The Ultimate and Complete ISYE 6644 Simulation Exam 2 Study Guide 2026–2027,
Covering Discrete-Event Simulation, Simulation Modeling, General Modeling
Principles, Arena Simulation, Arena Modules, Entity Flow, Resources, Queues, Seize-
Delay-Release Logic, Routing, Transfers, Process Modeling, Random Number
Generation, Uniform Random Variables, Random-Variate Generation, Inverse
Transform Method, Acceptance-Rejection Method, Discrete and Continuous
Probability Distributions, Input Analysis, Distribution Fitting, Parameter Estimation,
Goodness-of-Fit Tests, Chi-Square Tests, Kolmogorov-Smirnov Tests, Output Analysis,
Point Estimation, Confidence Intervals, Replication, Batch Means, Warm-Up Periods,
Steady-State Simulation, Comparing Alternative Systems, Variance Reduction,
Common Random Numbers, Antithetic Variates, Simulation Verification and Validation,
Arena Modeling Applications, Statistical Analysis, Numerical Problems, Scenario-
Based Questions With Detailed Solutions, and Comprehensive Preparation for the
Georgia Tech ISYE 6644 Simulation Exam 2
Question 1: In the context of input modeling for a simulation study, which distribution is most
appropriate for modeling the time between successive arrivals to a service facility when
arrivals occur completely at random and independently of each other?
A. Normal distribution
B. Uniform distribution
C. Exponential distribution
D. Lognormal distribution
CORRECT ANSWER: C. Exponential distribution
Rationale: The exponential distribution is the standard choice for modeling inter-arrival times in
a Poisson process, where arrivals are random and independent. Its memoryless property makes
it ideal for this purpose. The normal distribution is symmetric and unbounded, the uniform
distribution implies equal probability over a range, and the lognormal is typically used for
positively skewed data with a different generative process, none of which fit the random,
independent arrival scenario.
Question 2: In the output analysis of a steady-state simulation, what is the primary purpose
of using the method of batch means?
A. To reduce the variance of the simulation output.
B. To generate independent and identically distributed (i.i.d.) observations for analysis.
C. To obtain a valid point estimate and confidence interval for the steady-state mean.
D. To determine the optimal warm-up period for the simulation.
,CORRECT ANSWER: C. To obtain a valid point estimate and confidence interval for the steady-
state mean.
Rationale: The method of batch means is a technique used to address the issue of
autocorrelation in steady-state simulation output. By dividing a single long run into a small
number of large batches and treating the batch means as approximately independent, we can
construct a valid confidence interval for the steady-state mean. It does not primarily aim to
reduce variance (A) or create perfectly i.i.d. observations (B), nor is it used to find the warm-up
period (D).
Question 3: Which of the following is a common and robust statistical test used to compare
the means of two independent simulation systems when the variances are unknown and not
assumed to be equal?
A. Paired-t test
B. Welch's t-test
C. Chi-squared test
D. F-test
CORRECT ANSWER: B. Welch's t-test
Rationale: Welch's t-test is a two-sample location test that does not assume equal variances,
making it a robust choice for comparing two independent systems. The paired-t test is for
dependent samples, the Chi-squared test is for categorical data or goodness-of-fit, and the F-
test is primarily for comparing variances, not means.
Question 4: In a discrete-event simulation, what is the term for the simulation clock being
advanced to the time of the next imminent event, skipping over periods of inactivity?
A. Time-sliced advancement
B. Next-event time advance
C. Fixed-increment time advance
D. Continuous-time advancement
CORRECT ANSWER: B. Next-event time advance
Rationale: The next-event time advance mechanism is the core of a discrete-event simulation.
The clock jumps directly from the current event time to the time of the next event on the future
events list, ignoring inactive periods. This is distinct from fixed-increment time advance (C),
which advances by a constant delta, and the other terms are not standard.
,Question 5: A simulation model outputs a random variable X. After running 10 independent
replications, the sample variance is calculated. If the analyst aims to reduce the variance of
the sample mean by a factor of 4, by how much must the number of replications be
increased?
A. 2 times
B. 4 times
C. 16 times
D. 8 times
CORRECT ANSWER: B. 4 times
Rationale: The variance of the sample mean is given by σ²/n, where σ² is the population
variance and n is the number of replications. To reduce this variance by a factor of 4, the
denominator n must increase by a factor of 4. This is a direct application of the law of large
numbers.
Question 6: Which of the following variance reduction techniques (VRTs) is most directly
designed to force the simulation to sample more evenly across the range of an input
distribution?
