Question 1

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

Accepted Answer

A)  0.0625 
B)  0.25 
C)  0.75 
D)  0.9375 
E)  certain 
A)  0.0625 
B)  0.25 
C)  0.75 
D)  0.9375 
E)  certain

Question 2

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

(a) The utilization rate is = 100/150 =

Question 3

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?

Accepted Answer

Ls for the single server is 8 / (11-8) =

Question 4

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?

Accepted Answer

The number of vehicles out of

Question 5

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

Accepted Answer

A)  single channel 
B)  single phase 
C)  Poisson arrival rate pattern 
D)  exponential service time pattern 
E)  unlimited population size 
A)  single channel 
B)  single phase 
C)  Poisson arrival rate pattern 
D)  exponential service time pattern 
E)  unlimited population size

Question 6

Which of the following is most likely to violate a FIFO queue?

Accepted Answer

A)  supermarket with no express lanes 
B)  car repair garage 
C)  emergency room 
D)  fast-food restaurant 
E)  All of the above are equally likely to violate a FIFO queue. 
A)  supermarket with no express lanes 
B)  car repair garage 
C)  emergency room 
D)  fast-food restaurant 
E)  All of the above are equally likely to violate a FIFO queue.

Question 7

A(n) __________ queuing system is one in which the customer receives service from only one station and then exits the system.

Accepted Answer

The answer of A(n) __________ queuing system is one in...

Question 8

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. The average length of the queue Lq is approximately

Accepted Answer

A)  0.67 
B)  2.5 
C)  4.5 
D)  5.0 
E)  7.5 
A)  0.67 
B)  2.5 
C)  4.5 
D)  5.0 
E)  7.5

Question 9

LIFS (last-in, first-served) is a common queue discipline, most often seen where people, not objects, form the waiting line.

Accepted Answer

A) True 
 B)False

Question 10

A hospital emergency room always follows a first-in, first-served queue discipline in the interest of fairness.

Accepted Answer

A) True 
 B)False

Question 11

Which of the following is not a common queuing situation?

Accepted Answer

A)  grocery shoppers being served by checkout clerks 
B)  commuters slowing or stopping at toll plazas to pay highway tolls 
C)  machinery waiting to be repaired or maintained 
D)  parcel delivery truck following its computer-generated route 
E)  patients in a health clinic waiting to see one of several doctors 
A)  grocery shoppers being served by checkout clerks 
B)  commuters slowing or stopping at toll plazas to pay highway tolls 
C)  machinery waiting to be repaired or maintained 
D)  parcel delivery truck following its computer-generated route 
E)  patients in a health clinic waiting to see one of several doctors

Question 12

A small hair styling salon has several operators. While customers do not have appointments, each is waiting to be served by a specific operator. This scenario provides an example of a

Accepted Answer

A)  multiple-channel, multi-phase, limited queue length 
B)  single-channel, multi-phase, limited queue length 
C)  multi-channel, limited queue length 
D)  multiple single-channel systems, limited queue length 
E)  none of the above 
A)  multiple-channel, multi-phase, limited queue length 
B)  single-channel, multi-phase, limited queue length 
C)  multi-channel, limited queue length 
D)  multiple single-channel systems, limited queue length 
E)  none of the above

Question 13

The potential restaurant customer who says to her husband, "The line looks too long; let's eat somewhere else," is an illustration of which element of queue discipline?

Accepted Answer

A)  first-in, first-out 
B)  balk 
C)  renege 
D)  random departure 
E)  none of the above 
A)  first-in, first-out 
B)  balk 
C)  renege 
D)  random departure 
E)  none of the above

Question 14

A college registrar's office requires you to first visit with one of three advisors and then with one of two financial professionals. This system is best described as

Accepted Answer

A)  single channel, single phase system 
B)  single channel, multi-phase system 
C)  multi-channel, single phase system 
D)  multi-channel, multi-phase system 
E)  multi-channel, cross-phase system 
A)  single channel, single phase system 
B)  single channel, multi-phase system 
C)  multi-channel, single phase system 
D)  multi-channel, multi-phase system 
E)  multi-channel, cross-phase system

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

The service factor is X = T / (T + U) =

Question 16

In queuing problems, which of the following probability distributions is typically used to describe the time to perform the service?

Accepted Answer

A)  binomial 
B)  normal 
C)  Poisson 
D)  negative exponential 
E)  lognormal 
A)  binomial 
B)  normal 
C)  Poisson 
D)  negative exponential 
E)  lognormal

Question 17

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

Accepted Answer

The answer of The __________ of a waiting line and...

Question 18

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

(a) The utilization rate is = 140/150 =

Question 19

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.

Accepted Answer

Only the average queue length

Question 20

A waiting-line system with one waiting line and three sequential processing stages is a multi-channel single-phase system.

Accepted Answer

A) True 
 B)False

Exam 24: Waiting-Line Models

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

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

Which of the following is most likely to violate a FIFO queue?

A(n) __________ queuing system is one in which the customer receives service from only one station and then exits 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. The average length of the queue Lq is approximately

LIFS (last-in, first-served) is a common queue discipline, most often seen where people, not objects, form the waiting line.

A hospital emergency room always follows a first-in, first-served queue discipline in the interest of fairness.

Which of the following is not a common queuing situation?

A small hair styling salon has several operators. While customers do not have appointments, each is waiting to be served by a specific operator. This scenario provides an example of a

The potential restaurant customer who says to her husband, "The line looks too long; let's eat somewhere else," is an illustration of which element of queue discipline?

A college registrar's office requires you to first visit with one of three advisors and then with one of two financial professionals. This system is best described as

In queuing problems, which of the following probability distributions is typically used to describe the time to perform the service?

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

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 waiting-line system with one waiting line and three sequential processing stages is a multi-channel single-phase system.

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