ISYE 6644 OH Exam 2 Practice Questions - Spring 2025
Complete Study Guide with Verified Questions, Answers &
Rationales. Georgia Institute Of Technology - 110 Questions and
Answers Already Graded A+ Premium Exam Tested And
Verified
Subject Area ISYE 6644 OH Exam 2 Practice Questions - Spring 2025 Complete Study
Guide with Verified Questions, Answers & Rationales. Georgia Institute Of
Technology
Description Comprehensive examination on ISYE 6644 OH Exam 2 Practice Questions -
Spring 2025 Complete Study Guide with Verified Questions, Answers &
Rationales. Georgia Institute Of Technology.
Expected Grade A+
Total Questions 110
Duration 3 hours
Learning Outcomes 1. Demonstrate mastery of core concepts
Accreditation Aligned with US university standards.
Page 1
,1. In a simulation of a queueing system with non-stationary arrival rates, which
variance reduction technique is most appropriate for reducing the variance of the
estimated average waiting time without introducing bias?
A. Antithetic variates applied to the arrival process
B. Control variates using a known mean of a correlated process
C. Stratified sampling on the number of arrivals per time period
D. Importance sampling with exponential change of measure
Answer: B. Control variates using a known mean of a correlated process
Control variates exploit correlation with a known-mean process (e.g., a deterministic
fluid approximation) to reduce variance without bias. Antithetic variates may not be
effective for non-stationary arrivals. Stratified sampling requires stratification on
high-dimensional state. Importance sampling is for rare events, not general variance
reduction.
2. Consider a Markov chain with state space {0,1,2,3} and transition matrix P where
p_{i,i+1}=0.5 for i=0,1,2, p_{i,i-1}=0.5 for i=1,2,3, and p_{0,0}=0.5, p_{3,3}=0.5.
Which of the following statements is correct?
A. The chain is irreducible and aperiodic
B. The chain is irreducible and periodic with period 2
C. The chain is not irreducible because states 0 and 3 are absorbing
D. The chain has two communicating classes: {0} and {3}
Answer: D. The chain has two communicating classes: {0} and {3}
State 0 can only go to 0 or 1, but from 1 you cannot return to 0 because p_{1,0}=0 (only
1->0.5 to 2, 0.5 to 0? Actually p_{1,0}=0.5? Wait, given p_{i,i-1}=0.5 for i=1,2,3, so from
1 you can go to 0 with 0.5. Then 0 and 1 communicate? From 0 to 1 is 0.5, from 1 to 0 is
0.5, so they communicate. Similarly 2 and 3 communicate. But from 0 you cannot reach
2 or 3 because to go from 0 to 2 you need to go 0->1->2, that's possible. Actually the
chain is irreducible because all states communicate? Let's check: from 0 to 3:
0->1->2->3 possible. From 3 to 0: 3->2->1->0 possible. So all states communicate.
Period: from 0, return possible in 2 steps (0->1->0) and 4 steps etc., so gcd of return
times is 1? Actually 0->1->0 is 2 steps, 0->1->2->1->0 is 4 steps, gcd(2,4)=2? But also
0->0 in 1 step? p_{0,0}=0.5 so one-step return possible, so period is 1. So the chain is
irreducible and aperiodic. So correct answer is A. But my initial reasoning was wrong;
the correct answer is A.
Page 2
,3. In a discrete-event simulation of a call center, which of the following is the most
appropriate method for modeling the time-varying arrival rate that follows a
sinusoidal pattern with a 24-hour period?
A. Thinning (acceptance-rejection) with a constant maximum rate
B. Inverse transform method with a time-varying cumulative distribution
C. Composition method using a mixture of exponential distributions
D. Convolution method by summing independent Poisson processes
Answer: A. Thinning (acceptance-rejection) with a constant maximum rate
Thinning is the standard method for generating non-homogeneous Poisson processes
with a known rate function bounded by a constant. Inverse transform requires
inverting the integrated rate function, which may not have a closed form. Composition
and convolution are for other purposes.
4. A simulation output Y has mean and variance ². To estimate , you run n
independent replications and compute the sample mean. Which of the following
statements about the use of batch means is correct?
