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

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Innovations in Smart Cities Applications Edition 2 (SCA 2018)

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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.

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References

  1. Adams, W.F.: Road traffic considered as a random series. J. Inst. Civ. Eng. 4, 121–130 (1936)

    Article  Google Scholar 

  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. Pipes, L.A.: An operational analysis of traffic dynamics. J. Appl. Phys. 24(3), 274–281 (1953)

    Article  MathSciNet  Google Scholar 

  4. Chandle, R.E., Herman, R., Montroll, E.W.: Traffic dynamics: studies in car following. Oper. Res. 6, 165–184 (1958)

    Article  MathSciNet  Google Scholar 

  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. Richards, P.I.: Shock waves on the highway. Oper. Res. 4, 4251 (1956)

    Article  MathSciNet  Google Scholar 

  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. 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. 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)

    Article  MathSciNet  Google Scholar 

  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. 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. 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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  14. Bektas, T., Laporte, G.: The pollution-routing problem. Transp. Res. Part B 45, 12321250 (2011)

    Article  Google Scholar 

  15. Franceschetti, A., Honhon, D., Woensel, T.V., Bektas, T., Laporte, G.: The time-dependent pollution-routing problem (2013)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Sciences, E3MI Team, Faculty of Sciences and Techniques, University Moulay Ismail, Meknes, Morocco

    Sofiya Chergui & Said Agoujil

Authors
  1. Sofiya Chergui
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  2. Said Agoujil
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Corresponding author

Correspondence to Sofiya Chergui .

Editor information

Editors and Affiliations

  1. Association Méditerranéenne des Sciences et Technologies, Tangier, Morocco

    Mohamed Ben Ahmed

  2. Association Méditerranéenne des Sciences et Technologies, Tangier, Morocco

    Anouar Abdelhakim Boudhir

  3. Faculty of Sciences, Présidence UAE, Tétouan, Morocco

    Ali Younes

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Chergui, S., Agoujil, S. (2019). Finite Differences-Runge Kutta Schemes for Vehicle Occupancy-Aggregate Emission Rate Relationship. In: Ben Ahmed, M., Boudhir, A., Younes, A. (eds) Innovations in Smart Cities Applications Edition 2. SCA 2018. Lecture Notes in Intelligent Transportation and Infrastructure. Springer, Cham. https://doi.org/10.1007/978-3-030-11196-0_85

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