Question 1

A queuing model that follows the M/M/1 assumptions has λ = 10 and μ = 12.What is the average number of units in the system?
A)0.83
B)2
C)2.5
D)5
E)6

Accepted Answer

The answer of A queuing model that follows the M/M/1...

Question 2

Which one of the following is NOT a characteristic of a Model B or M/M/S system?
A)unlimited population size
B)single server
C)exponential service time pattern
D)single phase
E)Poisson arrival rate pattern

Accepted Answer

Model B or M/M/S systems are characterized by having multiple servers (S > 1), which contradicts option B that states it has a single server.

Question 3

Which one of the following is NOT a characteristic of a Model A or M/M/1 system?
A)exponential service time pattern
B)single number of servers
C)single number of phases
D)Poisson arrival rate pattern
E)limited population size

Accepted Answer

A Model A or M/M/1 system assumes an exponential service time pattern, a Poisson arrival rate pattern, a single server, and a single phase. However, it does not assume a limited population size.

Question 4

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.On average,how long does it take to service each student?
A)1 minute
B)2 minutes
C)3 minutes
D)5 minutes
E)20 minutes

Accepted Answer

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

Question 5

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute;the average queue length of the M/M/1 will be twice that of the M/D/1.

Accepted Answer

The average queue length for an M/M/1 model is given by ρ^2 / (1-ρ), where ρ is the traffic intensity, which is the ratio of the arrival rate to the service rate. In this case, ρ = 1/3, so the average queue length for the M/M/1 model is (1/3)^2 / (1-1/3) = 4/9. 
For the M/D/1 model, the average queue length is given by Ds^2/2(1-Ds), where Ds is the utilization of the server, which is the arrival rate divided by the service rate. In this case, Ds = 1/3, so the average queue length for the M/D/1 model is (1/3)^2 / [2(1-(1/3))] = 1/6.
Thus, the ratio of the average queue length of the M/M/1 model to that of the M/D/1 model is (4/9) / (1/6) = 8/3, which is indeed twice as large as the average queue length of the M/D/1 model.

Question 6

A waiting line meeting the assumptions of M/M/1 has an average time between arrivals of 20 minutes,and it services items in an average of 10 minutes each.What is the utilization factor?
A)0.25
B)0.33
C)0.50
D)0.67
E)3.00

Accepted Answer

The answer of A waiting line meeting the assumptions of...

Question 7

Which of the following is NOT an assumption of the M/M/1 model?
A)The first customers to arrive are the first customers served.
B)Each arrival comes independently of the arrival immediately before and after that arrival.
C)The population from which the arrivals come is very large or infinite in size.
D)Customers do not renege.
E)Service times occur according to a normal probability distribution.

Accepted Answer

The M/M/1 model assumes that service times occur according to an exponential probability distribution, not a normal distribution.

Question 8

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 8.The average number in the system Ls is ________ and the utilization of the system is ________.
A)3;100 percent
B)0.33;25 percent
C)4;33 percent
D)6;25 percent
E)4;25 percent

Accepted Answer

The answer of A queuing model that follows the M/M/1...

Question 9

In the basic queuing model (M/M/1),what probability distribution describes service times?
A)binomial
B)negative exponential
C)Poisson
D)normal
E)lognormal

Accepted Answer

The service time distribution in the M/M/1 queue is usually assumed to follow a negative exponential distribution, which is a continuous probability distribution often used to model waiting times.

Question 10

In the basic queuing model (M/M/1),what probability distribution describes arrival rates?
A)continuous
B)normal
C)negative exponential
D)Poisson
E)lognormal

Accepted Answer

The arrival process in M/M/1 queuing model follows a Poisson distribution. The Poisson distribution is commonly used to model the arrival rate of events occurring independently and at a constant average rate over a certain period of time.

Question 11

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 12 minutes on average.Service takes a constant 8 minutes.What is the average length of the queue Lq in units?
A)0.67
B)2.5
C)4.5
D)5.0
E)7.5

Accepted Answer

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

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;the service factor X is 0.25.

Accepted Answer

This waiting line model cannot be fully defined with just the given information. We would also need to know the population size or the arrival rate to determine key metrics such as the average waiting time or the average number of customers in the system. Therefore, it is not possible to confirm the accuracy of the statement that the service factor X is 0.25.