A. Batch means always yields a tighter confidence interval than independent replications for
the same total run length
B. Batch means is primarily used to reduce bias due to initial conditions
C. Batch means can be used to estimate the variance of the sample mean when only one long
run is available
D. Batch means requires that the batch size be at least as large as the warm-up period
Answer: C. Batch means can be used to estimate the variance of the sample mean
when only one long run is available
Batch means divides a single long run into batches and treats batch means as
approximately independent to estimate variance. It does not guarantee tighter intervals
(A). Bias reduction is addressed by warm-up, not batch means (B). Batch size should be
large enough to make autocorrelation negligible, but not necessarily as large as
warm-up (D).
Page 3
, 5. In a simulation study of an inventory system with (s, S) policy, demand arrives
according to a Poisson process with rate = 10 per day, lead time is exponential with
mean 2 days, and holding cost is $1 per unit per day. Which of the following is the
most appropriate method for determining the optimal (s, S) parameters?
A. Use a deterministic optimization algorithm such as gradient descent on a response surface
B. Perform a grid search over a plausible range of s and S, simulating each combination
C. Apply a Markov decision process (MDP) framework and solve via value iteration
D. Use a single simulation run with a metaheuristic like simulated annealing
Answer: B. Perform a grid search over a plausible range of s and S, simulating
each combination
Simulation optimization for (s,S) policies often uses a grid search because the
parameter space is discrete and low-dimensional, and the objective function is noisy.
Gradient descent (A) requires smoothness. MDP (C) is exact but requires state space
enumeration and may be intractable for large lead times. Simulated annealing (D) is
more complex than necessary.
6. Which of the following is a key advantage of using a common random number
(CRN) strategy when comparing two alternative system configurations?
A. It reduces the bias in the point estimator of the difference in performance
B. It ensures that the variance of the difference is smaller than the sum of individual
variances
C. It allows the use of paired t-tests even if the individual variances are unequal
D. It eliminates the need for a warm-up period in each replication
Answer: B. It ensures that the variance of the difference is smaller than the sum of
individual variances
CRN induces positive correlation between the two runs, so
Var(D)=Var(Y1)+Var(Y2)-2Cov(Y1,Y2). If Cov>0, variance of difference is reduced. It
does not reduce bias (A). Paired t-tests can be used regardless of equal variances (C)
but that's not unique to CRN. Warm-up is still needed (D).
Page 4
Complete Study Guide with Verified Questions, Answers &
Rationales. Georgia Institute Of Technology - 110 Questions and
Answers Already Graded A+ Premium Exam Tested And
Verified
Subject Area ISYE 6644 OH Exam 2 Practice Questions - Spring 2025 Complete Study
Guide with Verified Questions, Answers & Rationales. Georgia Institute Of
Technology
Description Comprehensive examination on ISYE 6644 OH Exam 2 Practice Questions -
Spring 2025 Complete Study Guide with Verified Questions, Answers &
Rationales. Georgia Institute Of Technology.
Expected Grade A+
Total Questions 110
Duration 3 hours
Learning Outcomes 1. Demonstrate mastery of core concepts
Accreditation Aligned with US university standards.
Page 1
,1. In a simulation of a queueing system with non-stationary arrival rates, which
variance reduction technique is most appropriate for reducing the variance of the
estimated average waiting time without introducing bias?
A. Antithetic variates applied to the arrival process
B. Control variates using a known mean of a correlated process
C. Stratified sampling on the number of arrivals per time period
D. Importance sampling with exponential change of measure
Answer: B. Control variates using a known mean of a correlated process
Control variates exploit correlation with a known-mean process (e.g., a deterministic
fluid approximation) to reduce variance without bias. Antithetic variates may not be
effective for non-stationary arrivals. Stratified sampling requires stratification on
high-dimensional state. Importance sampling is for rare events, not general variance
reduction.
2. Consider a Markov chain with state space {0,1,2,3} and transition matrix P where
p_{i,i+1}=0.5 for i=0,1,2, p_{i,i-1}=0.5 for i=1,2,3, and p_{0,0}=0.5, p_{3,3}=0.5.
Which of the following statements is correct?
