ISYE 6644 OH Exam 1 Solutions – Spring 2026 - Georgia Institute Of Technology.
,Question 1
What is the name of Arena's primary modeling approach "world view"?
a) Event-Scheduling
b) Continuous Modeling Flowchart
c) Mixed Modeling
d) Event-Interaction
e) Process-Interaction
Rationale: Arena is built upon the Process-Interaction (P-I) modeling approach.
This means the simulation considers the sequence of events and activities (the
"process") that a generic customer or "entity" undergoes as it moves through the
system. The software then automatically manages the interactions between all such
entities .
Question 2
TRUE or FALSE? Discrete-event simulations are particularly suitable for
analyzing continuous-flow phenomena such as the velocity and altitude of an
aircraft as it comes in for a landing.
a) TRUE
b) FALSE
Rationale: FALSE. Discrete-event simulation (DES) is designed for systems
where changes occur at discrete points in time (like a customer arriving or a server
finishing). Continuous-flow phenomena, like the changing velocity and altitude of
an aircraft, are better modeled using continuous simulation or system dynamics,
where state variables change continuously over time .
,Question 3
Consider a single-server queue simulation with i.i.d. exponential interarrivals, i.i.d.
exponential services, and a first-in-first-out service discipline. Suppose that the
arrival rate is 5 per hour, and the service rate is 4 per hour. What will happen in the
long run?
a) The server will be busy about 20% of the time.
b) The server will be busy all of the time.
c) The number of customers in the system will never exceed 9.
d) The length of the line will never exceed 5.
Rationale: The key metric for a queueing system is the traffic intensity, denoted
as ρ (rho). It is calculated as the arrival rate divided by the service rate (ρ = λ/μ).
Here, ρ = 5/4 = 1.25. Since ρ > 1, the system is unstable. The arrival rate exceeds
the service rate, meaning the server cannot keep up with the inflow of customers,
and the queue length will grow indefinitely. Therefore, in the long run, the server
will be busy 100% of the time .
Question 4
The planet Glubnor has 120-day years. Suppose there are four Glubnorians in the
room. What is the probability that at least two of them share the same birthday?
a) 0.015
b) 0.025
c) 0.049
d) 0.149
Rationale: This is a classic birthday problem application. It is easier to calculate
the complement: the probability that no one shares a birthday. For four people, this
, is (120/120) * (119/120) * (118/120) * (117/120) = 0.9509. The probability that at
least two share a birthday is 1 - 0.9509 = 0.0491 .
Question 5
Suppose X has a mean of 5 and a variance of 2. Find Var(20 − 4X).
a) -4
b) 4
c) 8
d) 16
e) 32
Rationale: We use the variance property Var(aX + b) = a² * Var(X).
Here, a = -4 and b = 20.
Var(20 - 4X) = (-4)² * Var(X) = 16 * 2 = 32.
Note that adding or subtracting a constant (20 in this case) does not affect the
variance .
Question 6
Suppose the arrivals of clients to a bank can be modeled as a Poisson process with
a given hourly rate λ. Then the number of clients arriving between 10:00–11:00 am
is independent of the number of clients arriving between 1:00–2:00 pm.
a) TRUE
b) FALSE
Rationale: TRUE. One of the defining properties of a Poisson process is that it
has independent increments. This means the number of arrivals in two non-
overlapping time intervals are independent random variables. The intervals 10-11
,Question 1
What is the name of Arena's primary modeling approach "world view"?
a) Event-Scheduling
b) Continuous Modeling Flowchart
c) Mixed Modeling
d) Event-Interaction
e) Process-Interaction
Rationale: Arena is built upon the Process-Interaction (P-I) modeling approach.
This means the simulation considers the sequence of events and activities (the
"process") that a generic customer or "entity" undergoes as it moves through the
system. The software then automatically manages the interactions between all such
entities .
Question 2
TRUE or FALSE? Discrete-event simulations are particularly suitable for
analyzing continuous-flow phenomena such as the velocity and altitude of an
aircraft as it comes in for a landing.
a) TRUE
b) FALSE
Rationale: FALSE. Discrete-event simulation (DES) is designed for systems
where changes occur at discrete points in time (like a customer arriving or a server
finishing). Continuous-flow phenomena, like the changing velocity and altitude of
an aircraft, are better modeled using continuous simulation or system dynamics,
where state variables change continuously over time .
,Question 3
Consider a single-server queue simulation with i.i.d. exponential interarrivals, i.i.d.
exponential services, and a first-in-first-out service discipline. Suppose that the
arrival rate is 5 per hour, and the service rate is 4 per hour. What will happen in the
long run?
a) The server will be busy about 20% of the time.
b) The server will be busy all of the time.
c) The number of customers in the system will never exceed 9.
d) The length of the line will never exceed 5.
Rationale: The key metric for a queueing system is the traffic intensity, denoted
as ρ (rho). It is calculated as the arrival rate divided by the service rate (ρ = λ/μ).
Here, ρ = 5/4 = 1.25. Since ρ > 1, the system is unstable. The arrival rate exceeds
the service rate, meaning the server cannot keep up with the inflow of customers,
and the queue length will grow indefinitely. Therefore, in the long run, the server
will be busy 100% of the time .
Question 4
The planet Glubnor has 120-day years. Suppose there are four Glubnorians in the
room. What is the probability that at least two of them share the same birthday?
a) 0.015
b) 0.025
c) 0.049
d) 0.149
Rationale: This is a classic birthday problem application. It is easier to calculate
the complement: the probability that no one shares a birthday. For four people, this
, is (120/120) * (119/120) * (118/120) * (117/120) = 0.9509. The probability that at
least two share a birthday is 1 - 0.9509 = 0.0491 .
Question 5
Suppose X has a mean of 5 and a variance of 2. Find Var(20 − 4X).
a) -4
b) 4
c) 8
d) 16
e) 32
Rationale: We use the variance property Var(aX + b) = a² * Var(X).
Here, a = -4 and b = 20.
Var(20 - 4X) = (-4)² * Var(X) = 16 * 2 = 32.
Note that adding or subtracting a constant (20 in this case) does not affect the
variance .
Question 6
Suppose the arrivals of clients to a bank can be modeled as a Poisson process with
a given hourly rate λ. Then the number of clients arriving between 10:00–11:00 am
is independent of the number of clients arriving between 1:00–2:00 pm.
a) TRUE
b) FALSE
Rationale: TRUE. One of the defining properties of a Poisson process is that it
has independent increments. This means the number of arrivals in two non-
overlapping time intervals are independent random variables. The intervals 10-11
