Question

**Question 2**

A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered:

- A single-channel operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes.
- A single-channel operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes.
- A two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 2 minutes for each channel.

Answer the following questions and recommend an alternative design for the fast-food franchise:

- What is the probability that no cars are in the system?
- What is the average number of cars waiting for service?
- What is the average number of cars in the system?
- What is the average time a car waits for service?
- What is the average time in the system?
- What is the probability that an arriving car will have to wait for service?

The following cost information is available for the fast-food franchise above:

- Customer waiting time is valued at $25 per hour to reflect the fact that waiting time is costly to the fast-food business.
- The cost of each employee is $6.50 per hour.
- To account for equipment and space, an additional cost of $20 per hour is attributable to each channel.

What is the lowest-cost design for the fast-food business?

These are two question of queuing theory which I am not certain that I understand could you please work out and provide me with explanation as to how the answer was found.

Answer #1

A fast-food franchise is considering operating a drive-up window
food-service operation. Assume that customer arrivals follow a
Poisson probability distribution, with an arrival rate of 24 cars
per hour, and that service times follow an exponential probability
distribution. Arriving customers place orders at an intercom
station at the back of the parking lot and then drive to the
service window to pay for and receive their orders. The following
three service alternatives are being considered:
System A: A single-server operation...

A fast-food franchise is considering operating a drive-up window
food-service operation. Assume that customer arrivals follow a
Poisson probability distribution, with an arrival rate of 25 cars
per hour, and that service times follow an exponential probability
distribution. Arriving customers place orders at an intercom
station at the back of the parking lot and then drive to the
service window to pay for and receive their orders. The following
service alternative is being considered:
System C: A two-server operation with...

Burrito King (a new fast-food franchise opening up nationwide)
has successfully automated burrito production for its drive-up
fast-food establishments. The Burro-Master 9000 requires a constant
45 seconds to produce a batch of burritos. It has been estimated
that customers will arrive at the drive-up window according to a
Poisson distribution at an average of one every 48 seconds. To help
determine the amount of space needed for the line at the drive-up
window, answer the following questions.
a. What is...

28. You are the manager of a restaurant for a fast-food
franchise. Last month, the mean waiting time at the drive-through
window for branches in your geographical region, as measured from
the time a customer places an order until the time the customer
receives the order, was 3.8 minutes. You select a random sample of
81 orders. The sample mean waiting time is 3.99 minutes, with a
sample standard deviation of 0.9 minute.
At the 0.10 level of significance, is...

You are the manager of a restaurant for a fast-food franchise.
Last month, the mean waiting time at the drive-through window for
branches in your geographical region, as measured from the time a
customer places an order until the time the customer receives the
order, was
3.7 minutes. You select a random sample of 64 orders. The sample
mean waiting time is 3.41 minutes, with a sample standard
deviation of 0.8 minute.
Find the p-value.
p-value= ( )
(Round to...

Burrito King (a new fast-food franchise opening up nationwide)
has successfully automated burrito production for its drive-up
fast-food establishments. The Burro-Master 9000 requires a constant
30 seconds to produce a batch of burritos. It has been estimated
that customers will arrive at the drive-up window according to a
Poisson distribution at an average of one every 55 seconds. To help
determine the amount of space needed for the line at the drive-up
window, answer the following questions.
a. What is...

You are the manager of a restaurant for a fast-food franchise.
Last month, the mean waiting time at the drive-through window for
branches in your geographical region, as measured from the time a
customer places an order until the time the customer receives the
order, was 3.7 minutes. You select a random sample of 81 orders.
The sample mean waiting time is 3.41 minutes, with a sample
standard deviation of 0.9 minute. At the 0.01 level of
significance, is there...

You are the manager of a restaurant for a fast-food franchise.
Last month, the mean waiting time at the drive- through window for
branches in your geographical region, as measured from the time a
customer places an order until the time the customer receives the
order, was 3.7 minutes. You select a random sample of 64 orders.
The sample mean waiting time is 3.57 minutes, with a sample
standard deviation of 0.8 minute.
1- At a 95% confidence level, is...

A new fast-food franchise has successfully automated burrito
production.
50 seconds are are required to produce a batch of
burritos.
It is estimated that customers will arrive at the drive-up window
at an average of one per 70 seconds according to
poisson distribution.
(Do not round intermediate calculations, round final answers to
2 decimals)
[a] What is average line length in cars?
[b] What is the average number of cars in the system (both in line
& at window)?
[c]...

Willow Brook National Bank operates a drive-up teller window
that allows customers to complete bank transactions without getting
out of their cars. On weekday mornings, arrivals to the drive-up
teller window occur at random, with an arrival rate of 30 customers
per hour or 0.5 customers per minute. In the same bank waiting line
system, assume that the service times for the drive-up teller
follow an exponential probability distribution with a service rate
of 36 customers per hour, or 0.6...

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