Deck 11: Waiting Line Models

Question 1

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.

Answer 1

False

Question 2

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 2

D

Question 3

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.

Answer 3

B

Question 4

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 5

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 6

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 7

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 8

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 9

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.

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

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

Question 12

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 13

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 14

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.

Question 15

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

Question 16

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 17

For all waiting lines, P₀ + P_w = 1.

Question 18

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

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

Question 19

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 20

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 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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 27

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

Question 28

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

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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.