Deck 16: Appendix: Queuing Analysis

Question 1

For a single-server queuing model, the utilization factor $\lambda$ / $\mu$ has to be:

A) less than one.
B) equal to one.
C) greater than one.
D) less than or equal to one.

Answer 1

less than one.

Question 2

_____ is the process of a customer evaluating the waiting line and server system and deciding not to join the queue.

A) Triage
B) Reneging
C) Balking
D) Preemption

Answer 2

C

Question 3

The process of customers leaving one waiting line to join another in a multiple-server (channel) configuration is called:

A) jockeying.
B) reneging.
C) balking.
D) preempting.

Answer 3

A

Question 4

Queuing models:

A) yield optimal solutions.
B) are generally deterministic.
C) cannot be used in manufacturing.
D) use formulas only when arrivals and service times follow certain distributions.

Question 5

Which of the following is NOT a psychological strategy for dealing with a long wait time?

A) Distraction
B) Specifying the wait time
C) Displaying artwork in the waiting area
D) Technology

Question 6

Since most service times follow an exponential distribution, there is no need to collect data on actual service times.

Question 7

Which of the following is NOT a key assumption of the multiple-server queuing model?

A) The waiting line has two or more identical servers.
B) The arrivals wait in two or more lines.
C) The mean service rate, $\mu$ is the same for each server.
D) No balking or reneging is allowed.

Question 8

_____ is the use of a criterion that allows new arrivals to displace members of the current queue and become the first to receive service.

A) Shortest Processing Time (SPT)
B) A random queue discipline
C) Preemption
D) Reservation

Question 9

For the multiple-server queuing model to apply, the overall mean service rate should be greater than the mean arrival rate.

Question 10

Many analytical queuing models exist, each based upon unique assumptions about the nature of arrivals.

Question 11

According to the single-server queuing model, when $\lambda$ = $\mu$ , the operating characteristics are not defined, which means that these times and numbers of items grow infinitely large.

Question 12

If the probability of a number of people waiting is 0.10, the probability of one person waiting is 0.09, and the probability of two people waiting is 0.08, what is the probability of three or more people waiting?

A) 0.27
B) 0.73
C) 0.90
D) Cannot be determined

Question 13

Arrival distributions for queuing models:

A) follow a normal distribution.
B) use arbitrary but consistent time periods.
C) follow exponential distributions.
D) assume a non-random pattern.

Question 14

The multiple-server queuing model assumes that jockeying can take place.

Question 15

For a single-server queuing model, which of the following is NOT a key assumption?

A) The pattern of arrivals follows a Poisson probability distribution.
B) Service times follow an exponential probability distribution.
C) The queue discipline is random.
D) No balking or reneging happens.

Question 16

Triage is a form of preemption.

Question 17

Generally for queuing models, the slower the rate of arrivals, the shorter is the time period chosen.

Question 18

The mean arrival rate is used to express demand; the mean service rate is used to express a system's capacity.

Question 19

In queuing models, what are channels?

A) The walking paths through service systems
B) Service phases
C) The number of waiting lines in a system
D) External sources from which customers originate

Question 20

The multiple-server queuing model assumes that the mean service rate, $\mu$ , varies from server to server.

Question 21

List the seven operating characteristics of a single-channel waiting line (no formulas).

Question 22

A sandwich shop near a college has a special counter, open from 11 am to 1 pm, which is used exclusively for selling pre-made sandwiches. This is much faster than making sandwiches-to-order at lunch time. The clerk can handle a customer in about one minute. Customers arrive at a rate of 40 per hour on average.
a. How long (in minutes) does a customer have to wait?
b. What percentage of the time is the employee working?
c. What is the average number of customers waiting in line?
d. What is the probability of there being 3 or more customers in the system?

Question 23

A small software company hired a Customer Service Representative (CSR) to handle technical support questions. It is estimated that during peak periods, the CSR would receive four alls per hour and follow a Poisson distribution. Based on past experience, a CSR can handle an average of five (5) calls per hour during the same time period and follow an exponential distribution.
a. Determine the probability that the CSR is idle.
b. Determine the probability that three customers are in the system, waiting or being served.
c. Determine the average number of callers waiting for service (on hold).
d. Determine the average number of callers in the system.
e. Determine the average time a caller spends waiting for service (on hold).
f. Determine the average time a caller spends in the system (waiting time plus service time).
g. Determine the probability that an arriving call will have to wait for service.

