A road pricing model involving social costs and infrastructure financing policies

This research develops a non-linear continuous optimisation model to estimate tolls for multi-class and multi-period traffic considering integral social costs such as congestion externalities, pavement damage, environmental emissions, operational travel costs, and user travel time cost, in addition...

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Autores:: Fuentes, Ricardo
Cantillo, Víctor
López-Ospina, Héctor

Tipo de recurso:: Article of journal

Fecha de publicación:: 2022

Institución:: Corporación Universidad de la Costa

Repositorio:: REDICUC - Repositorio CUC

Idioma:: eng

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dc.title.eng.fl_str_mv	A road pricing model involving social costs and infrastructure financing policies
title	A road pricing model involving social costs and infrastructure financing policies
spellingShingle	A road pricing model involving social costs and infrastructure financing policies Social welfare Particle swarm optimisation Tolling Road-financing policies
title_short	A road pricing model involving social costs and infrastructure financing policies
title_full	A road pricing model involving social costs and infrastructure financing policies
title_fullStr	A road pricing model involving social costs and infrastructure financing policies
title_full_unstemmed	A road pricing model involving social costs and infrastructure financing policies
title_sort	A road pricing model involving social costs and infrastructure financing policies
dc.creator.fl_str_mv	Fuentes, Ricardo Cantillo, Víctor López-Ospina, Héctor
dc.contributor.author.spa.fl_str_mv	Fuentes, Ricardo Cantillo, Víctor López-Ospina, Héctor
dc.subject.proposal.eng.fl_str_mv	Social welfare Particle swarm optimisation Tolling Road-financing policies
topic	Social welfare Particle swarm optimisation Tolling Road-financing policies
description	This research develops a non-linear continuous optimisation model to estimate tolls for multi-class and multi-period traffic considering integral social costs such as congestion externalities, pavement damage, environmental emissions, operational travel costs, and user travel time cost, in addition to maintenance and construction of road infrastructure costs. The approach uses social welfare principles, formulating a function to calculate the social welfare of a multi-class flow that moves in multiple periods based on a stochastic discrete choice model and considering infrastructure financing constraints. A case study was conducted applying the model to a road in the Colombian Caribbean region and estimated the value of tolls using the particle swarm optimisation heuristic. Results showed that infrastructure policies considering partial financing resulted in higher social welfare values. Scenarios requiring toll revenue to be higher than infrastructure cost can shrink demand and cause distributive issues.
publishDate	2022
dc.date.accessioned.none.fl_str_mv	2022-06-15T18:58:01Z
dc.date.available.none.fl_str_mv	2022-06-15T18:58:01Z 2024
dc.date.issued.none.fl_str_mv	2022
dc.type.spa.fl_str_mv	Artículo de revista
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dc.type.content.spa.fl_str_mv	Text
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dc.identifier.citation.spa.fl_str_mv	Ricardo Fuentes, Víctor Cantillo, Héctor López-Ospina, A road pricing model involving social costs and infrastructure financing policies, Applied Mathematical Modelling, Volume 105, 2022, Pages 729-750, ISSN 0307-904X, https://doi.org/10.1016/j.apm.2022.01.013
dc.identifier.issn.spa.fl_str_mv	0307-904X
