Deck 6: S: Advanced Waiting Line Theory and Simulation Modeling

Question 1

Nervous 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. About how many customers are waiting in line to receive her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)2.78
B)4.17
C)3.25
D)5.00

Answer 1

4.17

Question 2

Nervous 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. About how long does a customer spend waiting in line and receiving her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)12.5 minutes
B)4.17 minutes
C)5 minutes
D)15 minutes

Answer 2

15 minutes

Question 3

The department chair is out of town at a conference and you, as the assistant department chair, find yourself besieged by dozens of students needing permission to get into a very popular (but closed)class. Student arrivals are governed by the Poisson distribution with a mean of 10 minutes. Telling the students that they can't get into the closed class takes about 5 minutes, and this average is exponentially distributed. About how long do students wait outside your office door?

A)0.083 minutes
B)0.083 hours
C)0.50 minutes
D)0.50 hours

Answer 3

0.083 hours

Question 4

A customer enters a business and has the opportunity to select any one of three lines to receive service. The service is performed by one customer service representative after which the customer leaves the establishment. Which description of this waiting line system is appropriate?

A)single channel, single phase
B)single channel, multiple phase
C)multiple channel, single phase
D)multiple channel, multiple phase

Question 5

The department chair is out of town at a conference and you, as the assistant department chair, find yourself besieged by dozens of students needing permission to get into a very popular (but closed)class. Student arrivals are governed by the Poisson distribution with a mean of 5 minutes. Telling the students that they can't get into the closed class takes about 3 minutes, and this average is exponentially distributed. About how many students are waiting outside your office door and in your office?

A)0.5
B)1.0
C)1.5
D)2.0

Question 6

Anxious 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. About how many customers are clustered around her, either receiving service or waiting in line to receive her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)2.78
B)4.17
C)3.25
D)5.00

Question 7

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. About how long does a customer wait in line to receive their valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)6.50 minutes
B)5.00 minutes
C)2.13 minutes
D)1.36 minutes

Question 8

The department chair is out of town at a conference and you, as the assistant department chair, find yourself besieged by dozens of students needing permission to get into a very popular (but closed)class. Student arrivals are governed by the Poisson distribution with a mean of 5 minutes. Telling the students that they can't get into the closed class takes about 3 minutes, and this average is exponentially distributed. About how long does it take a student to wait in line and receive your valuable service?

A)0.125 minutes
B)0.075 hours
C)4.5 minutes
D)7.5 minutes

Question 9

The department chair is out of town at a conference and you, as the assistant department chair, find yourself besieged by dozens of students needing permission to get into a very popular (but closed)class. Student arrivals are governed by the Poisson distribution with a mean of 10 minutes. Telling the students that they can't get into the closed class takes about 3 minutes, and this average is exponentially distributed. About how many students are waiting outside your office door?

A)0.13 students
B)0.43 students
C)1.25 students
D)2.25 students

Question 10

Patrons line up to spin the giant slot machine at the entrance to Ace Rothstein's Tangiers casino. They pour in the door at the rate of 300 per hour and it takes exactly ten seconds every time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather than win a new Corvette. How many customers are in line on average?

A)2.08 customers
B)1.93 customers
C)1.67 customers
D)1.50 customers

Question 11

Frenzied 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. About how many customers are clustered around them, either receiving service or waiting in line to receive their valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)17.86
B)14.17
C)13.25
D)19.66

Question 12

Frenzied 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. What is the probability that there are no customers awaiting service or being served if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)0.000
B)0.043
C)0.025
D)0.066

Question 13

The bank manager of a busy downtown location found herself unable to find good teller help so she invested in an ATM to handle the routine withdrawals that tended to occupy an inordinate amount of the teller's time. Before she installed the ATM she found that customers were arriving on average every 60 seconds (Poisson distributed)and it took a teller 20 seconds (exponentially distributed)to process their request. The ATM is able to maintain a constant 30 second service time. What is the impact on the waiting time for the customers?

A)There is no change.
B)The wait in the ATM line is 50% shorter than the wait in the teller line.
C)The wait in the ATM line is 50% higher than the wait in the teller line.
D)The wait in the ATM line is 25% shorter than the teller line.

