ISYE 6644 FINAL EXAM VERSION 1 SIMULATION EXAM
COMPLETE QUESTIONS AND DETAILED SOLUTIONS
LATEST UPDATE THIS YEAR JUST RELEASED
Question 1: Which of the following scenarios might be well-suited
for a steady-state analysis?
Answer:
Simulate an assembly line working 24/7
Question 2: A Markov chain simulated until the transition
probabilities appear to converge Which of the following is useful
for analyzing steady-state simulation output?
Answer:
The method of batch means
Question 3: Which of the following statements is true?
A. The method of batch means is easy to use.
B. Batch means chops the consecutive observations into a number of
nonoverlapping, contiguous batches
C. You can use the method of batch means to obtain a confidence
interval for the steady-state mean ■ .
D. The batch means estimator for the variance parameter ■^2 is
asymptotically unbiased as the batch size ■→∞ .
E. All of the above
Answer:
All of the above
,Question 4: Which of the following methods can be used for
steady-state analysis?
A. Batch Means
B. Independent Replications (though it might suffer some minor(?)
initialization problems)
C. Overlapping Batch Means (something for nothing!)
D. Regeneration
E. Standardized Time Series
Answer:
f. All of the above
Question 5: It's GIGO time! Let's consider an M / M / 1 queueing
system with Exp(λ) interarrivals and Exp(µ) FIFO services at a
single server. You may recall from some class (either this one or
stochastic processes) that the steady-state expected cycle time
(i.e., the time that the customer is in the system, including wait +
service) is w = 1 / ( µ − λ ). If you were to try this out in Arena, let's
say with E X P O ( 10 = 1 / λ ) interarrivals and E X P O ( 8 = 1 / µ )
services (note the notation change between my usual "Exp" and
Arena's " E X P O "), then we'd get w = 1 / ( 0.125 − 0.1 ) = 40. Go
ahead, see for yourself in Arena, but make sure that you run the
system for 100,000 or so customers so that you can be sure that
you're in steady-state! Finally, here's the GIGO question, which will
show what can happen when you mis-model a component of your
process: What is the (approximate) steady-state expected cycle
time if you hav
Answer:
about 23
, Question 6: The U N I F case has waaaay smaller tails than the E X
P O, so it's reasonable to assume that the cycle times will tend to
be lower for the U N I F case. In fact, after 100,000 customers in
Arena, I got an average time of 23.5. Let's play Name That
Distribution! The number of times a "3" comes up in 10 dice tosses.
Answer:
Binomial
Question 7: Name That Distribution! The number of dice tosses
until a 3 comes up.
Answer:
Geometric
Question 8: Name That Distribution! The number of dice tosses
until a 3 comes up for the 4th time.
Answer:
Negative Binomial
Question 9: Name That Distribution! IQs
Answer:
Normal
Question 10: Name That Distribution! Cases in which you have
limited information, e.g., you only know the min, max, and "most
likely" values that a random variable can take.
Answer:
COMPLETE QUESTIONS AND DETAILED SOLUTIONS
LATEST UPDATE THIS YEAR JUST RELEASED
Question 1: Which of the following scenarios might be well-suited
for a steady-state analysis?
Answer:
Simulate an assembly line working 24/7
Question 2: A Markov chain simulated until the transition
probabilities appear to converge Which of the following is useful
for analyzing steady-state simulation output?
Answer:
The method of batch means
Question 3: Which of the following statements is true?
A. The method of batch means is easy to use.
B. Batch means chops the consecutive observations into a number of
nonoverlapping, contiguous batches
C. You can use the method of batch means to obtain a confidence
interval for the steady-state mean ■ .
D. The batch means estimator for the variance parameter ■^2 is
asymptotically unbiased as the batch size ■→∞ .
E. All of the above
Answer:
All of the above
,Question 4: Which of the following methods can be used for
steady-state analysis?
A. Batch Means
B. Independent Replications (though it might suffer some minor(?)
initialization problems)
C. Overlapping Batch Means (something for nothing!)
D. Regeneration
E. Standardized Time Series
Answer:
f. All of the above
Question 5: It's GIGO time! Let's consider an M / M / 1 queueing
system with Exp(λ) interarrivals and Exp(µ) FIFO services at a
single server. You may recall from some class (either this one or
stochastic processes) that the steady-state expected cycle time
(i.e., the time that the customer is in the system, including wait +
service) is w = 1 / ( µ − λ ). If you were to try this out in Arena, let's
say with E X P O ( 10 = 1 / λ ) interarrivals and E X P O ( 8 = 1 / µ )
services (note the notation change between my usual "Exp" and
Arena's " E X P O "), then we'd get w = 1 / ( 0.125 − 0.1 ) = 40. Go
ahead, see for yourself in Arena, but make sure that you run the
system for 100,000 or so customers so that you can be sure that
you're in steady-state! Finally, here's the GIGO question, which will
show what can happen when you mis-model a component of your
process: What is the (approximate) steady-state expected cycle
time if you hav
Answer:
about 23
, Question 6: The U N I F case has waaaay smaller tails than the E X
P O, so it's reasonable to assume that the cycle times will tend to
be lower for the U N I F case. In fact, after 100,000 customers in
Arena, I got an average time of 23.5. Let's play Name That
Distribution! The number of times a "3" comes up in 10 dice tosses.
Answer:
Binomial
Question 7: Name That Distribution! The number of dice tosses
until a 3 comes up.
Answer:
Geometric
Question 8: Name That Distribution! The number of dice tosses
until a 3 comes up for the 4th time.
Answer:
Negative Binomial
Question 9: Name That Distribution! IQs
Answer:
Normal
Question 10: Name That Distribution! Cases in which you have
limited information, e.g., you only know the min, max, and "most
likely" values that a random variable can take.
Answer:
