Topic Coverage
• Simulation Basics (Q1–20)
• Probability Basics (Q21–40)
• Common Distributions (Q41–60)
• Random Number Generation (Q61–80)
• Input Analysis (Q81–95)
• Statistics & Estimation (Q96–115)
• Output Analysis (Q116–125)
• Queueing Theory (Q126–140)
• Variance Reduction Techniques (Q141–150)
• Statistical Tests for RNGs (Q151–160)
• Simulation Languages & Tools (Q161–167)
• Markov Chains (Q168–173)
• Additional Probability (Q174–183)
• Stochastic Processes (Q184–190)
• Arena Simulation (Q191–205)
• Estimation & Regression (Q206–213)
• Simulation Design (Q214–223)
• PGFs & Further Topics (Q224–300)
Q1: What is simulation?
ANSWER Simulation is the process of designing a model of a real or
proposed system and conducting experiments with that model to understand
the system's behavior or evaluate strategies for its operation.
Q2: What are the main advantages of simulation?
ANSWER Advantages include: the ability to study complex systems, safe
testing without disrupting real systems, ability to compress or expand time,
and cost-effectiveness compared to real experiments.
Q3: What are disadvantages of simulation?
, ANSWER Disadvantages include: results may be difficult to interpret,
simulation models can be expensive and time-consuming to build, and they
only provide estimates rather than exact answers.
Q4: What is a discrete-event simulation (DES)?
ANSWER A DES models a system as a sequence of events that occur at
discrete points in time, where each event changes the system state.
Q5: What is continuous simulation?
ANSWER Continuous simulation models systems where state variables
change continuously over time, typically described by differential equations.
Q6: What is a system state in simulation?
ANSWER The system state is the collection of variables needed to describe
the system at any given time.
Q7: What is an entity in simulation?
ANSWER An entity is an object of interest that flows through the simulation
model, such as customers in a queue or parts in a manufacturing system.
Q8: What is an event in simulation?
ANSWER An event is an instantaneous occurrence that changes the state of
the system.
Q9: What is the future event list (FEL)?
ANSWER The FEL (also called the event calendar) is a list of all future
scheduled events ordered by the time at which they are to occur.
Q10: What is simulation clock?
ANSWER The simulation clock is a variable that keeps track of the current
simulated time.
Q11: What is the event-scheduling algorithm?
ANSWER It is a simulation algorithm that advances time to the next event,
processes that event, updates the system state, schedules future events, and
repeats.
Q12: What is the activity-scanning approach?
ANSWER A simulation approach where activities are checked at each time
step to see if conditions for their execution are met.
Q13: What is a resource in simulation?
ANSWER A resource is something required by entities to perform activities
(e.g., servers, machines, workers).
Q14: What is a queue in simulation context?
, ANSWER A queue is a waiting line where entities wait for a resource to
become available.
Q15: What is warm-up period in simulation?
ANSWER The warm-up period (initialization bias period) is the initial
transient phase of a simulation run that should often be discarded before
collecting steady-state statistics.
Q16: What is steady-state simulation?
ANSWER A steady-state simulation studies the long-run behavior of a
system, where performance measures are not dependent on initial conditions.
Q17: What is a terminating simulation?
ANSWER A simulation that runs for a natural or pre-specified finite time
horizon, such as one day of bank operations.
Q18: What is the difference between terminating and steady-state
simulation?
ANSWER Terminating simulations run until a stopping event and initial
conditions matter, while steady-state simulations study long-run behavior after
the system reaches statistical equilibrium.
Q19: What is verification in simulation?
ANSWER Verification is the process of ensuring the simulation model is
implemented correctly and behaves as the conceptual model intends.
Q20: What is validation in simulation?
ANSWER Validation is the process of determining whether the simulation
model accurately represents the real system being studied.
Q21: Define a sample space.
ANSWER The sample space S is the set of all possible outcomes of a
random experiment.
Q22: Define an event.
ANSWER An event is a subset of the sample space.
Q23: What is the complement of an event A?
ANSWER The complement of A, denoted A', is the set of all outcomes in S
that are NOT in A. P(A') = 1 - P(A).
Q24: State the addition rule for two events.
ANSWER P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Q25: When are two events mutually exclusive?
, ANSWER Two events are mutually exclusive (disjoint) if they cannot occur
simultaneously, i.e., A ∩ B = ∅, so P(A ∪ B) = P(A) + P(B).
Q26: Define conditional probability.
ANSWER P(A|B) = P(A ∩ B) / P(B), provided P(B) > 0. It is the probability of
A given that B has occurred.
Q27: When are two events independent?
ANSWER Events A and B are independent if P(A ∩ B) = P(A)·P(B), or
equivalently P(A|B) = P(A).
Q28: State Bayes' Theorem.
ANSWER P(A|B) = P(B|A)·P(A) / P(B), where P(B) = Σ P(B|Aᵢ)·P(Aᵢ) by total
probability.
Q29: What is the law of total probability?
ANSWER If B₁, B₂, ..., Bₙ are mutually exclusive and exhaustive events, then
P(A) = Σᵢ P(A|Bᵢ)·P(Bᵢ).
Q30: What is a random variable?
ANSWER A random variable is a function that assigns a numerical value to
each outcome in a sample space.
Q31: What is a discrete random variable?
ANSWER A discrete RV takes a countable number of distinct values.
Q32: What is a continuous random variable?
ANSWER A continuous RV can take any value in an interval (uncountable
range); probabilities are defined over intervals.
Q33: What is a PMF?
ANSWER A Probability Mass Function (PMF) f(x) = P(X = x) gives the
probability that a discrete RV X equals each possible value x.
Q34: What is a PDF?
ANSWER A Probability Density Function (PDF) f(x) satisfies: f(x) ≥ 0 and
∫f(x)dx = 1. P(a ≤ X ≤ b) = ∫[a to b] f(x)dx.
Q35: What is a CDF?
ANSWER The Cumulative Distribution Function F(x) = P(X ≤ x). For
continuous RVs, F(x) = ∫[-∞ to x] f(t)dt.
Q36: What is E[X] (expected value)?
ANSWER For discrete X: E[X] = Σ x·P(X=x). For continuous X: E[X] = ∫
x·f(x)dx.
Q37: What is Var(X)?
• Simulation Basics (Q1–20)
• Probability Basics (Q21–40)
• Common Distributions (Q41–60)
• Random Number Generation (Q61–80)
• Input Analysis (Q81–95)
• Statistics & Estimation (Q96–115)
• Output Analysis (Q116–125)
• Queueing Theory (Q126–140)
• Variance Reduction Techniques (Q141–150)
• Statistical Tests for RNGs (Q151–160)
• Simulation Languages & Tools (Q161–167)
• Markov Chains (Q168–173)
• Additional Probability (Q174–183)
• Stochastic Processes (Q184–190)
• Arena Simulation (Q191–205)
• Estimation & Regression (Q206–213)
• Simulation Design (Q214–223)
• PGFs & Further Topics (Q224–300)
Q1: What is simulation?
ANSWER Simulation is the process of designing a model of a real or
proposed system and conducting experiments with that model to understand
the system's behavior or evaluate strategies for its operation.
Q2: What are the main advantages of simulation?
ANSWER Advantages include: the ability to study complex systems, safe
testing without disrupting real systems, ability to compress or expand time,
and cost-effectiveness compared to real experiments.
Q3: What are disadvantages of simulation?
, ANSWER Disadvantages include: results may be difficult to interpret,
simulation models can be expensive and time-consuming to build, and they
only provide estimates rather than exact answers.
Q4: What is a discrete-event simulation (DES)?
ANSWER A DES models a system as a sequence of events that occur at
discrete points in time, where each event changes the system state.
Q5: What is continuous simulation?
ANSWER Continuous simulation models systems where state variables
change continuously over time, typically described by differential equations.
Q6: What is a system state in simulation?
ANSWER The system state is the collection of variables needed to describe
the system at any given time.
Q7: What is an entity in simulation?
ANSWER An entity is an object of interest that flows through the simulation
model, such as customers in a queue or parts in a manufacturing system.
Q8: What is an event in simulation?
ANSWER An event is an instantaneous occurrence that changes the state of
the system.
Q9: What is the future event list (FEL)?
ANSWER The FEL (also called the event calendar) is a list of all future
scheduled events ordered by the time at which they are to occur.