Question 14

Anxious 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. About how long does a customer wait in line to receive her valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)12.5 minutes
B)5 minutes
C)21 minutes
D)15 minutes

Question 15

The bank manager of a busy downtown location found herself unable to find good teller help so she invested in an ATM to handle the routine withdrawals that tended to occupy an inordinate amount of the teller's time. Before she installed the ATM she found that customers were arriving on average every 2 minutes (Poisson distributed)and it took a teller 30 seconds (exponentially distributed)to process their request. The ATM is able to maintain a constant 30 second service time. What is the impact on the number of customers waiting in line?

A)There is no change.
B)The ATM line is half as long as the teller line.
C)The ATM line is twice as long as the teller line.
D)The ATM line is 25% shorter than the teller line.

Question 16

Hysterical 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. About how many customers are waiting in line to receive their valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)2.78
B)3.17
C)4.52
D)5.00

Question 17

A customer enters a business and joins the one line that snakes back and forth through the lobby in order to receive service. The initial part of the service is performed by one customer service representative, after which the customer enters a second, shorter line to complete the service before leaving the establishment. Which description of this waiting line system is appropriate?

A)single channel, single phase
B)single channel, multiple phase
C)multiple channel, single phase
D)multiple channel, multiple phase

Question 18

The bank manager of a busy downtown location found herself unable to find good teller help so she invested in an ATM to handle the routine withdrawals that tended to occupy an inordinate amount of the teller's time. Before she installed the ATM she found that customers were arriving on average every 2 minutes (Poisson distributed)and it took a teller 30 seconds (exponentially distributed)to process their request. The ATM is able to maintain a constant 30 second service time. What is the impact on system utilization?

A)There is no change.
B)Utilization has dropped by 15%.
C)Utilization has dropped by 30%.
D)Utilization has dropped by 45%.

Question 19

Hysterical 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. About how long does a customer spend waiting in line and receiving their valuable service if the service times are exponentially distributed and the arrivals follow a Poisson distribution?

A)7.50 minutes
B)5.36 minutes
C)4.17 minutes
D)3.67 minutes

Question 20

Customer arrivals at a dry cleaning service occur randomly throughout the day. The distribution that is usually used to model the interval between arrivals is the:

A)Poisson distribution.
B)uniform distribution.
C)random distribution.
D)normal distribution.

Question 21

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). How long does a customer spend waiting for a haircut?

A)17 minutes
B)20 minutes
C)23 minutes
D)26 minutes

Question 22

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. Assume that service times are exponentially distributed and arrivals follow a Poisson distribution.

Question 23

If 5 minutes passes between customer arrivals then the ________ is 12/hour.

Question 24

One of the differences between a waiting line system with a constant service time and one with exponentially distributed service times. Customers using the system with the constant service time will have half the waiting time of the customers using the system with Poisson distributed service times.

Question 25

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.

Question 26

Customers pass by any one of forty ticket takers on their way in the arena for a WWE event. This is a single ________ system.

Question 27

Regulars line up to spin the giant slot machine at the entrance to Ace Rothstein's Tangiers casino. They pour in the door at the rate of 300 per hour and it takes exactly ten seconds every time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather than win a new Corvette. How long do customers wait in line on average?

A)10 seconds
B)15 seconds
C)20 seconds
D)25 seconds

Question 28

In waiting line theory, the number of channels refers to the number of customer waiting lines in the system.

Question 29

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 ________.

Question 30

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). What percentage of the time are the four stylists working with customers?

A)94%
B)90%
C)84%
D)80%

Question 31

A waiting line cannot be both multiple-channel and multiple-phase.

Question 32

In most waiting line models, customers are assumed to arrive at random intervals, based on a normal distribution.

Question 33

Hopeful patrons line up to spin the giant slot machine at the entrance to Ace Rothstein's Tangiers casino. They pour in the door at the rate of 300 per hour and it takes exactly ten seconds every time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather than win a new Corvette. How long do customers spend waiting in line and finding out the unhappy news on average?

A)35 seconds
B)30 seconds
C)25 seconds
D)20 seconds

Question 34

One assumption in most waiting line analyses is that the number of customers is ________.

Question 35

The Greek letter lambda (λ)is used to represent the service rate of a waiting line system.

Question 36

With only a half hour for lunch I screamed into the parking lot of the nearest Golden Arches Supper Club at 40 miles an hour. When I saw the drive-through line was 15 cars deep, I didn't bother getting in line; I was off to visit the Colonel. This behavior might be described as balking.

