did 25 runs. Performing a hypothesis test to determine whether any model performed better than the others, you found that the service with two employees was significantly better (α = 0.05): it had library patrons getting their books and leaving 25% faster than with no service and 5% faster than just one employee with this service. However, even just one employee working the service shows significantly better throughput of patrons over no service at all (again, at α = 0.05). Therefore, you recommend to the board of directors that the service is worthwhile and while two employees would be better, even just one employee would be worth the investment.

7. You have been hired to determine whether an intersection should be switched from using four-way stop signs to using a traffic light. You will be making a simulation to determine the effect on traffic flow through the area. What distribution should you use to describe the arrival of vehicles at the intersection? Why? How would you confirm your choice?
8. An local news website records the time between hits for news stories. They notice bursts of visits between 7:30 am and 8 am, noon and 1 pm, and 5 pm and 6 pm. What distribution should you use to describe the arrival of vehicles at the intersection? Why? How would you confirm your choice?