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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 136451, 13 pages
Research Article

An Improved Macro Model of Traffic Flow with the Consideration of Ramps and Numerical Tests

College of Automation, Northwestern Polytechnical University, No. 127 Youyi Road (West), Beilin, Xi’an, Shaanxi 710072, China

Received 8 April 2015; Revised 11 June 2015; Accepted 14 June 2015

Academic Editor: Xiaosong Hu

Copyright © 2015 Zhongke Shi et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We present an improved macro model for traffic flow based on the existing models. The equilibrium point equation of the model is obtained. The stop-and-go traffic phenomenon is described in phase plane and the relationship between traffic jams and system instability is clearly shown in the phase plane diagrams. Using the improved model, some traffic phenomena on a highway with ramps are found in this paper. The numerical simulation is carried out to investigate various nonlinear traffic phenomena with a single ramp generated by different initial densities and vehicle generation rates. According to the actual road sections of Xi’an-Baoji highways, the situations of morning peak with several ramps are also analyzed. All these results are consistent with real traffic, which shows that the improved model is reasonable.