The graph of average individual delay versus the repair period and use this graph to discuss the effect of the expected repair time on the average delay.
Explanation of Solution
Given:
We have been given the following information:
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 repair period of 1 hour.
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 90 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 foundusing 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 is
For the expected repair period of 1.5 hour.
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 90 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
Theaverage individualdelay is
For the expected repair period of 2.5 hour.
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 90 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 individualdelay is
For the expected repair period of 2.75 hour.
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 90 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
For the expected repair period of 3.0 hour.
We have the following formula for the determination of maximum queue length that will be formed:
Where,
Considering 90 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
Plot the graph of average individual delay versus the repair period is as follows:
Conclusion:
Therefore, for 1.0 hour : Themaximum queue length that will be formed is
For 1.5hour:
Themaximum queue length that will be formed is
For 2.50hour:
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 delayis
For 2.75hour:
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
For 3.0 hour:
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
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Chapter 6 Solutions
EBK TRAFFIC AND HIGHWAY ENGINEERING
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