Phase Plane Analysis of Traffic Phenomena with Different Input and Output Conditions
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In this paper, the traffic flow problem is converted into a system stability problem through variable substitution and a phase plane analysis method is presented for analyzing the complex nonlinear traffic phenomena. This method matches traffic congestion with the unstable system. So these theories and methods of stability can be applied directly to solve the traffic problem. Based on an anisotropic continuum model developed by Gupta and Katiyar (GK model), this paper uses this new method to describe various nonlinear phenomena due to different input and output conditions on ramps which were rarely studied in the past. The results show that the traffic phenomena described by the new method is consistent with that described by traditional methods. Moreover, the phase plane diagram highlights the unstable traffic phenomena we are chiefly concerned about and describes the variation of density or velocity with time or sections more clearly.
KeywordsPhase plane diagrams Nonlinear traffic phenomena Stability analysis Ramps
The authors would like to thank of the anonymous referees and the editor for their valuable opinions. This work is partially supported by the National Natural Science Foundation of China under the Grant No. 61863032 and the China Postdoctoral Science Foundation Funded Project (Project No.: 2018M633653XB) and the “Qizhi” Personnel Training Support Project of Lanzhou Institute of Technology (Grant No. 2018QZ-11) and the National Natural Science Foundation of China under the Grant No. 11965019.
Conflict of Interests
The authors declare that there is no conflict of interests regarding the publication of this paper.
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