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ISYE 6644 FINAL EXAM VERSION 1
SIMULATION EXAM NEWEST 2025/2026
COMPLETE QUESTIONS AND CORRECT
ANSWERS (VERIFIED ANSWERS ) |ALREADY
GRADED A+||BRAND NEW VERSION!!
Consider a particular data set of 100,000 stationary waiting times obtained from a large queueing system. Suppose your goal is to get a confidence interval for the unknown mean. Would you rather use (a) 50 batches of 2000 observations or (b) 10000 batches of 10 observations each? - ANSWER-50 batches of 2000 observations because the method of batch means requires a very large batch size
Consider the output analysis method of non overlapping batch means.Assuming that you have a sufficiently large batch size, it can be shown that when the number of batches b is even, the expected width of the 90% two-sided confidence interval for μ is proportional tot 0.05 , b − 1 b − 1 ( b − 1 2 ) ( b − 3 2 ) ⋯ 1 2 ( b − 2 2 ) ! .Using the above equation, determine which of the following values of b gives the smallest expected width. - ANSWER-b=6 Let h ( b ) denote the value of the above expression as a function of b.Then easy calculations reveal that h ( b ) = 3.157, h ( 4 ) = 1.019, and h (
- ) = 0.845. So the answer is b = 6
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Consider the following observations:
54 70 75 62
If we choose a batch size of 3, calculate all of the overlapping batch means for me. - ANSWER-66.3, 69.0 X1,3 = 1/3 ΣXi = 66.3 and X2,3 = 1/3 ΣXi = 69.
TRUE or FALSE? Simulation output (e.g., consecutive customer waiting times) is almost never i.i.d. normal - and that's a big fat problem -
ANSWER-TRUE
We often distinguish between two general types of simulations with regard to output analysis. What are they called? - ANSWER-Finite- horizon and steady-state
TRUE or FALSE? Suppose that X 1 , X 2 , . . . , X n are consecutive waiting times, and we define the sample mean X ¯ = ∑ i = 1 n X i / n. Then V a r ( X ¯ ) = V a r ( X i ) / n. - ANSWER-Very FALSE! (The issue is that correlation between the observations messes up the variance of the sample mean. In fact, this is one of the main reasons why output analysis is difficult!)
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Which of the following scenarios might be well-suited for a finite-
horizon analysis? - ANSWER-Simulate bank operations from 8:00 a.m. to
5:00 p.m.
Simulate an inventory system until the first stock-out occurs
TRUE or FALSE? The main method of attack for terminating simulations is via independent replications. - ANSWER-TRUE (Independent replications help to mitigate issues with simulation outputs not being i.i.d.)
TRUE or FALSE? You can also conduct finite-horizon estimation for
quantities other than expected values, e.g., simulate a bank from 8:00
a.m. to 5:00 p.m., and find a confidence interval for the 95th quantile of
customer waiting times. - ANSWER-TRUE (the method of independent replications allows us to determine sample variances, which subsequently allows us to determine confidence intervals)
How can we deal with initialization bias if we want to do a steady-state analysis? - ANSWER-Make an extremely long run in order to overwhelm it.Truncate (delete) some of the initial data.
Which of the following scenarios might be well-suited for a steady-state analysis? - ANSWER-Simulate an assembly line working 24/7
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