Question 1

The assumption of exponentially distributed service times indicates that

Accepted Answer

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. 
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 2

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

Accepted Answer

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

Question 3

In a waiting line situation,arrivals occur,on average,every 10 minutes,and 10 units can be received every hour.What are λ and μ?

Accepted Answer

A) λ = 10,μ = 10 
B) λ = 6,μ = 6 
C) λ = 6,μ = 10 
D) λ = 10,μ = 6 
A) λ = 10,μ = 10 
B) λ = 6,μ = 6 
C) λ = 6,μ = 10 
D) λ = 10,μ = 6

Question 4

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.

Accepted Answer

A) True 
 B)False

Question 5

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

Accepted Answer

A) True 
 B)False

Question 6

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.

Accepted Answer

A) True 
 B)False

Question 7

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.

Accepted Answer

A) True 
 B)False

Question 8

Which of the following can NOT be found by the queuing formulas presented in the textbook?

Accepted Answer

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. 
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 9

The Grand Movie Theater has one box office clerk.On average,each customer that comes to see a movie can be sold its ticket at the rate of 6 per minute.For the theater's normal offerings of older movies,customers arrive at the rate of 3 per minute.Assume arrivals follow the Poisson distribution and service times follow the exponential distribution.
a.What is the average number of customers waiting in line?
b.What is the average time a customer spends in the waiting line?
c.What is the average number of customers in the system?
d.What is a customer's average time in the system?
e.What is the probability that someone will be buying tickets when an arrival occurs?
The Grand has booked the Stars Wars Trilogy and expects more customers.From conversations with other theater owners,it estimates that the arrival rate will increase to 10 per minute.Output is supplied for a two-cashier and a three-cashier system. $$\begin{array} { | l | l | l | } 
\hline \text { Number of Channels } & 2 & 3 \
\hline \text { Arrival Rate } & 10 & 10 \
\hline \text { Service Rate } & 6 & 6 \
\hline \text { Probability of No Units in System } & 0909 & 1727 \
\hline \text { Average Waiting Time } & 3788 & 0375 \
\hline \text { Average Time in System } & 5455 & 2041 \
\hline \text { Average Number Waiting } & 3.7879 & 3747 \
\hline \text { Average Number in System } & 5.4545 & 2.0414 \
\hline \text { Probability of Waiting } & 7576 & 2998 \
\hline \text { Frobability of } 11 \text { in System } & .0245 & \text { 1ess than .0088 } \
\hline
\end{array}$$ 
 f The Grand has space for ten customers to wait indoors to buy tickets. Which system will be better?
g. Do you think it is more sensible for them to continue the one-cashier system?

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c. @#LAT-DLM&
d. @#LAT-DLM&
e. @#LAT-DLM&
f. The thr

Question 10

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

Accepted Answer

A) True 
 B)False

Question 11

​Diagram the servers and arrivals in the single and multiple channel models.Designate the line and the system.

Accepted Answer

In the single channel model, the server

Question 12

Arrivals at a box office in the hour before the show follow the Poisson distribution with λ = 7 per minute.Service times are constant at 7.5 seconds.Find the average length of the waiting line.

Accepted Answer

The answer of Arrivals at a box office in the...

Question 13

Quick Clean Rooter cleans out clogged drains.Due to the competitive nature of the drain cleaning business,if a customer calls Quick Clean and finds the line busy,they immediately try another company and Quick Clean loses the business.
Quick Clean management estimates that on the average,a customer tries to call Quick Clean every three minutes and the average time to take a service order is 200 seconds.The company wishes to hire enough operators so that at most 4% of its potential customers get the busy signal.
a.How many operators should be hired to meet this objective?
b.Given your answer to a),what is the probability that all the operators are idle?

Accepted Answer

The answer of Quick Clean Rooter cleans out clogged drains.Due...

Question 14

​The machine repair problem is an application of the M/M/1 model with

Accepted Answer

A) ​no waiting line. 
B) ​arbitrary service times. 
C) ​a finite calling population. 
D) ​blocked customers cleared. 
A) ​no waiting line. 
B) ​arbitrary service times. 
C) ​a finite calling population. 
D) ​blocked customers cleared.

Question 15

Little's flow equations apply to any waiting line model.

