OM5 Test Bank Supplementary Chapter B 1
Supplementary Chapter B—Queuing Analysis
TRUE/FALSE
1. Many analytical queuing models exist, each based upon unique assumptions about the nature
of arrivals.
2. Generally for queuing models, the slower the rate of arrivals, the shorter is the time period
chosen.
3. Since most service times follow an exponential distribution, there is no need to collect data on
actual service times.
4. Triage is a form of preemption.
5. According to the single-server queuing model, when
=
, the operating characteristics are
not defined, which means that these times and numbers of items grow infinitely large.
6. The multiple-server queuing model assumes that jockeying can take place.
7. For the multiple-server queuing model to apply, the overall mean service rate should be
greater than the mean arrival rate.
8. The multiple-server queuing model assumes that the mean service rate,
, varies from server
to server.
9. The mean arrival rate is used to express demand; the mean service rate is used to express a
system’s capacity.
MULTIPLE CHOICE
1. 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.
2. _____ 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
3. _____ 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
4. 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.
5. For a single-server queuing model, the utilization factor
/
has to be:
a.
less than one.
b.
equal to one.
c.
greater than one.
d.
less than or equal to one.
6. 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
OM5 Test Bank Supplementary Chapter B 3
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,
is the same for each server.
d.
No balking or reneging is allowed.
8. 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
trction
b.
c.
d.
9. 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.
10. 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.
11. 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
12. 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
13. 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.
14. 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
15. 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
SHORT ANSWER
1. List the seven operating characteristics of a single-channel waiting line (no formulas).
2. Discuss three categories of information necessary to develop a queuing model.
OM5 Test Bank Supplementary Chapter B 5
3.
The waiting-line or queue discipline
3. What are five key assumptions for the basic, single-channel waiting line model?
1.
The waiting line has two or more identical servers.
2.
Arrivals follow a Poisson probability distribution with a mean arrival rate of .
3.
Service times have an exponential distribution.
The mean service rate,
5.
Arrivals wait in a single line, moving to the first open server for service.
6.
The queue discipline is first-come, first-served (FCFS).
7.
No balking or reneging is allowed.
4. What are the seven key assumptions for the multiple-server waiting line model?
1.
First-come, first-served: the most customer-oriented discipline
processed at all.
of the FCFS rule.
5. Compare and contrast wait cost with server cost. Which is harder to estimate?
6. Discuss a passenger’s imputed cost of waiting.
7. Describe at least four queue disciplines.
1.
The waiting line has a single server.
2.
The pattern of arrivals follows a Poisson probability distribution.
3.
Service times follow an exponential probability distribution.
4.
The queue discipline is first-come, first served (FCFS).
5.
No balking or reneging.
PROBLEM
1. 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.
2. 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.
OM5 Test Bank Supplementary Chapter B 7
3. 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.
4. 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?
5. 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 customer
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 ejec-
tor?
b. (using the ice cream ejector) = 80/hour
Wq (time spent waiting in the line) = 50/ [80(80 – 50)] = 0.021 hours or 1.25 minutes
W (current time spent in the store including service time) = 1/(80 – 50) = 0.033 hours or 2
minutes
6. 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?
7. 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 cus-
tomers 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?
8. 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?