dc.identifier.uri.spa.fl_str_mv	https://hdl.handle.net/11323/9255
dc.identifier.url.spa.fl_str_mv	https://doi.org/10.1016/j.apm.2022.01.013
dc.identifier.doi.spa.fl_str_mv	10.1016/j.apm.2022.01.013
dc.identifier.instname.spa.fl_str_mv	Corporación Universidad de la Costa
dc.identifier.reponame.spa.fl_str_mv	REDICUC - Repositorio CUC
dc.identifier.repourl.spa.fl_str_mv	https://repositorio.cuc.edu.co/
identifier_str_mv	Ricardo Fuentes, Víctor Cantillo, Héctor López-Ospina, A road pricing model involving social costs and infrastructure financing policies, Applied Mathematical Modelling, Volume 105, 2022, Pages 729-750, ISSN 0307-904X, https://doi.org/10.1016/j.apm.2022.01.013 0307-904X 10.1016/j.apm.2022.01.013 Corporación Universidad de la Costa REDICUC - Repositorio CUC
url	https://hdl.handle.net/11323/9255 https://doi.org/10.1016/j.apm.2022.01.013 https://repositorio.cuc.edu.co/
dc.language.iso.none.fl_str_mv	eng
language	eng
dc.relation.ispartofjournal.spa.fl_str_mv	Applied Mathematical Modelling
dc.relation.references.spa.fl_str_mv	[1] G. De Rus, J. Campos, G. Nombela, Economia Del Transporte, Antoni Bosch, Barcelona, 2003. [2] K. Ozbay, B. Bartin, Estimation and evaluation of full marginal costs of highway transportation in New Jersey, J. Transp. Stat. 4 (1) (2001) 81–103. [3] Y. Nie, Y. Liu, Existence of self-financing and Pareto-improving congestion pricing: impact of value of time distribution, Transp. Res. Part A 44 (1) (2010) 39–51. [4] S. Jara-Díaz, Transport Economic Theory, Elsevier, 2007. [5] P. Cantos-Sánchez, R. Moner-Colonques, J. Sempere-Monerris, O. Álvarez-SanJaime, Alternative pricing regimes in interurban passenger transport with externalities and modal competition, Reg. Sci. Urban Econ. 39 (2) (2009) 128–137. [6] P. Samuel, The Role of Tolls in Financing 21st Century Highways, Reason Foundation, 2007. [7] X. Chen, L. Zhang, X. He, C. Xiong, Z. Zhu, Simulation-based pricing optimisation for improving network-wide travel time reliability, Transportmetr. A Transp. Sci. 14 (1–2) (2018) 155–176. [8] K.A. Small, E.T. Verhoef, The Economics of Urban Transportation, Routledge, New York, 2007. [9] W. Nicholson, C. Snyder, Microeconomic Theory: Basic Principles and Extensions, Thomson Higher Education, Mason, 2008. [10] J. Holguín-Veras, M. Cetin, Optimal tolls for multi-class traffic: analytical formulations and policy implications, Transp. Res. Part A 43 (4) (2009) 445–467. [11] J. Oh, S. Labi, K. Sinha, Implementation and evaluation of self-financing highway pricing schemes, Transp. Res. Rec. 1996 (1) (2007) 25–33. [12] G. De Rus, M. Romero, Private financing of roads and optimal pricing: is it possible to get both? Ann. Reg. Sci. 38 (3) (2004) 485–497. [13] T. Light, Optimal highway design and user welfare under value pricing, J. Urban Econ. 66 (2) (2009) 116–124. [14] E. Verhoef, Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points, Transp. Res. Part B 36 (8) (2002) 707–729. [15] D. Watling, S. Shepherd, A. Koh, Cordon toll competition in a network of two cities: formulation and sensitivity to traveller route and demand responses, Transp. Res. Part B 76 (2015) 93–116. [16] A. De Palma, M. Kilani, R. Linsey, Congestion pricing on a road network: a study using the dynamic equilibrium simulator METROPOLIS, Transp. Res. Part A Policy Pract. 39 (7–9) (2005) 588–611. [17] H. Iseki, Q. Li, An Empirical Analysis of the Pricing Structure of Toll Facilities Based on Social Costs of Driving by Vehicle Class and Its Effects on Traffic, Toll Revenue, Emission, and ESAL. Transportation Research Board 93rd Annual Meeting. Washington DC (No. 14-5275), https://trid.trb.org/view/1289850, 2014. [18] H. Williams, On the formation of travel demand models and economic evaluation measures of user benefit, Environ. Plan. A Econ. Space 9 (3) (1997) 285–344. [19] Z.C. Li, W.H. Lam, S.C. Wong, Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city, Transp. Res. Part B Methodol. 