Question 24

An ice cream shop is quite busy after the neighborhood high school lets out each day. From 3 pm to 5 pm customers arrive at the rate of 50 per hour, on average. Currently, the clerk can serve one customer per minute, on average. The store manager can buy an electrically heated scoop with an automatic ice cream ejector which will decrease the serving time to one custom-er per 45 seconds, on average.
a. What is the current time (in minutes) spent waiting in line?
b. What will the waiting time (in minutes) become using the automatic ice cream ejector?
c. What fraction of time is the clerk currently idle?
d. What fraction of time will the clerk be idle using the automatic ice cream ejector?
e. How many customers, on average, are in the shop under the current system?
f. How many customers would be in the shop, on average, using the automatic ice cream ejector?

Question 25

A university bookstore opens a booth and buys back used books during the final exam week. From 9 to 12 in the morning, students arrive at the rate of 35 per hour, on average. The bookstore employee can service an average of 40 students per hour.
a. What is the average length of the line?
b. What is the average time (in minutes) a student spends in the bookstore (system)?
c. What is the chance that the bookstore employee will be idle?

Question 26

What are the seven key assumptions for the multiple-server waiting line model?

Question 27

Which of the following variables is ordinarily NOT an output of waiting-line analysis?

A) The waiting cost per hour per passenger
B) The hourly cost associated with each server
C) The total cost per minute
D) The number of servers

Question 28

The arrival rate in queuing formulas is expressed as:

A) a fraction of the service rate.
B) arrivals per unit of time.
C) total number of arrivals.
D) the average time between arrivals.

Question 29

Compare and contrast wait cost with server cost. Which is harder to estimate?

Question 30

A flower shop has one employee in the front of the store to sell flowers out of a cooler. On Saturdays customers arrive every six minutes, on average. The employee can serve a customer every five minutes, on average. The owner of the store feels that if there are more than four customers in the store at one time, additional customers may not come in because the wait appears too long.
a. What is the chance of four or more customers being in the store at one time?
b. What is the total time (in minutes) a customer spends in the store?
c. What is the average number of customers in the store?

Question 31

A multiple-server queuing model has three servers with a mean service time of five customers per server per hour. It has been determined that arrivals will average 12 per hour. Arrivals follow a Poisson distribution and service times follow an exponential distribution.
a. Calculate the probability that all three service channels are idle.
b. Determine the probability of five customers in the system.
c. Determine the average number of customers waiting for service.
d. Determine the average number of customers in the system.
e. Determine the average time a customer spends waiting for service.
f. Determine the average time a customer spends in the system.
g. Determine the probability an arriving customer will wait for service.

Question 32

Which of the following CANNOT be found by queuing formulas?

A) The average number of units waiting for service
B) The average time a unit spends in the system
C) The probability that the service system is idle
D) The maximum time a unit is in the system

Question 33

A local bank has two drive-through teller windows with an essentially unlimited queue length. They estimate that the arrival rate during their most busy time will average about 40 cars per hour. They also estimate they can serve an average of 50 cars per hour. Management wants to make sure that the system is operating efficiently.
a. What is the probability that there will be no cars in the system?
b. On average, how many cars are in the system?
c. How long would a car be waiting (in seconds) in the drive-through, on average?

Question 34

Describe at least four queue disciplines.

Question 35

Discuss three categories of information necessary to develop a queuing model.

Question 36

What are five key assumptions for the basic, single-channel waiting line model?

Question 37

The manner in which new arrivals are ordered or prioritized for service is known as _____.

A) balking
B) reneging
C) queue discipline
D) queue behavior

Question 38

A local hamburger chain is considering adding a drive-through window. They estimate that during the dinner hour, customer arrival rate will average 18 per hour and follow a Poisson distribution. Service times during this same period are estimated to follow an exponential distribution with a mean of 24 customers per hour.
a. Determine the probability that the service facility (drive-through window) is idle.
b. Determine the probability of four vehicles in the system.
c. Determine the average number of vehicles waiting for service.
d. Determine the average number of vehicles in the system.
e. Determine the average time a vehicle spends waiting for service.
f. Determine the average time a vehicle spends in the system.
g. Determine the probability that an arriving vehicle has to wait for service.