Phase plane analysis method of nonlinear traffic phenomena. (English) Zbl 1331.93012
Summary: A new phase plane analysis method for analyzing the complex nonlinear traffic phenomena is presented in this paper. This method makes use of variable substitution to transform a traditional traffic flow model into a new model which is suitable for the analysis in phase plane. According to the new model, various traffic phenomena, such as the well-known shock waves, rarefaction waves, and stop-and-go waves, are analyzed in the phase plane. From the phase plane diagrams, we can see the relationship between traffic jams and system instability. So the problem of traffic flow could be converted into that of system stability. The results show that the traffic phenomena described by the new method are consistent with that described by traditional methods. Moreover, the phase plane analysis highlights the unstable traffic phenomena we are chiefly concerned about and describes the variation of density or velocity with time or sections more clearly.
MSC:
| 93A30 | Mathematical modelling of systems (MSC2010) |
| 90B20 | Traffic problems in operations research |
| 93D99 | Stability of control systems |
| 93B17 | Transformations |
Keywords:
nonlinear traffic phenomena; traffic flow model; shock waves; rarefaction waves; stop-and-go waves; traffic jams; system instability; phase plane analysisReferences:
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