ISYE 6644 - Simulation & Modeling for Engineering (2026/2027) - Final Exam |
QUESTIONS AND CORRECT ANSWERS WITH COMPLETE SOLUTION
Georgia Institute of Technology - ISYE 6644 Simulation & Modeling for Engineering Final Examination
| Core Domains: Discrete-Event Simulation, Random Number Generation, Input Modeling, Output
Analysis, Verification & Validation, Simulation Languages, Queueing Theory, Monte Carlo Methods,
Statistical Analysis, and Advanced Simulation Applications | Graduate-Level Engineering Focus |
Exam-Aligned Format
Exam Structure
The ISYE 6644 final exam for the 2026/2027 academic cycle is typically structured as follows:
● Comprehensive exam covering all course modules
● Multiple-choice, computational, and conceptual analysis questions
● Focus on application of simulation principles to engineering problems
● Time-limited format (typically 2–3 hours)
● Covers theoretical foundations and practical implementation of simulation models
Introduction
This ISYE 6644 Final Exam preparation guide for the 2026/2027 academic year reflects the latest
simulation methodologies and modeling techniques essential for engineering applications. The content
emphasizes computational thinking, statistical validation, and practical implementation of discrete-event
and Monte Carlo simulation systems.
Solution Format
All correct answers and key computational solutions must be presented in bold and green, followed by
detailed explanations of simulation methodologies, statistical reasoning, and engineering applications.
1. In discrete-event simulation, what defines the system state?
A. The simulation clock time only
B. The random number seed
C. A set of variables that describe the system at any point in time
D. The output statistics collected
, The system state consists of all variables necessary to describe the system’s condition at a given time
(e.g., number of customers in queue, server status). It evolves only at event times in discrete-event
simulation.
2. Which of the following is a requirement for a linear congruential generator (LCG) to
have full period?
A. The modulus m must be prime
B. The multiplier a must be even
C. The increment c and modulus m must be relatively prime
D. The seed must be zero
For an LCG Xn+1 = (aXn + c) mod m to have full period m, Hull-Dobell conditions require: (i) c and m
coprime, (ii) a−1 divisible by all prime factors of m, and (iii) if m divisible by 4, then a−1 divisible by
4.
3. Suppose you use the inverse transform method to generate an exponential random
variable with rate λ = 2. Given U = 0.3 (uniform(0,1)), what is the generated value?
A. 0.6
B. 1.2
C. 0.60199
D. 0.15
For exponential(λ), the inverse CDF is F⁻¹(U) = −(1/λ) ln(1−U). Using U = 0.3:
X = −(1/2) * ln(1 − 0.3) = −0.5 * ln(0.7) ≈ −0.5 * (−0.3567) ≈ 0.1783
Correction: ln(0.7) ≈ −0.3567, so X ≈ 0.1783. However, if using U directly (some texts use F⁻¹(U) =
−(1/λ) ln(U)): X = −0.5 * ln(0.3) ≈ −0.5 * (−1.2040) ≈ 0.6020. The standard inverse transform for
exponential uses F⁻¹(U) = −(1/λ) ln(1−U), but since U and 1−U are identically distributed, both are
acceptable. The common convention in simulation is to use X = −(1/λ) ln(U). Thus, with U = 0.3: X =
−0.5 * ln(0.3) ≈ 0.6020.
QUESTIONS AND CORRECT ANSWERS WITH COMPLETE SOLUTION
Georgia Institute of Technology - ISYE 6644 Simulation & Modeling for Engineering Final Examination
| Core Domains: Discrete-Event Simulation, Random Number Generation, Input Modeling, Output
Analysis, Verification & Validation, Simulation Languages, Queueing Theory, Monte Carlo Methods,
Statistical Analysis, and Advanced Simulation Applications | Graduate-Level Engineering Focus |
Exam-Aligned Format
Exam Structure
The ISYE 6644 final exam for the 2026/2027 academic cycle is typically structured as follows:
● Comprehensive exam covering all course modules
● Multiple-choice, computational, and conceptual analysis questions
● Focus on application of simulation principles to engineering problems
● Time-limited format (typically 2–3 hours)
● Covers theoretical foundations and practical implementation of simulation models
Introduction
This ISYE 6644 Final Exam preparation guide for the 2026/2027 academic year reflects the latest
simulation methodologies and modeling techniques essential for engineering applications. The content
emphasizes computational thinking, statistical validation, and practical implementation of discrete-event
and Monte Carlo simulation systems.
Solution Format
All correct answers and key computational solutions must be presented in bold and green, followed by
detailed explanations of simulation methodologies, statistical reasoning, and engineering applications.
1. In discrete-event simulation, what defines the system state?
A. The simulation clock time only
B. The random number seed
C. A set of variables that describe the system at any point in time
D. The output statistics collected
, The system state consists of all variables necessary to describe the system’s condition at a given time
(e.g., number of customers in queue, server status). It evolves only at event times in discrete-event
simulation.
2. Which of the following is a requirement for a linear congruential generator (LCG) to
have full period?
A. The modulus m must be prime
B. The multiplier a must be even
C. The increment c and modulus m must be relatively prime
D. The seed must be zero
For an LCG Xn+1 = (aXn + c) mod m to have full period m, Hull-Dobell conditions require: (i) c and m
coprime, (ii) a−1 divisible by all prime factors of m, and (iii) if m divisible by 4, then a−1 divisible by
4.
3. Suppose you use the inverse transform method to generate an exponential random
variable with rate λ = 2. Given U = 0.3 (uniform(0,1)), what is the generated value?
A. 0.6
B. 1.2
C. 0.60199
D. 0.15
For exponential(λ), the inverse CDF is F⁻¹(U) = −(1/λ) ln(1−U). Using U = 0.3:
X = −(1/2) * ln(1 − 0.3) = −0.5 * ln(0.7) ≈ −0.5 * (−0.3567) ≈ 0.1783
Correction: ln(0.7) ≈ −0.3567, so X ≈ 0.1783. However, if using U directly (some texts use F⁻¹(U) =
−(1/λ) ln(U)): X = −0.5 * ln(0.3) ≈ −0.5 * (−1.2040) ≈ 0.6020. The standard inverse transform for
exponential uses F⁻¹(U) = −(1/λ) ln(1−U), but since U and 1−U are identically distributed, both are
acceptable. The common convention in simulation is to use X = −(1/λ) ln(U). Thus, with U = 0.3: X =
−0.5 * ln(0.3) ≈ 0.6020.
