Question 1

Suppose that 1 customer arrives each minute in a Poisson distribution. Is it more likely that 2 customers or 0 customers will arrive each minute?

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Question 2

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 10 machines arrive each hour and must wait 6 minutes in the line, how long will the line be, on average?

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Question 3

A finite population waiting line model with a single server has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes. Calculate the service factor X. If the population consists of 5 elements, what are the average number waiting, the average number being serviced, and the average number running? Refer to Table D.8 in the text.

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Question 4

A finite population waiting line model with a single server has an average service time T of 50 minutes and an average time between service requirements U of 350 minutes. Calculate the service factor X. If the population consists of 5 elements, what are the average number waiting, the average number being serviced, and the average number running? Refer to Table D.8 in the text.

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Question 5

A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic is uniformly busy with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.
a. What is the probability that the clinic is empty (except for the dentist)?
b. What percentage of the time is the dentist busy?
c. What is the average number of patients in the waiting room?
d. What is the average time a patient spends in the office (wait plus service)?
e. What is the average time a patient waits for service?

Accepted Answer

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Question 6

Suppose that a service facility has an average line of 2 customers that must wait, on average, 5 minutes for service. How many customers are arriving per hour?

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Question 7

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 12 machines arrive each hour and must wait 8 minutes in the line, how long will the line be, on average?

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Question 8

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 10 machines arrive each hour and must wait 7 minutes in the line, how long will the line be, on average?

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The answer of A manufacturing plant is trying to determine...

Question 9

Suppose that a fast food restaurant wants the average line to be 5 customers and that 90 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

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Question 10

Suppose that customer arrivals are governed by a Poisson distribution. If the average arrival rate is 60 customers each hour, how many times will 60 customers arrive during a one hour period for each time that only 40 customers arrive.

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Question 11

At the order fulfillment centre of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 140 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.
a. What is the utilization rate of the system?
b. What is the average number of packages waiting to be sorted?
c. What is the average number of packages in the sorting system?
d. How long must the average package wait until it gets sorted?

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Question 12

Suppose that a fast food restaurant wants the average line to be 5 customers and that 80 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

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Question 13

Genco, Inc., a small manufacturer of diesel-generator sets has four shearing machines. Because of the age of these machines, they need minor repairs after 30 hours of use. Analysis of previous breakdowns indicates that breakdowns follow a Poisson distribution. The facility employs one repairman specifically to repair these machines. Average repair time is two hours following an exponential distribution.
a. What is the service factor for this system?
b. What is the average number of these machines in service?
c. What is the impact of adding a second repairman?

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Question 14

Suppose that a fast food restaurant wants the average line to be 4 customers and that 80 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

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Question 15

On a typical Friday, an average of 12 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is four minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find:
a) The average time in the line.
b) The average number in the line.
c) The average time in the system.
d) The average number in the system.
e) The probability that the bank is empty.
f) If the business is considering adding a second teller (who would
work at the same rate as the first) to reduce the waiting time
for customers. She assumes that this will cut the waiting time in
half. If a second teller is added, find the new answers to parts (a)
to (e).

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The answer of On a typical Friday, an average of...

Question 16

At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 100 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour. a. What is the utilization rate of the system? b. What is the average number of packages waiting to be sorted? c. What is the average number of packages in the sorting system? d. How long must the average package wait until it gets sorted? e. What would L_q and W_q be if the service rate were exponential, not constant?

Accepted Answer

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Question 17

A waiting-line system that meets the assumptions of M/M/1 has = 1, = 4. Calculate P_o. Build a table showing the probability of more than 0, 1, 2, 3, 4, 5, 6,and 7 units in the system. Round to six decimal places in your work

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Question 18

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.
a. What is the probability that the system is empty?
b. What is the probability that there is precisely one vehicle in the system?
c. What is the probability that there is more than one vehicle in the system?
d. What is the probability of 5 or more vehicles in the system?

Accepted Answer

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Question 19

A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.
a. What is the probability that the clinic is empty (except for the dentist)?
b. What is the probability that there are one or more patients in the system?
c. What is the probability that there are four patients in the system?
d. What is the probability that there are four or more patients in the system?

Accepted Answer

The answer of A dental clinic at which only one...

Question 20

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). Which is cheaper, the existing system with one service crew, or a revised system with two service crews?

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The answer of A crew of mechanics at the Highway...

Quiz 21: Waiting-Line Models

Suppose that 1 customer arrives each minute in a Poisson distribution. Is it more likely that 2 customers or 0 customers will arrive each minute?

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 10 machines arrive each hour and must wait 6 minutes in the line, how long will the line be, on average?

Suppose that a service facility has an average line of 2 customers that must wait, on average, 5 minutes for service. How many customers are arriving per hour?

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 12 machines arrive each hour and must wait 8 minutes in the line, how long will the line be, on average?

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 10 machines arrive each hour and must wait 7 minutes in the line, how long will the line be, on average?

Suppose that a fast food restaurant wants the average line to be 5 customers and that 90 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

Suppose that customer arrivals are governed by a Poisson distribution. If the average arrival rate is 60 customers each hour, how many times will 60 customers arrive during a one hour period for each time that only 40 customers arrive.

Suppose that a fast food restaurant wants the average line to be 5 customers and that 80 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

Suppose that a fast food restaurant wants the average line to be 4 customers and that 80 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

A waiting-line system that meets the assumptions of M/M/1 has = 1, = 4. Calculate Po. Build a table showing the probability of more than 0, 1, 2, 3, 4, 5, 6,and 7 units in the system. Round to six decimal places in your work

A waiting-line system that meets the assumptions of M/M/1 has = 1, = 4. Calculate P_o. Build a table showing the probability of more than 0, 1, 2, 3, 4, 5, 6,and 7 units in the system. Round to six decimal places in your work