ISYE 6644 Week 1 Homework Simulation
Week 1 Homework
Instructions
Attempt History
Score for this quiz: 11 out of 12
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:
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
Week 1 Homework
Instructions
Attempt History
Score for this quiz: 11 out of 12
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:
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
