33) Barber College is the best deal in town! For only $5, you can get a shampoo and cut by any
one of four untrained stylists completed in 7.5 minutes on average. Perhaps this is why
customers show up on average two minutes apart (both arrival times and service times are
exponentially distributed).
Management is concerned about the waiting time for customers and decides to train one more
student. If the arrival and service rates remain the same as in the original scenario, what happens
to the number of customers in the system?
A) There are about half as many as in the original scenario.
B) There are about a third as many as in the original scenario.
C) There are about a fourth as many as in the original scenario.
D) There are about a fifth as many as in the original scenario.
34) Many complex waiting line situations cannot be analyzed through neatly derived formulas.
In these cases, ________ is the best method of analysis.
35) Customers pass by any one of forty ticket takers on their way in the arena for a WWE event.
This is a single ________ system.
36) The only way to enter Jellystone Park is past Ranger Smith, who checks your camping gear
and warns you about the bears in the park. The next step of the entrance process is to pay your
site fee to Ranger Dwayne. This is a single ________ system.
37) A single channel single server system requires that the ________ rate be larger than the
________ rate.
38) One assumption in most waiting line analyses is that the number of customers is ________.
39) Customers that leave the system after waiting in line for a while are ________ but customers
that don’t even join the line because it looks too long are ________.
40) If 5 minutes passes between customer arrivals then the ________ is 12/hour.
41) Gerard is choosing between two methods of organizing his bakery. Method one will require a
counter person to wait on each customer individually before they proceed to the cashier to pay
for their purchases. In this system, customers will arrive at the rate of 8 per hour and can be
served by the counter person at the rate of 15 per hour. The cashier will be capable of serving
customers at the rate of 20 per hour. For simplification purposes, assume that the arrival rate at
the cashier phase is identical to the arrival rate at the first phase and that these waiting lines can
be analyzed independently and combined.
Method two will have the two employees wait on customers as they selected their pastries and
also collect their money once their selections have been made. Customers still arrive at the rate
of 8 per hour but now the total service time (pastry selection and payment collection) takes 5
minutes per customer. Calculate the average number of customers in the bakery and the average
time spent in the bakery for both systems and make your recommendations to Gerard.
42) Barber College is the best deal in town! For only $5, you can get a shampoo and cut by any
one of four untrained stylists completed in 7.5 minutes on average. Perhaps this is why
customers show up on average two minutes apart (both arrival times and service times are
exponentially distributed).Develop a full description of the system performance. How much does
performance improve if another barber is added to the customer service staff?
43) Frenzied cruise vacationers besiege Tatiana, their excursion coordinator, at the Port of
Cozumel when they realize that all water excursions have been cancelled for no reason in
particular. It takes her 2.5 minutes to find the customers an alternative excursion activity and
customers cluster around her at the rate of 20 per hour. Calculate system performance
characteristics if service times are exponentially distributed and the arrivals follow a Poisson
distribution.
44) Anxious cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen
assistants at the Port of Cozumel when they realize that all water excursions have been cancelled
for no reason in particular. It takes them 4 minutes to find the customers an alternative excursion
activity and customers cluster around them at the rate of 200 per hour. Calculate system
performance characteristics if service times are exponentially distributed and the arrivals follow
a Poisson distribution.
45) It’s a beautiful sunny day after a week of rainy weather and both of the local car washes are
busy. One car wash is fully automated, touchless, and can wash a vehicle of any size to a
dazzling luster in 5 minutes flat. The other car wash is a fund raiser staffed by eager amateurs
that work on one car at a time and can finish it in about 4 minutes (their time is governed by the
Poisson distribution). Customer arrivals at both car washes are Poisson distributed with a mean
of 10 per hour. How long does it take the average customer to work his way through either
system? How many customers are in the systems on average?
Learning Objective 6S-2
1) The term “time compression” refers to the phenomenon that a server tends to speed up the
service process if the waiting line exceeds some critical number of customers.
2) It is more costly to create a more realistic simulation than one that is less realistic.
3) Monte Carlo simulation uses statistical sampling to create outcomes for a large number of
trials.
4) In most cases, simulation models provide optimal solutions to problems just like most of the
equations presented in your textbook.
5) Customers enter the stadium and purchase refreshments before they are shown to their seats
by experienced ushers. The customers are considered objects in the simulation model.
6) Customers enter the stadium and purchase refreshments before they are shown to their seats
by experienced ushers. The concession stand lines are considered elements in the simulation
model.
7) One advantage of simulation modeling is:
A) it allows the user to conduct a “what if” analysis.
B) the many simplifying assumptions that are often made when using it.
C) the fact that an optimal solution is reached.
D) the time and cost required to make a perfectly realistic simulation
8) Which of the following statements about simulation is BEST?
A) Tools like optimization and regression analysis work best when they are simulated.
B) Simulation permits managers to test the effects of new policies and procedures without
disrupting customer service.
C) As computers have increased in power, simulation results have become less accurate.
D) Computer-based simulation is the only “true” simulation.
9) Which of the following is characteristic of Monte Carlo simulation?
A) Results are usually not valid, but provide managers with an approximation.
B) Time compression is not possible using this technique.
C) Statistical sampling is used to create outcomes for many trials.
D) Computer packages such as SimQuick and Arena can show on-screen graphics of customers
moving through the system or inventory accumulation.
10) Each outcome of flipping a fair coin is completely independent of the previous flip. This
outcome is known as:
A) simulation.
B) Monte Carlo.
C) 50/50.
D) memoryless.
11) The effect of the Excel formula =20*RAND()
A) is that twenty entries of a random variable with a mean of zero will be created.
B) is that twenty entries of a random variable with a mean of one will be created.
C) is that one entry of a random variable with a mean of twenty will be created.
D) is that one entry of a random variable with a mean of ten will be created.
12) Just before he retired for the evening, Saba started his simulation program to simulate five
years of hospital operations as he slept. His ability to generate five years of data overnight is a
textbook example of ________.
13) Simulation permits the modeler to discover what might happen should certain events occur,
for example, extreme levels of customer demand, equipment malfunction, etc.
This type of analysis is known as ________ analysis.
14) One approach to mathematical simulation where statistical sampling is used to generate
outcomes for a large number of trials is ________.
15) A process is ________ if the outcome of one trial does not have any impact on the next trial.
16) ________ is an Excel function that generates a uniformly distributed random number
between 0 and 1.
17) Why would someone choose to use simulation to analyze a waiting line problem rather than
use a formula? What are the advantages and disadvantages of a simulation approach?
18) What is Monte Carlo simulation and how is one conducted?