9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
Week 1 Homework
Due Sep 4 at 11:59pm
Points 12
Questions 12
Available Aug 28 at 8am - Sep 7 at 11:59pm
Time Limit None
Instructions
Please answer all the questions below.
This quiz was locked Sep 7 at 11:59pm.
Attempt History
Attempt Time Score
LATEST Attempt 1 827 minutes 12 out of 12
Score for this quiz: 12 out of 12
Submitted Aug 29 at 6:13pm
This attempt took 827 minutes.
Correct answer
Question 1
pts
(Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having height = 1000 feet.
You're a strong bloke, so the initial downward velocity is = -100 feet/sec (slightly under 70 miles/hr).
Further, in this neck of the woods, it turns out there is no friction in the atmosphere - amazing! Now you
remember from your Baby Physics class that the height after time is
When does the rock hit the ground?
a. -11.625 sec
b. 2 sec
c. 5.375 sec
Set
and solve for t. Quadratics are easy:
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 1/9
, 9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
which we take as the answer since the negative answer doesn't make practical sense.
d. 11.625 sec
e. 10 sec
Set
and solve for t. Quadratics are easy:
which we take as the answer since the negative answer doesn't make practical sense.
Correct answer
Question 2
pts
(Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between
customer arrivals are independent, identically distributed Exp(λ = 2/hr) random variables; and the service
times are i.i.d. Exp(µ = 3/hr). Unfortunately, if a potential arriving customer sees that the server is
occupied, he gets mad and leaves the system. Thus, the system can have either 0 or 1 customer in it at
any time. This is what’s known as an M/M/1/1 queue. If denotes the probability that a customer is
being served at time t, trust me that it can be shown that
If the system is empty at time 0, i.e., , what is the probability that there will be no people in the
system at time 1 hr?
a. 1
b. 2/3
c. 0.397
d. 0.603
At time , we have
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 2/9
Week 1 Homework
Due Sep 4 at 11:59pm
Points 12
Questions 12
Available Aug 28 at 8am - Sep 7 at 11:59pm
Time Limit None
Instructions
Please answer all the questions below.
This quiz was locked Sep 7 at 11:59pm.
Attempt History
Attempt Time Score
LATEST Attempt 1 827 minutes 12 out of 12
Score for this quiz: 12 out of 12
Submitted Aug 29 at 6:13pm
This attempt took 827 minutes.
Correct answer
Question 1
pts
(Lesson 1.3: Deterministic Model.) Suppose you throw a rock off a cliff having height = 1000 feet.
You're a strong bloke, so the initial downward velocity is = -100 feet/sec (slightly under 70 miles/hr).
Further, in this neck of the woods, it turns out there is no friction in the atmosphere - amazing! Now you
remember from your Baby Physics class that the height after time is
When does the rock hit the ground?
a. -11.625 sec
b. 2 sec
c. 5.375 sec
Set
and solve for t. Quadratics are easy:
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 1/9
, 9/27/26, 2:17 PM Week 1 Homework: Simulation - ISYE-6644-OAN/O01/Q/ASY
which we take as the answer since the negative answer doesn't make practical sense.
d. 11.625 sec
e. 10 sec
Set
and solve for t. Quadratics are easy:
which we take as the answer since the negative answer doesn't make practical sense.
Correct answer
Question 2
pts
(Lesson 1.3: Stochastic Model.) Consider a single-server queueing system where the times between
customer arrivals are independent, identically distributed Exp(λ = 2/hr) random variables; and the service
times are i.i.d. Exp(µ = 3/hr). Unfortunately, if a potential arriving customer sees that the server is
occupied, he gets mad and leaves the system. Thus, the system can have either 0 or 1 customer in it at
any time. This is what’s known as an M/M/1/1 queue. If denotes the probability that a customer is
being served at time t, trust me that it can be shown that
If the system is empty at time 0, i.e., , what is the probability that there will be no people in the
system at time 1 hr?
a. 1
b. 2/3
c. 0.397
d. 0.603
At time , we have
https://gatech.instructure.com/courses/538298/quizzes/799003?module_item_id=6187718 2/9