Question 37

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.

Question 38

Many complex waiting line situations cannot be analyzed through neatly derived formulas. In these cases, ________ is the best method of analysis.

Question 39

All waiting line formulas assume that customers are served on a first-come first-served (FCFS)basis.

Question 40

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). On average, how many customers are waiting in line?

A)9
B)11
C)13
D)15

Question 41

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.

Question 42

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.

Question 43

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
$$\begin{array} { | c | c | c | } \hline \text { Range } & \text { Interarrival (min) } & \text { Service (min) } \\\hline 0.000 - 0.200 & 3 & 6 \\\hline 0.201 - 0.400 & 6 & 7 \\\hline 0.401 - 0.600 & 9 & 8 \\\hline 0.601 - 0.800 & 12 & 9 \\\hline 0.801 - 1.000 & 15 & 10 \\\hline\end{array}$$ The stream of random number for a Monte Carlo simulation of the system appear in this table>
$$\begin{array} { | c | c | } \hline \text { Interarrival } & \text { Service } \\\hline .114 & .979 \\\hline .899 & .297 \\\hline .925 & .162 \\\hline .085 & .574 \\\hline .824 & .235 \\\hline .151 & .593 \\\hline .223 & .956 \\\hline .477 & .845 \\\hline\end{array}$$

-Use the data from Figure 6S-1. What is the total time the owner/operator is idle (has no customers)from 8:00 am to 9:15 am?

A)3 minutes
B)8 minutes
C)16 minutes
D)20 minutes

Question 44

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.

Question 45

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 processing power, simulation results have become less accurate.
D)Computer-based simulation is the only "true" simulation.

Question 46

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
$$\begin{array} { | c | c | c | } \hline \text { Range } & \text { Interarrival (min) } & \text { Service (min) } \\\hline 0.000 - 0.200 & 3 & 6 \\\hline 0.201 - 0.400 & 6 & 7 \\\hline 0.401 - 0.600 & 9 & 8 \\\hline 0.601 - 0.800 & 12 & 9 \\\hline 0.801 - 1.000 & 15 & 10 \\\hline\end{array}$$ The stream of random number for a Monte Carlo simulation of the system appear in this table>
$$\begin{array} { | c | c | } \hline \text { Interarrival } & \text { Service } \\\hline .114 & .979 \\\hline .899 & .297 \\\hline .925 & .162 \\\hline .085 & .574 \\\hline .824 & .235 \\\hline .151 & .593 \\\hline .223 & .956 \\\hline .477 & .845 \\\hline\end{array}$$

-Use the data from Figure 6S-1. What time does the last customer exit the haberdashery if it opens at 8:00 a.m.?

A)9:19
B)9:10
C)9:16
D)9:26

Question 47

It is more costly to create a more realistic simulation than one that is less realistic.

Question 48

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.

Question 49

In most cases, simulation models provide optimal solutions to problems just like most of the equations presented in your textbook.

Question 50

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.

Question 51

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?

Question 52

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
$$\begin{array} { | c | c | c | } \hline \text { Range } & \text { Interarrival (min) } & \text { Service (min) } \\\hline 0.000 - 0.200 & 3 & 6 \\\hline 0.201 - 0.400 & 6 & 7 \\\hline 0.401 - 0.600 & 9 & 8 \\\hline 0.601 - 0.800 & 12 & 9 \\\hline 0.801 - 1.000 & 15 & 10 \\\hline\end{array}$$ The stream of random number for a Monte Carlo simulation of the system appear in this table>
$$\begin{array} { | c | c | } \hline \text { Interarrival } & \text { Service } \\\hline .114 & .979 \\\hline .899 & .297 \\\hline .925 & .162 \\\hline .085 & .574 \\\hline .824 & .235 \\\hline .151 & .593 \\\hline .223 & .956 \\\hline .477 & .845 \\\hline\end{array}$$

-Use the data from Figure 6S-1. What is the total time that customers must wait from 8:00 am to 9:15 am?