Accepted Answer

A) True 
 B)False

Question 16

The Arctic Flyers minor league hockey team has one box office clerk.On average,each customer that comes to see a game can be sold a ticket at the rate of 8 per minute.For normal games,customers arrive at the rate of 5 per minute.Assume arrivals follow the Poisson distribution and service times follow the exponential distribution.
a.What is the average number of customers waiting in line?
b.What is the average time a customer spends in the waiting line?
c.What is the average number of customers in the system?
d.What is a customer's average time in the system?
e.What is the probability that someone will be buying tickets when an arrival occurs?
The Flyers are playing in the league playoffs and anticipate more fans,estimating that the arrival rate will increase to 12 per minute.Output is supplied for a two-cashier and a three-cashier system. $$\begin{array} { | l | l | l | } 
\hline \text { Number of Channels } & 2 & 3 \
\hline \text { Arrival Rate } & 12 & 12 \
\hline \text { Service Rate } & 8 & 8 \
\hline \text { Probability of No Units in System } & 1429 & 2105 \
\hline \text { Average Waiting Time } & 1607 & 0197 \
\hline \text { Average Time in System } & 2857 & 1447 \
\hline \text { Average Number Waiting } & 1.9286 & 2368 \
\hline \text { Average Number in System } & 3.4286 & 1.7368 \
\hline \text { Probability of Waiting } & 6429 & 2368 \
\hline \text { Probability of } 7 \text { in System } & .0381 & .0074 \
\hline
\end{array}$$ 
 The rink has space for six customers to wait indoors to buy tickets. Which system will be better?
g. Do you think it is more sensible for them to continue the one cashier system?

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c. @#LAT-DLM&
d. @#LAT-DLM&
e. @#LAT-DLM&
f. The thr

Question 17

The post office uses a multiple channel queue,where customers wait in a single line for the first available window.If the average service time is 1 minute and the arrival rate is 7 customers every five minutes,find,when two service windows are open,
a.the probability both windows are idle.
b.the probability a customer will have to wait.
c.the average time a customer is in line.
d.the average time a customer is in the post office.

Accepted Answer

a. @#LAT-DLM&
b. @#LAT-DLM&
c. @#LAT-DLM& (of a fi

Question 18

In a multiple channel system

Accepted Answer

A) each server has its own queue. 
B) each server has the same service rate. 
C) μ > λ 
D) All of the alternatives are correct. 
A) each server has its own queue. 
B) each server has the same service rate. 
C) μ > λ 
D) All of the alternatives are correct.

Question 19

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

Accepted Answer

A) True 
 B)False

Question 20

The assumption that arrivals follow a Poisson probability distribution is equivalent to the assumption that the time between arrivals has​

Accepted Answer

A) ​a normal probability distribution 
B) ​an exponential probability distribution 
C) ​a uniform probability distribution 
D) ​a Poisson probability distribution 
A) ​a normal probability distribution 
B) ​an exponential probability distribution 
C) ​a uniform probability distribution 
D) ​a Poisson probability distribution

The assumption of exponentially distributed service times indicates that

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

In a waiting line situation,arrivals occur,on average,every 10 minutes,and 10 units can be received every hour.What are λ and μ?

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.

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

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.

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.

Which of the following can NOT be found by the queuing formulas presented in the textbook?

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

Diagram the servers and arrivals in the single and multiple channel models.Designate the line and the system.

Arrivals at a box office in the hour before the show follow the Poisson distribution with λ = 7 per minute.Service times are constant at 7.5 seconds.Find the average length of the waiting line.

The machine repair problem is an application of the M/M/1 model with

Little's flow equations apply to any waiting line model.

In a multiple channel system

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

The assumption that arrivals follow a Poisson probability distribution is equivalent to the assumption that the time between arrivals has

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Simulation

Markov Processes

Filters

Exam 15: Waiting Line Models

The assumption of exponentially distributed service times indicates that

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

In a waiting line situation,arrivals occur,on average,every 10 minutes,and 10 units can be received every hour.What are λ and μ?

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.

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

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.

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.

Which of the following can NOT be found by the queuing formulas presented in the textbook?

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

​Diagram the servers and arrivals in the single and multiple channel models.Designate the line and the system.

Arrivals at a box office in the hour before the show follow the Poisson distribution with λ = 7 per minute.Service times are constant at 7.5 seconds.Find the average length of the waiting line.

​The machine repair problem is an application of the M/M/1 model with

Little's flow equations apply to any waiting line model.

In a multiple channel system

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

The assumption that arrivals follow a Poisson probability distribution is equivalent to the assumption that the time between arrivals has​

Introduction

Introduction to Probability

Probability Distributions

Decision Analysis

Utility Game Theory

Time Series Analysis Forecasting

Intro to Linear Programming

LP Sensitivity Analysis

LP Applications

Distribution Network Models

Integer Linear Programming

Advanced Optimization Applications

Project Scheduling

Inventory Models

Simulation

Markov Processes

Filters

Diagram the servers and arrivals in the single and multiple channel models.Designate the line and the system.

The machine repair problem is an application of the M/M/1 model with

The assumption that arrivals follow a Poisson probability distribution is equivalent to the assumption that the time between arrivals has