Q10: What is simulation clock?
ANSWER The simulation clock is a variable that keeps track of the current
simulated time.
Q11: What is the event-scheduling algorithm?
ANSWER It is a simulation algorithm that advances time to the next event,
processes that event, updates the system state, schedules future events, and
repeats.
Q12: What is the activity-scanning approach?
ANSWER A simulation approach where activities are checked at each time
step to see if conditions for their execution are met.
Q13: What is a resource in simulation?
ANSWER A resource is something required by entities to perform activities
(e.g., servers, machines, workers).
Q14: What is a queue in simulation context?
, ANSWER A queue is a waiting line where entities wait for a resource to
become available.
Q15: What is warm-up period in simulation?
ANSWER The warm-up period (initialization bias period) is the initial
transient phase of a simulation run that should often be discarded before
collecting steady-state statistics.
Q16: What is steady-state simulation?
ANSWER A steady-state simulation studies the long-run behavior of a
system, where performance measures are not dependent on initial conditions.
Q17: What is a terminating simulation?
ANSWER A simulation that runs for a natural or pre-specified finite time
horizon, such as one day of bank operations.
Q18: What is the difference between terminating and steady-state
simulation?
ANSWER Terminating simulations run until a stopping event and initial
conditions matter, while steady-state simulations study long-run behavior after
the system reaches statistical equilibrium.
Q19: What is verification in simulation?
ANSWER Verification is the process of ensuring the simulation model is
implemented correctly and behaves as the conceptual model intends.
Q20: What is validation in simulation?
ANSWER Validation is the process of determining whether the simulation
model accurately represents the real system being studied.
Q21: Define a sample space.
ANSWER The sample space S is the set of all possible outcomes of a
random experiment.
Q22: Define an event.
ANSWER An event is a subset of the sample space.
Q23: What is the complement of an event A?
ANSWER The complement of A, denoted A', is the set of all outcomes in S
that are NOT in A. P(A') = 1 - P(A).
Q24: State the addition rule for two events.
ANSWER P(A ∪ B) = P(A) + P(B) - P(A ∩ B).
Q25: When are two events mutually exclusive?
, ANSWER Two events are mutually exclusive (disjoint) if they cannot occur
simultaneously, i.e., A ∩ B = ∅, so P(A ∪ B) = P(A) + P(B).
Q26: Define conditional probability.
ANSWER P(A|B) = P(A ∩ B) / P(B), provided P(B) > 0. It is the probability of
A given that B has occurred.
Q27: When are two events independent?
ANSWER Events A and B are independent if P(A ∩ B) = P(A)·P(B), or
equivalently P(A|B) = P(A).
Q28: State Bayes' Theorem.
ANSWER P(A|B) = P(B|A)·P(A) / P(B), where P(B) = Σ P(B|Aᵢ)·P(Aᵢ) by total
probability.
Q29: What is the law of total probability?
ANSWER If B₁, B₂, ..., Bₙ are mutually exclusive and exhaustive events, then
P(A) = Σᵢ P(A|Bᵢ)·P(Bᵢ).
Q30: What is a random variable?
ANSWER A random variable is a function that assigns a numerical value to
each outcome in a sample space.
Q31: What is a discrete random variable?
ANSWER A discrete RV takes a countable number of distinct values.
Q32: What is a continuous random variable?
ANSWER A continuous RV can take any value in an interval (uncountable
range); probabilities are defined over intervals.
Q33: What is a PMF?
ANSWER A Probability Mass Function (PMF) f(x) = P(X = x) gives the
probability that a discrete RV X equals each possible value x.
Q34: What is a PDF?
ANSWER A Probability Density Function (PDF) f(x) satisfies: f(x) ≥ 0 and
∫f(x)dx = 1. P(a ≤ X ≤ b) = ∫[a to b] f(x)dx.
Q35: What is a CDF?
ANSWER The Cumulative Distribution Function F(x) = P(X ≤ x). For
continuous RVs, F(x) = ∫[-∞ to x] f(t)dt.
Q36: What is E[X] (expected value)?
ANSWER For discrete X: E[X] = Σ x·P(X=x). For continuous X: E[X] = ∫
x·f(x)dx.
Q37: What is Var(X)?