Question 13

Four of the most widely used waiting line models-M/M/1 or A,M/M/S or B,M/D/1 or C,and Limited population or D-all share which of the following three characteristics?
A)normal arrivals,FIFO discipline,and normal service times
B)Poisson arrivals,FIFO discipline,and a single-service phase
C)Poisson arrivals,FIFO discipline,and exponential service times
D)Poisson arrivals,no queue discipline,and exponential service times
E)Poisson arrivals,single-server,and FIFO discipline

Accepted Answer

The answer of Four of the most widely used waiting...

Question 14

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 3.What is the average time in the system?
A)2/3
B)1
C)1.5
D)2
E)6

Accepted Answer

The answer of A queuing model that follows the M/M/1...

Question 15

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 3.What is the average number of units in the system?
A)2/3
B)1
C)1.5
D)2
E)6

Accepted Answer

The answer of A queuing model that follows the M/M/1...

Question 16

A queuing model that follows the M/M/1 assumptions has λ = 3 and μ = 2.What is the average number of units in the system?
A)-3
B)3
C)0.667
D)150 percent
E)Growing without limit,since λ is larger than μ.

Accepted Answer

In an M/M/1 queue, the system is stable only if λ < μ, meaning the arrival rate is less than the service rate. If λ is greater than μ, as in this case (λ = 3, μ = 2), the queue will grow indefinitely, leading to an unstable system.

Question 17

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 12 minutes on average.Service takes a constant 8 minutes.What is the average number in the system Ls in units?
A)2.25
B)2.5
C)3.0
D)1.33
E)5.0

Accepted Answer

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

Question 18

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 10 minutes on average.Service takes a constant 4 minutes.What is the average length of the queue Lq in units?
A)0.4
B)0.133
C)4.167
D)4.583
E)6

Accepted Answer

We can use the M/D/1 formula to solve this problem:
Lq = (λ/μ)^2 / (μ - λ)
where λ represents arrival rate and μ represents service rate.
λ = 1/10 per minute
μ = 1/4 per minute
Plugging in the values, we get:
Lq = ((1/10)/(1/4))^2 / (1/4 - 1/10) = 0.133 
Therefore, the average length of the queue Lq in units is 0.133.

Question 19

A waiting line model meeting the assumptions of M/M/1 has an arrival rate of 2 per hour and a service rate of 6 per hour.What is the utilization factor for the system?
A)0.25
B)0.33
C)0.50
D)0.67
E)3.00

Accepted Answer

The answer of A waiting line model meeting the assumptions...

Question 20

Which one of the following is NOT a characteristic of a Model C or M/D/1 system?
A)single server
B)single phase
C)Poisson arrival rate pattern
D)exponential service time pattern
E)unlimited population size

Accepted Answer

The answer of Which one of the following is NOT...

Quiz 25: Queuing Models

A queuing model that follows the M/M/1 assumptions has λ = 10 and μ = 12.What is the average number of units in the system?

Which one of the following is NOT a characteristic of a Model B or M/M/S system?

Which one of the following is NOT a characteristic of a Model A or M/M/1 system?

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute;the average queue length of the M/M/1 will be twice that of the M/D/1.

A waiting line meeting the assumptions of M/M/1 has an average time between arrivals of 20 minutes,and it services items in an average of 10 minutes each.What is the utilization factor?

Which of the following is NOT an assumption of the M/M/1 model?

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 8.The average number in the system Ls is and the utilization of the system is .

In the basic queuing model (M/M/1) ,what probability distribution describes service times?

In the basic queuing model (M/M/1) ,what probability distribution describes arrival rates?

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 12 minutes on average.Service takes a constant 8 minutes.What is the average length of the queue Lq in units?

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;the service factor X is 0.25.

Four of the most widely used waiting line models-M/M/1 or A,M/M/S or B,M/D/1 or C,and Limited population or D-all share which of the following three characteristics?

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 3.What is the average time in the system?

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 3.What is the average number of units in the system?

A queuing model that follows the M/M/1 assumptions has λ = 3 and μ = 2.What is the average number of units in the system?

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 12 minutes on average.Service takes a constant 8 minutes.What is the average number in the system Ls in units?

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 10 minutes on average.Service takes a constant 4 minutes.What is the average length of the queue Lq in units?

A waiting line model meeting the assumptions of M/M/1 has an arrival rate of 2 per hour and a service rate of 6 per hour.What is the utilization factor for the system?

Which one of the following is NOT a characteristic of a Model C or M/D/1 system?