Concept explainers
(a)
The maximum queue length that will be formed, total delay, number of vehicles that will be affected by the incident, the average individual delay for the expected demand flow of 70%of the capacity of the highway.
Answer to Problem 20P
For 70 % expected demand flow:
Themaximum queue length that will be formed is
The total delay is
The number of vehicles that will be affected by the incident is
The average individual delay is
Explanation of Solution
Given:
We have been given the following information:
Total number of lanes = 3,
Mean free flow speed of the highway
Jam density
Following is the lay out of the given highway section:
Calculation:
For the expected 70 % demand flow:
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 70 percent of the flow and that the capacity of each lane is 2000 Veh/ h
Substituting the values in the following equation, we have
The maximum queue length that will be formed is
Now, the total delay, we have the following formula
Where,
And C is the total capacity and can be found as
Now, substituting the values in the required equation, we have
The total delay is
The number of vehicles that will be affected by the incident.
To calculate the number of vehicles that will be affected by the incident can be found using the following formula:
Number of vehicles affected =
Substituting the values, we have
The number of vehicles that will be affected by the incident is
To calculate the average individual delay, we have the following formula:
Average individual delay
Substituting the values, we have
The average individual delay is
Conclusion:
Therefore, for 70 % expected demand flow:
Themaximum queue length that will be formed is
The number of vehicles that will be affected by the incident is
(b)
The maximum queue length that will be formed, total delay, number of vehicles that will be affected by the incident, the average individual delay for the expected demand flow of 75%of the capacity of the highway.
Answer to Problem 20P
For 75 % expected demand flow:
Themaximum queue length that will be formed is
The total delay is
The number of vehicles that will be affected by the incident is
The average individual delay is
Explanation of Solution
Given:
We have been given the following information:
Total number of lanes = 3,
Mean free flow speed of the highway
Jam density
Following is the lay out of the given highway section:
Calculation:
For the expected 75 % demand flow:
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 75 percent of the flow and that the capacity of each lane is 2000 Veh/ h
Substituting the values in the following equation, we have
Themaximum queue length that will be formed is
Now, the total delay, we have the following formula
Where,
And C is the total capacity and can be found as
Now, substituting the values in the required equation, we have
The total delay is
The number of vehicles that will be affected by the incident.
To calculate the number of vehicles that will be affected by the incident can be found using the following formula:
Number of vehicles affected =
Substituting the values, we have
The number of vehicles that will be affected by the incident is
To calculate the average individual delay, we have the following formula:
Average individual delay
Substituting the values, we have
The average individual delay is
Conclusion:
For 75 % expected demand flow:
Themaximum queue length that will be formed is
(c)
The maximum queue length that will be formed, total delay, number of vehicles that will be affected by the incident, the average individual delay for the expected demand flow of 80% of the capacity of the highway.
Answer to Problem 20P
For 80 % expected demand flow:
Themaximum queue length that will be formed is
The total delay is
The number of vehicles that will be affected by the incident is
The average individual delay is
Explanation of Solution
Given:
We have been given the following information:
Total number of lanes = 3,
Mean free flow speed of the highway
Jam density
Following is the lay out of the given highway section:
Calculation:
For the expected 80 % demand flow:
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 80 percent of the flow and that the capacity of each lane is 2000 Veh/ h
Substituting the values in the following equation, we have
The maximum queue length that will be formed is
Now, the total delay, we have the following formula
Where,
And C is the total capacity and can be found as
Now, substituting the values in the required equation, we have
The total delay is
The number of vehicles that will be affected by the incident.
To calculate the number of vehicles that will be affected by the incident can be found using the following formula:
Number of vehicles affected =
Substituting the values, we have
Therefore, the number of vehicles that will be affected by the incident is
To calculate the average individual delay, we have the following formula:
Average individual delay
Substituting the values, we have
The average individual delay is
Conclusion:
For 80 % expected demand flow:
Themaximum queue length that will be formed is
the average individual delay is
(d)
The maximum queue length that will be formed, total delay, number of vehicles that will be affected by the incident, the average individual delay for the expected demand flowof 85% of the capacity of the highway.
Answer to Problem 20P
For 85 % expected demand flow:
Themaximum queue length that will be formed is
The total delay is
The number of vehicles that will be affected by the incident is
The average individual delay is
Explanation of Solution
Given:
We have been given the following information:
Total number of lanes = 3,
Mean free flow speed of the highway
Jam density
Following is the lay out of the given highway section:
Calculation:
For the expected 85 % demand flow:
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 85 percent of the flow and that the capacity of each lane is 2000 Veh/ h
Substituting the values in the following equation, we have
Therefore, the maximum queue length that will be formed is
Now, the total delay, we have the following formula
Where,
And C is the total capacity and can be found as
Now, substituting the values in the required equation, we have
Therefore, the total delay is
The number of vehicles that will be affected by the incident.
To calculate the number of vehicles that will be affected by the incident can be found using the following formula:
Number of vehicles affected =
Substituting the values, we have
The number of vehicles that will be affected by the incident is
To calculate the average individual delay, we have the following formula:
Average individual delay
Substituting the values, we have
the average individual delay is
The graph of average individual delay versus the expected demand flow is as follows:
Conclusion:
For 85 % expected demand flow:
Themaximum queue length that will be formed is
the average individual delay is
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Chapter 6 Solutions
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