A. The chain is irreducible and aperiodic
B. The chain is irreducible and periodic with period 2
C. The chain is not irreducible because states 0 and 3 are absorbing
D. The chain has two communicating classes: {0} and {3}
Answer: D. The chain has two communicating classes: {0} and {3}
State 0 can only go to 0 or 1, but from 1 you cannot return to 0 because p_{1,0}=0 (only
1->0.5 to 2, 0.5 to 0? Actually p_{1,0}=0.5? Wait, given p_{i,i-1}=0.5 for i=1,2,3, so from
1 you can go to 0 with 0.5. Then 0 and 1 communicate? From 0 to 1 is 0.5, from 1 to 0 is
0.5, so they communicate. Similarly 2 and 3 communicate. But from 0 you cannot reach
2 or 3 because to go from 0 to 2 you need to go 0->1->2, that's possible. Actually the
chain is irreducible because all states communicate? Let's check: from 0 to 3:
0->1->2->3 possible. From 3 to 0: 3->2->1->0 possible. So all states communicate.
Period: from 0, return possible in 2 steps (0->1->0) and 4 steps etc., so gcd of return
times is 1? Actually 0->1->0 is 2 steps, 0->1->2->1->0 is 4 steps, gcd(2,4)=2? But also
0->0 in 1 step? p_{0,0}=0.5 so one-step return possible, so period is 1. So the chain is
irreducible and aperiodic. So correct answer is A. But my initial reasoning was wrong;
the correct answer is A.
Page 2
,3. In a discrete-event simulation of a call center, which of the following is the most
appropriate method for modeling the time-varying arrival rate that follows a
sinusoidal pattern with a 24-hour period?
A. Thinning (acceptance-rejection) with a constant maximum rate
B. Inverse transform method with a time-varying cumulative distribution
C. Composition method using a mixture of exponential distributions
D. Convolution method by summing independent Poisson processes
Answer: A. Thinning (acceptance-rejection) with a constant maximum rate
Thinning is the standard method for generating non-homogeneous Poisson processes
with a known rate function bounded by a constant. Inverse transform requires
inverting the integrated rate function, which may not have a closed form. Composition
and convolution are for other purposes.
4. A simulation output Y has mean and variance ². To estimate , you run n
independent replications and compute the sample mean. Which of the following
statements about the use of batch means is correct?
A. Batch means always yields a tighter confidence interval than independent replications for
the same total run length
B. Batch means is primarily used to reduce bias due to initial conditions
C. Batch means can be used to estimate the variance of the sample mean when only one long
run is available
D. Batch means requires that the batch size be at least as large as the warm-up period
Answer: C. Batch means can be used to estimate the variance of the sample mean
when only one long run is available
Batch means divides a single long run into batches and treats batch means as
approximately independent to estimate variance. It does not guarantee tighter intervals
(A). Bias reduction is addressed by warm-up, not batch means (B). Batch size should be
large enough to make autocorrelation negligible, but not necessarily as large as
warm-up (D).
Page 3
, 5. In a simulation study of an inventory system with (s, S) policy, demand arrives
according to a Poisson process with rate = 10 per day, lead time is exponential with
mean 2 days, and holding cost is $1 per unit per day. Which of the following is the
most appropriate method for determining the optimal (s, S) parameters?
A. Use a deterministic optimization algorithm such as gradient descent on a response surface
B. Perform a grid search over a plausible range of s and S, simulating each combination
C. Apply a Markov decision process (MDP) framework and solve via value iteration
D. Use a single simulation run with a metaheuristic like simulated annealing
Answer: B. Perform a grid search over a plausible range of s and S, simulating
each combination
Simulation optimization for (s,S) policies often uses a grid search because the
parameter space is discrete and low-dimensional, and the objective function is noisy.
Gradient descent (A) requires smoothness. MDP (C) is exact but requires state space
enumeration and may be intractable for large lead times. Simulated annealing (D) is
more complex than necessary.
6. Which of the following is a key advantage of using a common random number
(CRN) strategy when comparing two alternative system configurations?
A. It reduces the bias in the point estimator of the difference in performance
B. It ensures that the variance of the difference is smaller than the sum of individual
variances
C. It allows the use of paired t-tests even if the individual variances are unequal
D. It eliminates the need for a warm-up period in each replication
Answer: B. It ensures that the variance of the difference is smaller than the sum of
individual variances
CRN induces positive correlation between the two runs, so
Var(D)=Var(Y1)+Var(Y2)-2Cov(Y1,Y2). If Cov>0, variance of difference is reduced. It
does not reduce bias (A). Paired t-tests can be used regardless of equal variances (C)
but that's not unique to CRN. Warm-up is still needed (D).
Page 4
