Finite Differences-Runge Kutta Schemes for Vehicle Occupancy-Aggregate Emission Rate Relationship
Conference paper
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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.
Keywords
LWR Traffic congestion Traffic pollution Traffic vehicle emission Finite differences Runge KuttaReferences
- 1.Adams, W.F.: Road traffic considered as a random series. J. Inst. Civ. Eng. 4, 121–130 (1936)CrossRefGoogle 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)MathSciNetCrossRefGoogle Scholar
- 4.Chandle, R.E., Herman, R., Montroll, E.W.: Traffic dynamics: studies in car following. Oper. Res. 6, 165–184 (1958)MathSciNetCrossRefGoogle 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)MathSciNetCrossRefGoogle 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)MathSciNetCrossRefGoogle 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)CrossRefGoogle 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)CrossRefGoogle Scholar
- 14.Bektas, T., Laporte, G.: The pollution-routing problem. Transp. Res. Part B 45, 12321250 (2011)CrossRefGoogle Scholar
- 15.Franceschetti, A., Honhon, D., Woensel, T.V., Bektas, T., Laporte, G.: The time-dependent pollution-routing problem (2013)CrossRefGoogle 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)CrossRefGoogle 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
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