Investigating the Dynamics of Traffic Flow on a Highway in a Class of Discontinuous Functions

  • Bahaddin SinsoysalEmail author
  • Hakan Bal
  • E. Ilhan Sahin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9045)


This work is devoted to finding a solution of Riemann problem for the first order nonlinear partial equation which describes the traffic flow on highway. When \(\rho _{\ell }>\rho _r\), the solution is presented as a piecewise continuous function, where \(\rho _{\ell }\) and \(\rho _r\) are the densities of cars on the left and right side of the intersection respectively. On the contrary case, a shock of which the location is unknown beforehand arises in the solution. In this case, a special auxiliary problem is introduced, the solution of which makes it possible to write the exact solution showing the locations of shock. For the realization of the proposed method, the parameters of the flow are also found.


Traffic flow equation Shock Characteristics Weak solution 


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Bahaddin Sinsoysal
    • 1
    Email author
  • Hakan Bal
    • 2
  • E. Ilhan Sahin
    • 3
  1. 1.Department of Mathematics and ComputingBeykent UniversityIstanbulTurkey
  2. 2.Department of International TradeBeykent UniversityIstanbulTurkey
  3. 3.Satellite Communication and Remote SensingITU, Informatics InstituteIstanbulTurkey

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