Question 1

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,what is the probability of fewer than two units in the system?
A)0.0625
B)0.25
C)0.75
D)0.9375
E)1.00

Accepted Answer

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Question 2

A finite population waiting line model has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes.What is the service factor X?
A)0.20
B)0.40
C)0.60
D)0.67
E)2.5

Accepted Answer

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Question 3

Students arrive randomly at the help desk of the computer lab.There is only one service agent,and the time required for inquiry varies from student to student.Arrival rates have been found to follow the Poisson distribution,and the service times follow the negative exponential distribution.The average arrival rate is 12 students per hour,and the average service rate is 20 students per hour.How many students,on average,will be waiting in line at any one time?
A)0.9 students
B)1.5 students
C)3 students
D)4 students
E)36 students

Accepted Answer

The average number of students waiting in line can be calculated using the formula $L_q = \frac{\lambda^2}{\mu(\mu - \lambda)}$, where $\lambda$ is the arrival rate and $\mu$ is the service rate. Plugging in $\lambda = 12$ students per hour and $\mu = 20$ students per hour, we get $L_q = \frac{12^2}{20(20 - 12)} = \frac{144}{160} = 0.9$ students.

Question 4

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,what is the probability of more than two units in the system?
A)zero
B)0.015625
C)0.0625
D)0.25
E)0.9375

Accepted Answer

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Question 5

What are Ls and Lq,as used in waiting line terminology? Which is larger,Ls or Lq? Explain.

Accepted Answer

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Question 6

A waiting-line system that meets the assumptions of M/M/S has λ = 5,μ = 4,and M = 2.For these values,Po is approximately 0.23077,and Ls is approximately 2.05128.What is the average number of units waiting in the queue?
A)approximately 0.1603
B)approximately 0.4103
C)approximately 0.8013
D)approximately 1.0417
E)Cannot be calculated because λ is larger than μ.

Accepted Answer

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Question 7

The ________ of a waiting line and the probability that the queue is empty add to one.

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Question 8

A waiting-line system that meets the assumptions of M/M/S has λ = 5,μ = 4,and M = 2.For these values,Po is approximately 0.23077,and Ls is approximately 2.05128.What is the average time a unit spends in this system?
A)approximately 0.1603
B)approximately 0.2083
C)approximately 0.4103
D)approximately 0.8013
E)Cannot be calculated because λ is larger than μ.

Accepted Answer

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Question 9

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,Po is ________ and utilization is ________.
A)0.75; 0.25
B)0.80; .20
C)-3; -4
D)3; 4
E)none of the above

Accepted Answer

Using the M/M/1 assumptions, we can calculate Po as:
Po = 1 - (λ/μ) = 1 - (1/4) = 0.75
Utilization is calculated as:
Utilization = λ/μ = 1/4 = 0.25
Therefore, the correct choice is A.

Question 10

In a finite or limited population waiting line,the ________ is calculated from the average service time and average time between service requirements before the problem can be completed.

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Question 11

You have seen that,in an M/D/1 problem,the average queue length is exactly one-half the average queue length of an otherwise identical M/M/1 problem.Are all other performance statistics one-half as large also? Explain.

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Question 12

A finite population waiting line model has an average service time T of 100 minutes and an average time between service requirements U of 400 minutes.What is the service factor X?
A)0.20
B)0.25
C)4
D)5
E)300 minutes

Accepted Answer

The service factor X is the ratio of the average service time T to the average time between service requirements U. Therefore, X = T/U = 100/400 = 0.25.

Question 13

Little's Law is not applicable in which of the following situations?
A)the opening of a toy store on Black Friday morning
B)a 24-hour supermarket
C)a gas station with 24-hour self-service pumps
D)B and C
E)It is applicable to A,B,and C.

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Question 14

Which of the following is a requirement for application of Little's Law to be valid?
A)arrival rates that follow the Poisson distribution
B)FIFO queue discipline
C)steady state conditions
D)single-server system
E)multiphase system

Accepted Answer

Little's Law requires that the system is in steady state conditions, meaning that the arrival rate, service rate, and queue size are all stable and not changing over time. The other choices (A, B, D, E) are not requirements for the application of Little's Law.

Question 15

What are the six assumptions underlying the M/M/1 waiting line model? Which of these also hold for the M/D/1 model?

Accepted Answer

The answer of What are the six assumptions underlying the...

Question 16

Students arrive randomly at the help desk of the computer lab.There is only one service agent,and the time required for inquiry varies from student to student.Arrival rates have been found to follow the Poisson distribution,and the service times follow the negative exponential distribution.The average arrival rate is 12 students per hour,and the average service rate is 20 students per hour.What is the utilization factor?
A)20%
B)30%
C)40%
D)50%
E)60%

Accepted Answer

The answer of Students arrive randomly at the help desk...

Question 17

A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 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)?

Accepted Answer

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Question 18

Why must the service rate be greater than the arrival rate in a single-server system?

Accepted Answer

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Question 19

Students arrive randomly at the help desk of the computer lab.There is only one service agent,and the time required for inquiry varies from student to student.Arrival rates have been found to follow the Poisson distribution,and the service times follow the negative exponential distribution.The average arrival rate is 12 students per hour,and the average service rate is 20 students per hour.A student has just entered the system.How long is she expected to stay in the system?
A)0.125 minutes
B)0.9 minutes
C)1.5 minutes
D)7.5 minutes
E)0.075 hours

Accepted Answer

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Question 20

A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour.What is the probability that the waiting line is empty?

Accepted Answer

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Quiz 25: Waiting-Line Models

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,what is the probability of fewer than two units in the system?

A finite population waiting line model has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes.What is the service factor X?

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,what is the probability of more than two units in the system?

What are Ls and Lq,as used in waiting line terminology? Which is larger,Ls or Lq? Explain.

A waiting-line system that meets the assumptions of M/M/S has λ = 5,μ = 4,and M = 2.For these values,Po is approximately 0.23077,and Ls is approximately 2.05128.What is the average number of units waiting in the queue?

The ________ of a waiting line and the probability that the queue is empty add to one.

A waiting-line system that meets the assumptions of M/M/S has λ = 5,μ = 4,and M = 2.For these values,Po is approximately 0.23077,and Ls is approximately 2.05128.What is the average time a unit spends in this system?

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,Po is and utilization is .

In a finite or limited population waiting line,the ________ is calculated from the average service time and average time between service requirements before the problem can be completed.

You have seen that,in an M/D/1 problem,the average queue length is exactly one-half the average queue length of an otherwise identical M/M/1 problem.Are all other performance statistics one-half as large also? Explain.

A finite population waiting line model has an average service time T of 100 minutes and an average time between service requirements U of 400 minutes.What is the service factor X?

Little's Law is not applicable in which of the following situations?

Which of the following is a requirement for application of Little's Law to be valid?

What are the six assumptions underlying the M/M/1 waiting line model? Which of these also hold for the M/D/1 model?

A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 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)?

Why must the service rate be greater than the arrival rate in a single-server system?

A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour.What is the probability that the waiting line is empty?