Deck 11: Waiting Line Models

Question 1

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

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

Answer 1

A

Question 2

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.

Answer 2

D

Question 3

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.

Answer 3

A

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

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 6

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 7

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 8

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

Question 9

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 10

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 11

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

Question 12

For all waiting lines, P₀ + P_w = 1.

Question 13

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 14

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 15

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 16

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 17

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 18

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.

Question 19

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 20

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 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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 27

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.

Question 28

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

Question 29

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

Question 30

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.

Question 31

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

Question 32

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 33

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

Question 34

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 35

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

Question 36

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

Question 37

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

Question 38

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.

Question 39

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.

Question 40

A multiple-channel system has more than one waiting line.