Question 1

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ= 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 2

A dental clinic at which only one dentist works is open only two days a week.During those two days,patients arrive 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 and staff)?
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?

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Question 3

Service times in an automobile repair shop tend to follow which probability distribution?
A)exponential
B)normal
C)triangular
D)binomial
E)Erlang

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Question 4

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 5

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).What is the expected cost of this system?

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Question 6

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_qand W_q be if the service rate were exponential,not constant?

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Question 7

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7 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.
a.What is the utilization rate for this service system?
b.What is the average time before the facility can return a breakdown to service?
c.How much of that time is spent waiting for service?
d.How many vehicles are likely to be waiting for service at any one time?

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Question 8

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?

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Question 9

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 5 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?

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Question 10

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 11

A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the probability that the waiting line is empty?

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Question 12

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7.5 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 utilization rate for this service system?
b.What is the average time before the facility can return a breakdown to service?
c.How much of that time is spent waiting for service?
d.How many vehicles are likely to be in the system at any one time?

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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 and staff)?
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?

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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 hour.How many minutes will the average customer be forced to wait in line?

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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.

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Question 16

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 17

A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the average time a unit spends in the system and the average time a unit spends waiting (in hours)?

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Question 18

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 19

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...

Quiz 25: Waiting-Line Models

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ= 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

Service times in an automobile repair shop tend to follow which probability distribution?

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 10 machines arrive each hour and must wait 6 minutes in the line,how long will the line be,on average?

A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the probability that the waiting line is empty?

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

A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the average time a unit spends in the system and the average time a unit spends waiting (in hours)?

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ= 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