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Finite Differences-Runge Kutta Schemes for Vehicle Occupancy-Aggregate Emission Rate Relationship

  • Sofiya CherguiEmail author
  • Said Agoujil
Conference paper
Part of the Lecture Notes in Intelligent Transportation and Infrastructure book series (LNITI)

Abstract

Although transportation offers many benefits for humanity by facilitating life, it has negative effects especially the environmental ones, due to vehicular emissions which are related to highest congestions. Our paper studies the relationship between the vehicle occupancy and the aggregate emission rate. Such relation can be exploited as objective functions and/or constraints of optimization problems. The methodology used in this paper consists on considering a homogeneous dynamic road where the traffic is described by the Lighthill Whitham-Richard (LWR) model resolved using a finite differences scheme in space and a Runge Kutta scheme in time, while emissions are calculated using a modal model.

Keywords

LWR Traffic congestion Traffic pollution Traffic vehicle emission Finite differences Runge Kutta 

References

  1. 1.
    Adams, W.F.: Road traffic considered as a random series. J. Inst. Civ. Eng. 4, 121–130 (1936)CrossRefGoogle Scholar
  2. 2.
    Wardrop, J.G.: Some theoretical aspects of road traffic research. Proc. Inst. Civ. Eng. Part II 1(2), 325–362 (1952)Google Scholar
  3. 3.
    Pipes, L.A.: An operational analysis of traffic dynamics. J. Appl. Phys. 24(3), 274–281 (1953)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Chandle, R.E., Herman, R., Montroll, E.W.: Traffic dynamics: studies in car following. Oper. Res. 6, 165–184 (1958)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Lighthill, M.J., Whitham, G.B.: On the kinematic waves II. A theory of traffic flow on long crowded roads. Proc. R. Soc. Lond. Ser. A 199, 317–345 (1955)Google Scholar
  6. 6.
    Richards, P.I.: Shock waves on the highway. Oper. Res. 4, 4251 (1956)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Catalin, D., Genevive, D.T., Popescu, D.: Macroscopic modeling of road traffic by using hydrodynamic flow models. In: 20th Mediterranean Conference on Control and Automation (2012)Google Scholar
  8. 8.
    Catalin, D., Popescu, D., Stefanoiu, D.: Fuzzy modeling and control for a road section. In: 18th International Conference on System Theory (2014)Google Scholar
  9. 9.
    Darbha, S., Rajagopal, K.R., Tyagi, V.: A review of mathematical models for the flow of traffic and some recent results. Nonlinear Anal. 69 (2008)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Palmer, A.: The development of an integrated routing and carbon dioxide emissions model for goods vehicles. Ph.D., thesis. Cranfield University, School of Management (2007)Google Scholar
  11. 11.
    Jabali, O., Woensel, T. Van de Kok, A.G.: Analysis of travel times and CO2 emissions in time-dependent vehicle routing. Technical report, Eindhoven University of Technology (2009)Google Scholar
  12. 12.
    Maden, W., Eglese, R.W., Black, D.: Vehicle routing and scheduling with time varying data: a case study. J. Oper. Res. Soc. 61(3), 515522 (2010)CrossRefGoogle Scholar
  13. 13.
    Fagerholt, K., Laporte, G., Norstad, I.: Reducing fuel emissions by optimizing speed on shipping routes. J. Oper. Res. Soc. 61(3), 523–529 (2010)CrossRefGoogle Scholar
  14. 14.
    Bektas, T., Laporte, G.: The pollution-routing problem. Transp. Res. Part B 45, 12321250 (2011)CrossRefGoogle Scholar
  15. 15.
    Franceschetti, A., Honhon, D., Woensel, T.V., Bektas, T., Laporte, G.: The time-dependent pollution-routing problem (2013)CrossRefGoogle Scholar
  16. 16.
    Demir, E., Bektas, T., Laporte, G.: A comparative analysis of several vehicle emission models for road freight transportation. Transp. Res. Part D 16, 347357 (2011)CrossRefGoogle Scholar
  17. 17.
    Post, K., Kent, J.H., Tomlin, J., Carruthers, N.: Fuel Consumption and emission modeling by power demand and a comparative with other models. Transp. Res. A l8A(3), 191–213 (1984)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Computer Sciences, E3MI Team, Faculty of Sciences and TechniquesUniversity Moulay IsmailMeknesMorocco

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