# Quiz 11: Waiting Line Models

Business

Q 1Q 1

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.

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Multiple Choice

B

Q 2Q 2

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.

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Multiple Choice

D

Q 3Q 3

If arrivals occur according to the Poisson distribution every 20 minutes, then which is NOT true?
A) = 20 arrivals per hour
B) = 3 arrivals per hour
C) = 1/20 arrivals per minute
D) = 72 arrivals per day

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Multiple Choice

A

Q 4Q 4

The manner in which units receive their service, such as FCFS, is the
A) queue discipline.
B) channel.
C) steady state.
D) operating characteristic.

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Multiple Choice

Q 5Q 5

In a waiting line situation, arrivals occur, on average, every 10 minutes, and 10 units can be received every hour. What are and ?
A) = 10, = 10
B) = 6, = 6
C) = 6, = 10
D) = 10, = 6

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Multiple Choice

Q 6Q 6

Operating characteristics formulas for the single-channel queue do NOT require
A) .
B) Poisson distribution of arrivals.
C) an exponential distribution of service times.
D) an FCFS queue discipline.

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Multiple Choice

Q 7Q 7

In a multiple channel system
A) each server has its own queue.
B) each server has the same service rate.
C) >
D) All of the alternatives are correct.

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Multiple Choice

Q 8Q 8

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.Free

Multiple Choice

Q 9Q 9

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.

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Multiple Choice

Q 10Q 10

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.

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Multiple Choice

Q 11Q 11

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.

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Multiple Choice

Q 12Q 12

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.

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Multiple Choice

Q 13Q 13

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.

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Multiple Choice

Q 14Q 14

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.

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Multiple Choice

Q 15Q 15

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.

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Multiple Choice

Q 16Q 16

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.

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True False

Q 17Q 17

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.

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True False

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True False

Q 19Q 19

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

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True False

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True False

Q 21Q 21

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

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True False

Q 22Q 22

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

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True False

Q 23Q 23

Little's flow equations indicate that the relationship of L to L

_{q}is the same as that of W to W_{q}.Free

True False

Q 24Q 24

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

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True False

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True False

Q 26Q 26

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

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True False

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True False

Q 28Q 28

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

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True False

Q 29Q 29

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

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True False

Q 30Q 30

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

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True False

Q 31Q 31

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

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True False

Q 32Q 32

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.

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True False

Q 33Q 33

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.

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True False

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True False

Q 35Q 35

For an M/M/k system, the average number of customers in the system equals the customer arrival rate times the average time a customer spends waiting in the system.

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True False

Q 36Q 36

For a single-server queuing system, the average number of customers in the waiting line is one less than the average number in the system.

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True False

Q 37Q 37

In waiting line applications, the exponential probability distribution indicates that approximately 63 percent of the service times are less than the mean service time.

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True False

Q 38Q 38

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?

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Essay

Q 39Q 39

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

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Essay

Q 40Q 40

The insurance department at Shear's has two agents, each working at a mean speed of 8 customers per hour. Customers arrive at the insurance desk at a mean rate of one every six minutes and form a single queue. Management feels that some customers are going to find the wait at the desk too long and take their business to Word's, Shear's competitor.
In order to reduce the time required by an agent to serve a customer Shear's is contemplating installing one of two minicomputer systems: System A which leases for $18 per day and will increase an agent's efficiency by 25%; or, System B which leases for $23 per day and will increase an agent's efficiency by 50%. Agents work 8-hour days.
If Shear's estimates its cost of having a customer in the system at $3 per hour, determine if Shear's should install a new minicomputer system, and if so, which one.

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Essay