Deck 11: Waiting Line Models

Question 1

The arrival rate in queuing formulas is expressed as

A)the mean time between arrivals.
B)the minimum number of arrivals per time period.
C)the mean number of arrivals per channel.
D)the mean number of arrivals per time period.

Answer 1

D

Question 2

A waiting line situation where every customer waits in the same line before being served by the same server is called a single server waiting line.

Answer 2

False

Question 3

Little's flow equations

A)require Poisson and exponential assumptions.
B)are applicable to any waiting line model.
C)require independent calculation of W, L, W_q, and L_q.
D)All of the alternatives are correct.

Answer 3

B

Question 4

If arrivals occur according to the Poisson distribution every 20 minutes, then which is NOT true?

A) $\lambda$ = 20 arrivals per hour
B) $\lambda$ = 3 arrivals per hour
C) $\lambda$ = 1/20 arrivals per minute
D) $\lambda$ = 72 arrivals per day

Question 5

Use of the Poisson probability distribution assumes that arrivals are not random.

Question 6

The manner in which units receive their service, such as FCFS, is the

A)queue discipline.
B)channel.
C)steady state.
D)operating characteristic.

Question 7

For all waiting lines, P₀ + P_w = 1.

Question 8

Performance measures dealing with the number of units in line and the time spent waiting are called

A)queuing facts.
B)performance queues.
C)system measures.
D)operating characteristics.

Question 9

For an M/M/1 queuing system, if the service rate, µ, is doubled, the average wait in the system, W, is cut in half.

Question 10

In a multiple channel system

A)each server has its own queue.
B)each server has the same service rate.
C) $\mu$ > $\lambda$
D)All of the alternatives are correct.

Question 11

In a waiting line situation, arrivals occur, on average, every 10 minutes, and 10 units can be received every hour. What are $\lambda$ and $\mu$ ?

A) $\lambda$ = 10, $\mu$ = 10
B) $\lambda$ = 6, $\mu$ = 6
C) $\lambda$ = 6, $\mu$ = 10
D) $\lambda$ = 10, $\mu$ = 6

Question 12

Models with a finite calling population

A)have an arrival rate independent of the number of units in the system.
B)have a service rate dependent on the number of units in the system.
C)use the size of the population as a parameter in the operating characteristics formulas.
D)All of the alternatives are correct.

Question 13

Operating characteristics formulas for the single-channel queue do NOT require

A) $\lambda$ $\ge$ $\mu$ .
B)Poisson distribution of arrivals.
C)an exponential distribution of service times.
D)an FCFS queue discipline.

Question 14

Decision makers in queuing situations attempt to balance

A)operating characteristics against the arrival rate.
B)service levels against service cost.
C)the number of units in the system against the time in the system.
D)the service rate against the arrival rate.

Question 15

What queue discipline is assumed by the waiting line models presented in the textbook?

A)first-come first-served.
B)last-in first-out.
C)shortest processing time first.
D)No discipline is assumed.

Question 16

The total cost for a waiting line does NOT specifically depend on

A)the cost of waiting.
B)the cost of service.
C)the number of units in the system.
D)the cost of a lost customer.

Question 17

For many waiting line situations, the arrivals occur randomly and independently of other arrivals and it has been found that a good description of the arrival pattern is provided by

A)a normal probability distribution.
B)an exponential probability distribution.
C)a uniform probability distribution.
D)a Poisson probability distribution.

Question 18

Which of the following can NOT be found by the queuing formulas presented in the textbook?

A)the probability that no units are in the system.
B)the average number of units in the system.
C)the maximum time a unit spends in the system.
D)the average time a unit spends in the system.

Question 19

The assumption of exponentially distributed service times indicates that

A)37% of the service times are less than the mean service time.
B)50% of the service times are less than the mean service time.
C)63% of the service times are less than the mean service time.
D)service time increase at an exponential rate as the waiting line grows.

Question 20

Queue discipline refers to the assumption that a customer has the patience to remain in a slow moving queue.

Question 21

Diagram the servers and arrivals in the single and multiple channel models. Designate the line and the system.

Question 22

For a single-channel waiting line, the utilization factor is the probability that an arriving unit must wait for service.

Question 23

Waiting line models describe the transient-period operating characteristics of a waiting line.

