Steady-State Solutions of Traffic Flow in a Simple Circled Road Network

ZHANG Peng; Lü Yupei; GUO Mingmin; LIN Zhiyang; FANG Rui; LI Xiaoyang; ZHANG Xiaoning

doi:10.21656/1000-0887.410100

Volume 42 Issue 2

Feb. 2021

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Article Navigation > Applied Mathematics and Mechanics > 2021 > 42(2): 123-132

ZHANG Peng, Lü Yupei, GUO Mingmin, LIN Zhiyang, FANG Rui, LI Xiaoyang, ZHANG Xiaoning. Steady-State Solutions of Traffic Flow in a Simple Circled Road Network[J]. Applied Mathematics and Mechanics, 2021, 42(2): 123-132. doi: 10.21656/1000-0887.410100

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Steady-State Solutions of Traffic Flow in a Simple Circled Road Network

doi: 10.21656/1000-0887.410100

¹Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai 200072, P.R.China;²Department of Aeronautics and Astronautics, Fudan University, Shanghai 200433, P.R.China;³National Engineering Laboratory for Surface Transportation Weather Impacts Prevention, Broadvision Engineering Consultants Co., Ltd., Kunming 650200, P.R.China;⁴School of Economics and Management, Tongji University, Shanghai 200092, P.R.China

Funds: The National Natural Science Foundation of China（11672348;11972121）

Received Date: 2020-04-06
Rev Recd Date: 2020-12-28
Publish Date: 2021-02-01

Abstract

Abstract

The steady-state solutions of traffic flow in a circled road network composed of 3 road sections and 2 junctions were studied under the assumption of the user equilibrium principle at the diverging junction. The results show that, the solution parameters and the dynamic behavior depend continuously on the total number of vehicles in the network. More precisely, the solution suggests a constant density in each road section when the total number of vehicles is not greater than the 1st critical density and not smaller than the 2nd critical density. When the total number of vehicles is between the 2 critical densities, the shock discontinuity or queuing appears upstream towards a bottleneck or a junction where the upstream capacity is greater than the downstream capacity. Complete analytical results were presented with the diverging and the merging junctions as bottlenecks, respectively.
- LWR model,
- user equilibrium principle,
- transportation assignment model,
- shock discontinuity,
- bottleneck effect

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References(22)

References

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