Coupling Pipes Car-Following Model with GM Model

Abstract:

This paper proposes coupling the Pipes car-following model with the GM model to formulate a new car-following model that can generate consistent separation distances between the leading and following vehicles. First, an example is given to show that the GM car-following model can lead to different separation distances at the same steady speed. Secondly, a new model is formulated by coupling the Pipes model with the GM model and it is shown that the only meaningful attractor of the new model is one producing consistent separation distances at the same steady speed. Furthermore, the relationship of those macroscopic traffic flow quantities inherent in the new car-following model has also been investigated. In the steady state, the resulting speed-density relationship is exactly the same as one derived from the Pipes model. In the dynamic case, the derived speed-density relationship is a partial differential equation. Numerical experiments are carried out to show that the new car-following model can generate consistent separation distances between the leading and following vehicles.

• Periodical: Advanced Materials Research (Volumes 243-249)
• Pages: 4392-4401
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.243-249.4392
• Online since: May 2011
• Authors: Ying En Ge, Na Wu, Bing Rong Sun
• Keywords: Acceleration, Car-Following Model, Deceleration, GM Model, Pipes Model, Separation Distance

References

[1] D. C. Gazis, R. Herman and R. W. Rothery: Nonlinear Follow-the-Leader Models of Traffic Flow. Operations Research Vol. 9 (1961), p.545.

DOI: 10.1287/opre.9.4.545

[2] R. E. Chandler, R. Herman and E. W. Montroll: Traffic dynamics: Studies in car following. Operations Research Vol. 6 (1958), p.165.

DOI: 10.1287/opre.6.2.165

[3] D . C. Gazis, R. Herman, A. Maradudin and R. B. Potts: Car following theory of steady state traffic flow. Operations Research Vol. 7 (1959), p.499.

DOI: 10.1287/opre.7.4.499

[4] L. C. Edie: Car-following and steady-state theory for noncongested traffic. Operations Research Vol. 9 (1961), p.66.

DOI: 10.1287/opre.9.1.66

[5] L. A. Pipes: An Operational Analysis of traffic analysis. Journal of Applied Physics Vol. 24 (1953), p.274.

[6] L.A. Pipes: Wave theories of traffic flow. Journal of the Franklin Institute Vol. 280 (1965), p.23.

[7] C.F. Daganzo: The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory. Transportation Research Part B, Vol. 28 (1994), p.269.

DOI: 10.1016/0191-2615(94)90002-7

[8] C.F. Daganzo: A finite difference approximation of the kinematic wave model of traffic flow. Transportation Research Part B, Vol. 29 (1995), p.261.

DOI: 10.1016/0191-2615(95)00004-w

[9] H.M. Zhang: A finite difference approximation of a non-equilibrium traffic flow model. Transportation Research Part B, Vol. 35 (2001), p.337.

DOI: 10.1016/s0191-2615(99)00054-5