46 (1) (2012) 30–49. [20] A.Y. Bigazzi, M.A. Figliozzi, Marginal costs of freeway traffic congestion with on-road pollution exposure externality, Transp. Res. Part A Policy Pract. 57 (2013) 12–24. [21] M. Miralinaghi, S. Peeta, Promoting zero-emissions vehicles using robust multi-period tradable credit scheme, Transp. Res. Part D Transp. Environ. 75 (2019) 265–285. [22] X. Guo, D. Xu, Profit maximisation by a private toll road with cars and trucks, Transp. Res. Part B Method 91 (2016) 113–129. [23] J. Wang, X. Hu, C. Li, Optimisation of the freeway truck toll by weight policy, including external environmental costs, J. Clean. Prod. 184 (2018) 220–226. [24] A. Beziat, M. Koning, F. Toilier, Marginal congestion costs in the case of multi-class traffic: a macroscopic assessment for the Paris Region, Transp. Policy 60 (2017) 87–98. [25] X. Fu, V.A. Van Den Berg, E.T. Verhoef, Private road supply in networks with heterogeneous users, Transp. Res. Part A Policy Pract. 118 (2018) (2018) 430–443. [26] H. López-Ospina, A. Agudelo-Bernal, L. Reyes-Muñoz, G. Zambrano-Rey, J. Pérez, Design of a location and transportation optimization model including quality of service using constrained multinomial logit, Appl. Math. Model. 89 (2021) 428–453. [27] J. Holguín-Veras, M. Silas, J. Polimeni, B. Cruz, An investigation on the effectiveness of joint receiver-carrier policies to increase truck traffic in the off-peak hours, Netw. Spat. Econ. 8 (1) (2008) 327–354. [28] M. Adnan, Passenger car equivalent factors in heterogenous traffic environment-are we using the right numbers? Procedia Eng. 77 (2014) 106–113. [29] A. Kudhiaer, Estimation of free flow speeds and passenger car equivalent factors for multilane highways, Int. J. Sci. Eng. Res. 7 (6) (2016) 721–727. [30] INVIASManual de Diseño Geometrico de Carreteras, Ministerio de Transporte de Colombia, Bogotá, 2008. [31] Transportation Research BoardHighway Capacity Manual, TRB, 2010. [32] B.Q. Liu, C.C. Huang, Multi-class time reliability-based congestion pricing model based on a degradable transportation network, Appl. Math. Model. 40 (5–6) (2016) 3483–3497. [33] E.G. Talbi, Metaheuristics: From Design to Implementation, Wiley, 2009. [34] B. Farnad, A. Jafarian, D. Baleanu, A new hybrid algorithm for continuous optimisation problem, Appl. Math. Mod. 55 (2018) 652–673. [35] V. Hajipour, M. Tavana, D. Di Caprio, M. Akhgar, Y. Jabbari, An optimisation model for traceable closed-loop supply chain networks, Appl. Math. Mod. 71 (2019) 673–699. [36] X. Jiang, J. Na, Online surrogate multiobjective optimisation algorithm for contaminated groundwater remediation designs, Appl. Math. Model. 78 (2020) 519–538. [37] R. Eberhart, J. Kennedy, Particle swarm optimisation, in: Proceedings of the IEEE International Conference on Neural Networks, 4, 1995, pp. 1942–1948. [38] S. Palmer, Evolutionary algorithms and computational methods for derivatives pricing, Doctoral dissertation, UCL University College London. 334p, https://discovery.ucl.ac.uk/id/eprint/10068568/, 2019. [39] F. Etebari, A simultaneous facility location, vehicle routing and dynamic pricing in a distribution network, Appl. Soft Comp. 83 (2019) 105647. [40] A. Faza, A. Al-Mousa, PSO-based optimisation toward intelligent dynamic pricing schemes parameterisation, Sustain. Cities Soc. 51 (2019) 101776. [41] G. Zambrano-Rey, H. López-Ospina, J. Pérez, Retail store location and pricing within a competitive environment using constrained multinomial logit, Appl. Math. Model. 