Question 1

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 2

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 3

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 4

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 5

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 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?

Accepted Answer

The answer of At the order fulfillment center of a...

Question 6

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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Question 7

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 8

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.

Accepted Answer

The answer of A finite population waiting line model with...

Question 9

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?

Accepted Answer

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Question 10

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 11

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 12

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 Lq and Wq be if the service rate were exponential, not constant?

Accepted Answer

The answer of At the order fulfillment center of a...

Question 13

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 14

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

Accepted Answer

The answer of A waiting-line system that meets the assumptions...

Question 15

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.

Accepted Answer