On the Urban Link Fundamental Diagram Based on Velocity-Weighted Flow and Queue Length
Abstract
:1. Introduction
- (a)
- A variable named the velocity-weighted flow combining the flow and space-mean velocity of each vehicle is proposed, which contains characteristics of both velocities and flows.
- (b)
- A new kind of link fundamental diagram (LFD) based on the velocity-weighted flow and queue length is presented in this paper, which can show the relationship between traffic condition and queue length.
- (c)
- Features of the proposed LFD related to cycle times, green times, and splits are presented: The LFD shape is generally determined by the splits. Both the critical queue length and critical velocity-weighted flow increase with increasing green time. The critical queue length is more closely related to the green time than the cycle time.
2. Problem Formulation
2.1. Traffic Flow Description
2.2. Vehicle Velocity Description
3. Link Fundamental Diagram Based on Queue
3.1. The Definition of Velocity-Weighted Flow
3.2. Drawing Link Fundamental Diagram
4. Characters of the Link Fundamental Diagram
4.1. Impact of Green Time on the Link Fundamental Diagram
4.2. The Impact of Split on the Link Fundamental Diagram
4.3. The Impact of Cycle Time on the Link Fundamental Diagram
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
FD | Fundamental diagram |
MFD | Macroscopic fundamental diagram |
LFD | Link fundamental diagram |
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Symbol | Explanation |
---|---|
the velocity of vehicle i at time step t | |
free-flow velocity | |
following velocity | |
distance from vehicle i to stop line at time step t | |
queue length at time step t | |
Discharge shock wave | |
queuing shock wave | |
density when following with vehicles | |
jam density | |
s | saturation flow |
g | green time |
r | red time |
C | cycle time |
beginning of the cycle | |
q | traffic flow |
traffic flow passing an intersection in one cycle | |
arriving flow during green time | |
velocity-weighted traffic flow |
Symbol | Quantity | Sample |
---|---|---|
i | vehicle number | No. 549 |
moment of being positioned | 600 (s) | |
instantaneous velocity | 31.27 (km/h) | |
distance from vehicle to link entrance | 386.48 (m) | |
The number of the link where the vehicle is located | No. 30 | |
length of the link | 826.41 (m) |
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Yu, H.; Kong, J.; Ren, Y.; Yin, C. On the Urban Link Fundamental Diagram Based on Velocity-Weighted Flow and Queue Length. Symmetry 2020, 12, 1852. https://doi.org/10.3390/sym12111852
Yu H, Kong J, Ren Y, Yin C. On the Urban Link Fundamental Diagram Based on Velocity-Weighted Flow and Queue Length. Symmetry. 2020; 12(11):1852. https://doi.org/10.3390/sym12111852
Chicago/Turabian StyleYu, Hansong, Junwei Kong, Ye Ren, and Chenkun Yin. 2020. "On the Urban Link Fundamental Diagram Based on Velocity-Weighted Flow and Queue Length" Symmetry 12, no. 11: 1852. https://doi.org/10.3390/sym12111852