A. Common Random Numbers
B. Antithetic Variates
C. Latin Hypercube Sampling
D. Control Variates
CORRECT ANSWER: C. Latin Hypercube Sampling
Rationale: Latin Hypercube Sampling (LHS) is a stratified sampling technique that ensures a
more uniform coverage of the input distribution's range by dividing the cumulative distribution
function into equal intervals and sampling from each interval once. Common Random Numbers
(A) is for comparing systems, Antithetic Variates (B) introduces negative correlation, and
Control Variates (D) uses a correlated variable to reduce variance.
Question 7: In the context of random number generation, a linear congruential generator
(LCG) is defined by the recurrence X_{i+1} = (aX_i + c) mod m. For this generator to have a full
period (m), which of the following conditions is NOT a requirement according to Hull-Dobell
theorem?
A. c and m are relatively prime.
B. a - 1 is divisible by all prime factors of m.
, C. a is an even number.
D. a - 1 is divisible by 4 if m is divisible by 4.
CORRECT ANSWER: C. a is an even number.
Rationale: The Hull-Dobell theorem states that for an LCG to have a full period of m, (1) c and m
must be relatively prime, (2) a-1 is divisible by all prime factors of m, and (3) a-1 is divisible by 4
if m is divisible by 4. There is no requirement that 'a' itself must be even; in fact, a-1 must be
divisible by prime factors, often making 'a' an odd number.
Question 8: In a simulation model of an M/M/1 queueing system, which of the following
performance measures would be most directly calculated using Little's Law?
A. Server utilization (ρ).
B. Average number in the system (L).
C. Probability of zero customers in the system (P₀).
D. Variance of the waiting time.
CORRECT ANSWER: B. Average number in the system (L).
Rationale: Little's Law states that L = λW, relating the average number in the system (L) to the
average arrival rate (λ) and the average time spent in the system (W). While utilization (A) is
ρ=λ/μ, and P₀ (C) is a state probability, the primary direct application of Little's Law is for L or
W.
Question 9: What is the primary limitation of using a single run of a simulation to estimate a
steady-state performance measure?
A. It is computationally more expensive than multiple runs.
B. It does not allow for the construction of a valid confidence interval.
C. It is impossible to estimate the mean from a single run.
D. It requires a larger sample size.
CORRECT ANSWER: B. It does not allow for the construction of a valid confidence interval.
Rationale: A single simulation run, even if long, produces a single estimate of the performance
measure. Without multiple independent observations or replications, it is impossible to
estimate the variability of that estimate and therefore cannot construct a valid statistical
confidence interval. Multiple runs or special techniques like batch means are needed.
Covering Discrete-Event Simulation, Simulation Modeling, General Modeling
Principles, Arena Simulation, Arena Modules, Entity Flow, Resources, Queues, Seize-
Delay-Release Logic, Routing, Transfers, Process Modeling, Random Number
Generation, Uniform Random Variables, Random-Variate Generation, Inverse
Transform Method, Acceptance-Rejection Method, Discrete and Continuous
Probability Distributions, Input Analysis, Distribution Fitting, Parameter Estimation,
Goodness-of-Fit Tests, Chi-Square Tests, Kolmogorov-Smirnov Tests, Output Analysis,
Point Estimation, Confidence Intervals, Replication, Batch Means, Warm-Up Periods,
Steady-State Simulation, Comparing Alternative Systems, Variance Reduction,
Common Random Numbers, Antithetic Variates, Simulation Verification and Validation,
Arena Modeling Applications, Statistical Analysis, Numerical Problems, Scenario-
Based Questions With Detailed Solutions, and Comprehensive Preparation for the
Georgia Tech ISYE 6644 Simulation Exam 2
Question 1: In the context of input modeling for a simulation study, which distribution is most
appropriate for modeling the time between successive arrivals to a service facility when
arrivals occur completely at random and independently of each other?
A. Normal distribution
B. Uniform distribution
C. Exponential distribution
D. Lognormal distribution
CORRECT ANSWER: C. Exponential distribution
Rationale: The exponential distribution is the standard choice for modeling inter-arrival times in
a Poisson process, where arrivals are random and independent. Its memoryless property makes
it ideal for this purpose. The normal distribution is symmetric and unbounded, the uniform
distribution implies equal probability over a range, and the lognormal is typically used for
positively skewed data with a different generative process, none of which fit the random,
independent arrival scenario.
Question 2: In the output analysis of a steady-state simulation, what is the primary purpose
of using the method of batch means?
A. To reduce the variance of the simulation output.
B. To generate independent and identically distributed (i.i.d.) observations for analysis.
C. To obtain a valid point estimate and confidence interval for the steady-state mean.
D. To determine the optimal warm-up period for the simulation.
,CORRECT ANSWER: C. To obtain a valid point estimate and confidence interval for the steady-
state mean.
