Deck 13: Queuing Models

Question 1

In a process where interarrival times are exponentially distributed, the time since the last arrival is irrelevant.

Answer 1

True

Question 2

Which of the following is not one of the important issues defining types of arrivals in a queuing system?

A)Whether customers arrive one at a time or in batches.
B)Whether customers are all essentially alike or are in separate priority classes.
C)Whether customers have been through the system before or not
D)Whether customers will wait in line or not

Answer 2

C

Question 3

Almost all queuing systems are alike in that customers enter a system, possibly wait in one or more queues, get served, and then depart.

Answer 3

True

Question 4

Server utilization is the:

A)amount of time a typical server is busy
B)fraction of time a typical server is busy
C)number of servers being used in a system
D)number of times a server is used in a system

Question 5

The two basic modeling approaches for queuing systems are optimization and simulation.

Question 6

Which of the following is not one of the types of service disciplines?

A)Longest-processing-time
B)First-come-first-served
C)Service-in-random-order
D)Last-come-first-served

Question 7

The mean and standard deviation of an exponential distribution are both equal to the parameter λ.

Question 8

The parameter λ in an exponential distribution can be interpreted as a:

A)time
B)rate
C)mean
D)standard deviation

Question 9

Congestion in a queuing system will be unaffected by changes in the variability of the interarrival time and service time distributions, as long as the distributions retain the same means.

Question 10

The server utilization U in an M/M/s system is always the same as the traffic intensity.

Question 11

When a customer already in line in a queuing system becomes impatient and leaves the system before starting service, this is called:

A)balking
B)limited waiting
C)quitting
D)reneging

Question 12

The exponential distribution is:

A)flat
B)bell-shaped
C)heavily right-skewed
D)heavily left-skewed

Question 13

In queuing systems with a finite number of customers allowed, there is no need to require that the traffic intensity be less than 1 to ensure stability.

Question 14

In an Erlang loss model, customers who arrive when all servers are busy are lost to the system.

Question 15

A queuing system where customers join a single line and then are served by the first available server are said to be:

A)in parallel
B)in series
C)random
D)networked

Question 16

As the traffic intensity approaches 1:

A)there is no waiting
B)waiting lines stabilize
C)waiting lines grow extremely rapidly
D)at least one server will be idle

Question 17

A requirement for steady state analysis of a queuing system is that:

A)the initial conditions are still in effect
B)the waiting time must be exponentially distributed
C)the analysis period is at least two hours
D)the service rate must be constant

Question 18

Exponentially distributed service times are often more realistic than exponentially distributed interarrival times.

Question 19

The decision to balk at entering a queuing system can be made by the customer or the system.

Question 20

Traffic intensity is a very useful measure of:

A)whether the system is stable or not
B)the number of customers in a system
C)the distribution of interarrival times
D)the amount of congestion in the system

Question 21

Exhibit 13-2An oil-change facility serves customers that enter at a rate of 8 per hour. There are five servers available to perform oil changes for entering customers. Customers wait in a single line and enter the facility, in first-come-first-serve fashion, to the first of the five servers who is available. Each server can change the oil of one customer's car every 30 minutes on average.
Refer to Exhibit 13-2. What is the server utilization?

Question 22

Exhibit 13-4Consider a fast-food restaurant where customers arrive at a Poisson rate of 100 per hour. Four equally capable servers work at the restaurant during a typical hour of operation. Each employee takes, on average, 2 minutes to serve a customer, and service times are exponentially distributed. Customers who arrive and find all 4 servers busy join a single queue and are then served in first-come-first-served fashion.
Refer to Exhibit 13-4. Use the M/M/s template to find the expected number of busy servers, and the expected fraction of time each server is busy

Question 23

Exhibit 13-1A grocery store manager would like to use an analytical queueing model to study the lines of customers that form in front of the checkout stations in the store. During a period of time when business is steady, several store employees have gathered data on customer interarrival times, which are shown below.

[Part 3] Refer to Exhibit 13-1. Again assuming an exponential distribution with the parameter λ you obtained in Part 2, what is the probability that a customer interarrival time will be more than 2 minutes, but less than 5 minutes?

Question 24

Exhibit 13-4Consider a fast-food restaurant where customers arrive at a Poisson rate of 100 per hour. Four equally capable servers work at the restaurant during a typical hour of operation. Each employee takes, on average, 2 minutes to serve a customer, and service times are exponentially distributed. Customers who arrive and find all 4 servers busy join a single queue and are then served in first-come-first-served fashion.
Refer to Exhibit 13-4. What percentage of customers do not wait in the queue?

Question 25

Exhibit 13-1A grocery store manager would like to use an analytical queueing model to study the lines of customers that form in front of the checkout stations in the store. During a period of time when business is steady, several store employees have gathered data on customer interarrival times, which are shown below.

[Part 2] Refer to Exhibit 13-1. Assuming an exponential distribution with the parameter λ you obtained in Part 1, what is the probability that a customer interarrival time will be less than 2 minutes?

Question 26

Exhibit 13-2An oil-change facility serves customers that enter at a rate of 8 per hour. There are five servers available to perform oil changes for entering customers. Customers wait in a single line and enter the facility, in first-come-first-serve fashion, to the first of the five servers who is available. Each server can change the oil of one customer's car every 30 minutes on average.
Refer to Exhibit 13-2. How many of the servers are busy on average?

Question 27

Exhibit 13-3A Credit Union has a small branch in which a single customer service representative serves the needs of customers who arrive at an average rate of 24 per hour. The service representative can typically handle 30 customers per hour. Based on an analysis of historical data, it is reasonable to assume that customer interarrival times and service times are exponentially distributed. Assume that all arriving customers enter the branch, regardless of the number already waiting in line.
Refer to Exhibit 13-3. What is the average length of the waiting line?

Question 28

Exhibit 13-3A Credit Union has a small branch in which a single customer service representative serves the needs of customers who arrive at an average rate of 24 per hour. The service representative can typically handle 30 customers per hour. Based on an analysis of historical data, it is reasonable to assume that customer interarrival times and service times are exponentially distributed. Assume that all arriving customers enter the branch, regardless of the number already waiting in line.
Refer to Exhibit 13-3. What percentage of all customers have to spend at least some small amount of time waiting in line?

Question 29

Exhibit 13-1A grocery store manager would like to use an analytical queueing model to study the lines of customers that form in front of the checkout stations in the store. During a period of time when business is steady, several store employees have gathered data on customer interarrival times, which are shown below.

[Part 1] Refer to Exhibit 13-1. Is it reasonable to assume exponentially distributed interarrival times for the grocery store customers? If so, what is λ?

Question 30

Exhibit 13-3A Credit Union has a small branch in which a single customer service representative serves the needs of customers who arrive at an average rate of 24 per hour. The service representative can typically handle 30 customers per hour. Based on an analysis of historical data, it is reasonable to assume that customer interarrival times and service times are exponentially distributed. Assume that all arriving customers enter the branch, regardless of the number already waiting in line.
Refer to Exhibit 13-3. What is the average length of time (in hours) spent waiting in line?