A)17 minutes
B)18 minutes
C)19 minutes
D)20 minutes

Question 53

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
$$\begin{array} { | c | c | c | } \hline \text { Range } & \text { Interarrival (min) } & \text { Service (min) } \\\hline 0.000 - 0.200 & 3 & 6 \\\hline 0.201 - 0.400 & 6 & 7 \\\hline 0.401 - 0.600 & 9 & 8 \\\hline 0.601 - 0.800 & 12 & 9 \\\hline 0.801 - 1.000 & 15 & 10 \\\hline\end{array}$$ The stream of random number for a Monte Carlo simulation of the system appear in this table>
$$\begin{array} { | c | c | } \hline \text { Interarrival } & \text { Service } \\\hline .114 & .979 \\\hline .899 & .297 \\\hline .925 & .162 \\\hline .085 & .574 \\\hline .824 & .235 \\\hline .151 & .593 \\\hline .223 & .956 \\\hline .477 & .845 \\\hline\end{array}$$

-Use the data from Figure 6S-1. How many customers are in the haberdashery at 8:02?

A)0
B)1
C)2
D)3

Question 54

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.

Question 55

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
$$\begin{array} { | c | c | c | } \hline \text { Range } & \text { Interarrival (min) } & \text { Service (min) } \\\hline 0.000 - 0.200 & 3 & 6 \\\hline 0.201 - 0.400 & 6 & 7 \\\hline 0.401 - 0.600 & 9 & 8 \\\hline 0.601 - 0.800 & 12 & 9 \\\hline 0.801 - 1.000 & 15 & 10 \\\hline\end{array}$$ The stream of random number for a Monte Carlo simulation of the system appear in this table>
$$\begin{array} { | c | c | } \hline \text { Interarrival } & \text { Service } \\\hline .114 & .979 \\\hline .899 & .297 \\\hline .925 & .162 \\\hline .085 & .574 \\\hline .824 & .235 \\\hline .151 & .593 \\\hline .223 & .956 \\\hline .477 & .845 \\\hline\end{array}$$

-Use the data from Figure 6S-1. How many customers are in the haberdashery at 8:38?

A)0
B)1
C)2
D)3

Question 56

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
$$\begin{array} { | c | c | c | } \hline \text { Range } & \text { Interarrival (min) } & \text { Service (min) } \\\hline 0.000 - 0.200 & 3 & 6 \\\hline 0.201 - 0.400 & 6 & 7 \\\hline 0.401 - 0.600 & 9 & 8 \\\hline 0.601 - 0.800 & 12 & 9 \\\hline 0.801 - 1.000 & 15 & 10 \\\hline\end{array}$$ The stream of random number for a Monte Carlo simulation of the system appear in this table>
$$\begin{array} { | c | c | } \hline \text { Interarrival } & \text { Service } \\\hline .114 & .979 \\\hline .899 & .297 \\\hline .925 & .162 \\\hline .085 & .574 \\\hline .824 & .235 \\\hline .151 & .593 \\\hline .223 & .956 \\\hline .477 & .845 \\\hline\end{array}$$

-Use the data from Figure 6S-1. How many customers are in the haberdashery at 9:08?

A)0
B)1
C)2
D)3

Question 57

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.

Question 58

Monte Carlo simulation uses statistical sampling to create outcomes for a large number of trials.

Question 59

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?

Question 60

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.

Question 61

What is Monte Carlo simulation and how is it conducted?

Question 62

One approach to mathematical simulation where statistical sampling is used to generate outcomes for a large number of trials is ________.

Question 63

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.

Question 64

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
The stream of random number for a Monte Carlo simulation of the system appear in this table

Use the data from Figure 6S-1. What are the exit times of the system for the first eight customers of the day?

Question 65

________ is an Excel function that generates a uniformly distributed random number between 0 and 1.

Question 66

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?

Question 67

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 ________.

Question 68

Figure 6S-1
Customers enter a haberdashery that sells only ascots, cufflinks and suspenders and are served by the owner operator. The owner is the only employee, so if customer B arrives while customer A is being served, customer B must patiently wait until customer A exits the system. Customers are always willing to wait regardless of how long their wait is. The interarrival and service times are uniformly distributed and shown in the table below.
The stream of random number for a Monte Carlo simulation of the system appear in this table

Use the data from Figure 6S-1. Which customers wait and how long does each one wait? How many minutes of idle time does the owner/operator enjoy from opening time at 8:00 am until his eighth customer departs?

Question 69

A process is ________ if the outcome of one trial does not have any impact on the next trial.

Question 70

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.