Rationale: The method of batch means is a technique used to address the issue of
autocorrelation in steady-state simulation output. By dividing a single long run into a small
number of large batches and treating the batch means as approximately independent, we can
construct a valid confidence interval for the steady-state mean. It does not primarily aim to
reduce variance (A) or create perfectly i.i.d. observations (B), nor is it used to find the warm-up
period (D).
Question 3: Which of the following is a common and robust statistical test used to compare
the means of two independent simulation systems when the variances are unknown and not
assumed to be equal?
A. Paired-t test
B. Welch's t-test
C. Chi-squared test
D. F-test
CORRECT ANSWER: B. Welch's t-test
Rationale: Welch's t-test is a two-sample location test that does not assume equal variances,
making it a robust choice for comparing two independent systems. The paired-t test is for
dependent samples, the Chi-squared test is for categorical data or goodness-of-fit, and the F-
test is primarily for comparing variances, not means.
Question 4: In a discrete-event simulation, what is the term for the simulation clock being
advanced to the time of the next imminent event, skipping over periods of inactivity?
A. Time-sliced advancement
B. Next-event time advance
C. Fixed-increment time advance
D. Continuous-time advancement
CORRECT ANSWER: B. Next-event time advance
Rationale: The next-event time advance mechanism is the core of a discrete-event simulation.
The clock jumps directly from the current event time to the time of the next event on the future
events list, ignoring inactive periods. This is distinct from fixed-increment time advance (C),
which advances by a constant delta, and the other terms are not standard.
,Question 5: A simulation model outputs a random variable X. After running 10 independent
replications, the sample variance is calculated. If the analyst aims to reduce the variance of
the sample mean by a factor of 4, by how much must the number of replications be
increased?
A. 2 times
B. 4 times
C. 16 times
D. 8 times
CORRECT ANSWER: B. 4 times
Rationale: The variance of the sample mean is given by σ²/n, where σ² is the population
variance and n is the number of replications. To reduce this variance by a factor of 4, the
denominator n must increase by a factor of 4. This is a direct application of the law of large
numbers.
Question 6: Which of the following variance reduction techniques (VRTs) is most directly
designed to force the simulation to sample more evenly across the range of an input
distribution?
A. Common Random Numbers
B. Antithetic Variates
C. Latin Hypercube Sampling
D. Control Variates
CORRECT ANSWER: C. Latin Hypercube Sampling
Rationale: Latin Hypercube Sampling (LHS) is a stratified sampling technique that ensures a
more uniform coverage of the input distribution's range by dividing the cumulative distribution
function into equal intervals and sampling from each interval once. Common Random Numbers
(A) is for comparing systems, Antithetic Variates (B) introduces negative correlation, and
Control Variates (D) uses a correlated variable to reduce variance.
Question 7: In the context of random number generation, a linear congruential generator
(LCG) is defined by the recurrence X_{i+1} = (aX_i + c) mod m. For this generator to have a full
period (m), which of the following conditions is NOT a requirement according to Hull-Dobell
theorem?
A. c and m are relatively prime.
B. a - 1 is divisible by all prime factors of m.
, C. a is an even number.
D. a - 1 is divisible by 4 if m is divisible by 4.
CORRECT ANSWER: C. a is an even number.
Rationale: The Hull-Dobell theorem states that for an LCG to have a full period of m, (1) c and m
must be relatively prime, (2) a-1 is divisible by all prime factors of m, and (3) a-1 is divisible by 4
if m is divisible by 4. There is no requirement that 'a' itself must be even; in fact, a-1 must be
divisible by prime factors, often making 'a' an odd number.
Question 8: In a simulation model of an M/M/1 queueing system, which of the following
performance measures would be most directly calculated using Little's Law?
A. Server utilization (ρ).
B. Average number in the system (L).
C. Probability of zero customers in the system (P₀).
D. Variance of the waiting time.
CORRECT ANSWER: B. Average number in the system (L).
Rationale: Little's Law states that L = λW, relating the average number in the system (L) to the
average arrival rate (λ) and the average time spent in the system (W). While utilization (A) is
ρ=λ/μ, and P₀ (C) is a state probability, the primary direct application of Little's Law is for L or
W.
Question 9: What is the primary limitation of using a single run of a simulation to estimate a
steady-state performance measure?
A. It is computationally more expensive than multiple runs.
B. It does not allow for the construction of a valid confidence interval.
C. It is impossible to estimate the mean from a single run.
D. It requires a larger sample size.
CORRECT ANSWER: B. It does not allow for the construction of a valid confidence interval.
Rationale: A single simulation run, even if long, produces a single estimate of the performance
measure. Without multiple independent observations or replications, it is impossible to
estimate the variability of that estimate and therefore cannot construct a valid statistical
confidence interval. Multiple runs or special techniques like batch means are needed.