75 (2019) 521–534. [42] J. Güiza, R. Luque, J. Murillo, R. Romero, D. Barrera, H. López-Ospina, Integrating pricing and coordinated inventory decisions between one warehouse and multiple retailers, J. Ind. Prod. Eng. 38 (7) (2021) 536–546. [43] K. Page, J. Pérez, C. Telha, A. García-Echalar, H. López-Ospina, Optimal bundle composition in competition for continuous attributes, Eur. J. Oper. Res. 293 (3) (2021) 1168–1187. [44] J.A. Nelder, R. Mead, A simplex method for function minimisation, Comput. J. 7 (4) (1965) 308–313. [45] R.H. Byrd, P. Lu, J. Nocedal, C. Zhu, A limited memory algorithm for bound constrained optimisation, SIAM J. Sci. Comput. 16 (5) (1995) 1190–1208. [46] C.J. Bélisle, Convergence theorems for a class of simulated annealing algorithms on Rd, J. Appl. Probab. 29 (4) (1992) 885–895. [47] J. Galvan, V. Cantillo, J. Arellana, Factors influencing demand for buses powered by alternative energy sources, J. Public Transp. 19 (2) (2016) 23–37. [48] S. Call, W. Holahan, Microeconomía, Grupo Editorial Iberoamérica, Mexico DF, 1983. [49] M. Börjesson, J. Eliasson, C. Hamilton, Why experience changes attitudes to congestion pricing: the case of Gothenburg, Transp. Res. Part A 85 (2016) 1–16. [50] Z. Gu, Z. Liu, Q. Cheng, M. Saberi, Congestion pricing practices and public acceptance: a review of evidence, Case Stud. Transp. Policy 6 (1) (2018) 94–101. [51] L.G. Márquez, V. Cantillo, Appraisal of cost function parameters in the strategic freight transportation network in Colombia, Ing. Desarro. 29 (2) (2011) 286–307. [52] V. Cantillo, M. Jaller, J. Holguín-Veras, The Colombian strategic freight transport model based on product analysis, Promet Traffic Transp. 26 (6) (2014) 487–496. [53] H. Cai, A. Burnham, M. Wang, Updated Emission Factors of Air Pollutants from Vehicle Operations in GREETTM Using MOVES, Argonne National Laboratory, 2013. [54] P. Castro, L. Escobar, Estimación De Las Emisiones Contaminantes Por Fuentes Móviles a Nivel Nacional y Formulación De Lineamientos Técnicos Para El Ajuste De Las Normas De Emisión, Universidad de la Salle, Facultad de Ingeniería Ambiental y Sanitaría, Bogotá, 2006. [55] D. Herrera, Modelo De Emisiones Vehiculares Para La Ciudad De Bogotá, Universidad de los Andes, Departamento de Ingeniería Civil y Ambiental., Bogotá, 2007. [56] IVE webpage, International vehicle emissions model. http://www.issrc.org/ive/, 2018 (accessed may 2018). [57] A. Setyawan, I. Kusdiantoro, The effect of pavement condition on vehicle speeds and motor vehicles emissions, Procedia Eng. 125 (2015) 424–430. [58] G. Duarte, G. Goncalves, T. Farias, A methodology to estimate real-world vehicle fuel use and emissions based on certification cycle data, Procedia Soc. Behav. Sci. 111 (2014) 702–710. [59] L. Macea, L. Fuentes, A. Alvarez, Evaluación de factores camión de los vehículos comerciales de carga que circulan por la red vial principal Colombiana, in: Rev. Fac. Ing., 66, Universidad de Antioquia, 2013, pp. 57–69. [60] Mid-America Freight Coalition, Understanding freight vehicle pavement impacts: how do passenger vehicles and trucks compare? National center for freight and infrastructure, Res. Educ. 1 (2015) 1–7. [61] United States Department of Transportation, Comprehensive truck size and weight (TS and W) study: phase 1 – synthesis (pavement and truck size and weight regulations) working paper 3. Columbus, OH, https://rosap.ntl.bts.gov/view/dot/4729, 1995 (accessed may 2018). [62] D. Newbery, Road damage externalities and road user charges, