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Chin. Phys. B, 2010, Vol. 19(11): 110503    DOI: 10.1088/1674-1056/19/11/110503
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Nonlinear analysis of traffic jams in an anisotropic continuum model

Arvind Kumar Guptaa, Sapna Sharmab
a Department of Mathematics, IIT Ropar-140001, India; b Mathematics Group, Birla Institute of Technology and Science, Pilani-333031, India
Abstract  This paper presents our study of the nonlinear stability of a new anisotropic continuum traffic flow model in which the dimensionless parameter or anisotropic factor controls the non-isotropic character and diffusive influence. In order to establish traffic flow stability criterion or to know the critical parameters that lead, on one hand, to a stable response to perturbations or disturbances or, on the other hand, to an unstable response and therefore to a possible congestion, a nonlinear stability criterion is derived by using a wavefront expansion technique. The stability criterion is illustrated by numerical results using the finite difference method for two different values of anisotropic parameter. It is also been observed that the newly derived stability results are consistent with previously reported results obtained using approximate linearisation methods. Moreover, the stability criterion derived in this paper can provide more refined information from the perspective of the capability to reproduce nonlinear traffic flow behaviors observed in real traffic than previously established methodologies.
Keywords:  traffic flow      non-linear stability      wavefront method  
Received:  04 November 2009      Revised:  18 May 2010      Accepted manuscript online: 
PACS:  02.30.Sa (Functional analysis)  
  89.40.Bb (Land transportation)  

Cite this article: 

Arvind Kumar Gupta, Sapna Sharma Nonlinear analysis of traffic jams in an anisotropic continuum model 2010 Chin. Phys. B 19 110503

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