Question 24

In developing the total cost for a waiting line, waiting cost takes into consideration both the time spent waiting in line and the time spent being served.

Question 25

In waiting line systems where the length of the waiting line is limited, the mean number of units entering the system might be less than the arrival rate.

Question 26

Adding more channels always improves the operating characteristics of the waiting line and reduces the waiting cost.

Question 27

If service time follows an exponential probability distribution, approximately 63% of the service times are less than the mean service time.

Question 28

The time to process a registration at the Sea View Resort follows the exponential distribution and has a mean of 6 minutes.
a.What is the probability of a registration time shorter than 3 minutes?
b.What is the probability of a registration time shorter than 6 minutes?
c.What is the probability of a registration time between 3 and 6 minutes?

Question 29

How can a system be changed to improve the service rate?

Question 30

In a multiple channel system it is more efficient to have a separate waiting line for each channel.

Question 31

If some maximum number of customers is allowed in a queuing system at one time, the system has a finite calling population.

Question 32

Queue discipline refers to the manner in which waiting units are arranged for service.

Question 33

Explain what is meant by the following statement, "operating characteristics are non-optimizing."

Question 34

Discuss the importance of the utilization factor in a queuing system and the assumptions made about its value.

Question 35

When blocked customers are cleared, an important decision is how many channels to provide.

Question 36

During summer weekdays, boats arrive at the inlet drawbridge according to the Poisson distribution at a rate of 3 per hour. In a 2-hour period,
a.what is the probability that no boats arrive?
b.what is the probability that 2 boats arrive?
c.what is the probability that 8 boats arrive?

Question 37

Before waiting lines can be analyzed economically, the arrivals' cost of waiting must be estimated.

Question 38

Give examples of systems you have seen in which a) blocked arrivals are cleared, and b) there is a finite calling population.

Question 39

When a waiting system is in steady-state operation, the number of units in the system is not changing.

Question 40

Little's flow equations indicate that the relationship of L to L_q is the same as that of W to W_q.

Question 41

For an M/G/1 system with $\lambda$ = 6 and $\mu$ = 9, with $\sigma$ = .03, find
a.the probability the system is idle.
b.the average length of the queue.
c.the average number in the system.

Question 42

Circle Electric Supply is considering opening a second service counter to better serve the electrical contractor customers. The arrival rate is 10 per hour. The service rate is 14 per hour. If the cost of waiting is $30 and the cost of each service counter is $22 per hour, then should the second counter be opened?

Question 43

Two new checkout scanning systems are under consideration by a retail store. Arrivals to the checkout stand follow the Poisson distribution with $\lambda$ = 2 per minute. The cost for waiting is $18 per hour. The first system has an exponential service rate of 5 per minute and costs $10 per hour to operate. The second system has an exponential service rate of 8 per minute and costs $20 per hour to operate. Which system should be chosen?

Question 44

The post office uses a multiple channel queue, where customers wait in a single line for the first available window. If the average service time is 1 minute and the arrival rate is 7 customers every five minutes, find, when two service windows are open,
a.the probability both windows are idle.
b.the probability a customer will have to wait.
c.the average time a customer is in line.
d.the average time a customer is in the post office.

Question 45

The 8 students in a seminar class must come to the professor's office to turn in a paper and give a 5-minute oral summary. Assume there is a service rate of 10 per hour and adequate time is available for all. The arrival rate for each unit is 5 per hour. What is the probability there is no one in the office or waiting when you come?

Question 46

For an M/G/1 system with $\lambda$ = 20 and $\mu$ = 35, with $\sigma$ = .005, find
a.the probability the system is idle.
b.the average length of the queue.
c.the average number in the system.

Question 47

The Sea View Resort uses a multiple-channel queue registration system. If the average service time is 8 minutes, there are three registration clerks, and guests arrive at the rate of one every 5 minutes, find
a. $\lambda$ and $\mu$ .
b.the probability all three clerks are idle.
c.the probability a guest will have to wait.
d.the average time a customer is in line.
e.the average number of customers in line.

Question 48

Arrivals at a box office in the hour before the show follow the Poisson distribution with $\lambda$ = 7 per minute. Service times are constant at 7.5 seconds. Find the average length of the waiting line.