Consider a city center where the traffic conditions are described by a Macroscopic Fundamental Diagram (MFD) of network outflow (g- rate of trips finished) vs. accumulation (n- number of cars) with a trapezoidal shape, as shown in the figure below. The values of the parameters are: • • maximum trip completion rate gmax=100 [veh/min] critical accumulations ncr1=1000 [veh] and ncr2=1500 [veh] jam accumulation njam=4000 [veh]. gmax ncr1 ncr2 njam There are two types of demands in the morning peak hour (7-8am): trips generated from outside the city center with rate q1=80 [veh/min], and trips generated from within the city center with rate q2=50 [veh/min]. In addition, a perimeter traffic control, u, is available that only restricts vehicles entering the city from outside. If at 7am there are already no=500 [veh] in the city center: a. Write the dynamic equations (mass conservation equation) in a continuous form for the center of the city. b. Convert the continuous dynamic into the discrete form. Use a time unit of 5min. C. What would the accumulation of the system be at 7:30am, if the perimeter control is inactive, i.e. u=1? d. Choose perimeter control value (u) which starts after 7:30am, so that the network outflow (g) remains at its maximum value at 8:00am. Explain your choice. Hint: You can choose a constant or a time-dependent perimeter control. Both solutions will be considered correct. e. How many vehicles will be queued outside the city center at 8am, when the control restriction, chosen in part d, stops? f. Repeat part (c) with a time unit of 2min. Report the difference between part (c) and (f) and elaborate. You may use Excel or other software for part (f) only.
Consider a city center where the traffic conditions are described by a Macroscopic Fundamental Diagram (MFD) of network outflow (g- rate of trips finished) vs. accumulation (n- number of cars) with a trapezoidal shape, as shown in the figure below. The values of the parameters are: • • maximum trip completion rate gmax=100 [veh/min] critical accumulations ncr1=1000 [veh] and ncr2=1500 [veh] jam accumulation njam=4000 [veh]. gmax ncr1 ncr2 njam There are two types of demands in the morning peak hour (7-8am): trips generated from outside the city center with rate q1=80 [veh/min], and trips generated from within the city center with rate q2=50 [veh/min]. In addition, a perimeter traffic control, u, is available that only restricts vehicles entering the city from outside. If at 7am there are already no=500 [veh] in the city center: a. Write the dynamic equations (mass conservation equation) in a continuous form for the center of the city. b. Convert the continuous dynamic into the discrete form. Use a time unit of 5min. C. What would the accumulation of the system be at 7:30am, if the perimeter control is inactive, i.e. u=1? d. Choose perimeter control value (u) which starts after 7:30am, so that the network outflow (g) remains at its maximum value at 8:00am. Explain your choice. Hint: You can choose a constant or a time-dependent perimeter control. Both solutions will be considered correct. e. How many vehicles will be queued outside the city center at 8am, when the control restriction, chosen in part d, stops? f. Repeat part (c) with a time unit of 2min. Report the difference between part (c) and (f) and elaborate. You may use Excel or other software for part (f) only.
Traffic and Highway Engineering
5th Edition
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Garber, Nicholas J.
Chapter4: Traffic Engineering Studies
Section: Chapter Questions
Problem 20P
Related questions
Question
![Consider a city center where the traffic conditions are described by a Macroscopic
Fundamental Diagram (MFD) of network outflow (g- rate of trips finished) vs. accumulation (n-
number of cars) with a trapezoidal shape, as shown in the figure below. The values of the
parameters are:
•
•
maximum trip completion rate gmax=100 [veh/min]
critical accumulations ncr1=1000 [veh] and ncr2=1500 [veh]
jam accumulation njam=4000 [veh].
gmax
ncr1
ncr2
njam
There are two types of demands in the morning peak hour (7-8am): trips generated from
outside the city center with rate q1=80 [veh/min], and trips generated from within the city
center with rate q2=50 [veh/min]. In addition, a perimeter traffic control, u, is available that
only restricts vehicles entering the city from outside.
If at 7am there are already no=500 [veh] in the city center:
a. Write the dynamic equations (mass conservation equation) in a continuous form for the
center of the city.
b. Convert the continuous dynamic into the discrete form. Use a time unit of 5min.
C. What would the accumulation of the system be at 7:30am, if the perimeter control is
inactive, i.e. u=1?
d. Choose perimeter control value (u) which starts after 7:30am, so that the network
outflow (g) remains at its maximum value at 8:00am. Explain your choice.
Hint: You can choose a constant or a time-dependent perimeter control. Both solutions will
be considered correct.
e. How many vehicles will be queued outside the city center at 8am, when the control
restriction, chosen in part d, stops?
f. Repeat part (c) with a time unit of 2min. Report the difference between part (c) and (f) and
elaborate. You may use Excel or other software for part (f) only.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4d9d51c-cee3-4855-8494-55e8cc009ab5%2Fc42187e8-3ec3-4664-af80-18b1a79cf185%2F5dmpq2d_processed.png&w=3840&q=75)
Transcribed Image Text:Consider a city center where the traffic conditions are described by a Macroscopic
Fundamental Diagram (MFD) of network outflow (g- rate of trips finished) vs. accumulation (n-
number of cars) with a trapezoidal shape, as shown in the figure below. The values of the
parameters are:
•
•
maximum trip completion rate gmax=100 [veh/min]
critical accumulations ncr1=1000 [veh] and ncr2=1500 [veh]
jam accumulation njam=4000 [veh].
gmax
ncr1
ncr2
njam
There are two types of demands in the morning peak hour (7-8am): trips generated from
outside the city center with rate q1=80 [veh/min], and trips generated from within the city
center with rate q2=50 [veh/min]. In addition, a perimeter traffic control, u, is available that
only restricts vehicles entering the city from outside.
If at 7am there are already no=500 [veh] in the city center:
a. Write the dynamic equations (mass conservation equation) in a continuous form for the
center of the city.
b. Convert the continuous dynamic into the discrete form. Use a time unit of 5min.
C. What would the accumulation of the system be at 7:30am, if the perimeter control is
inactive, i.e. u=1?
d. Choose perimeter control value (u) which starts after 7:30am, so that the network
outflow (g) remains at its maximum value at 8:00am. Explain your choice.
Hint: You can choose a constant or a time-dependent perimeter control. Both solutions will
be considered correct.
e. How many vehicles will be queued outside the city center at 8am, when the control
restriction, chosen in part d, stops?
f. Repeat part (c) with a time unit of 2min. Report the difference between part (c) and (f) and
elaborate. You may use Excel or other software for part (f) only.
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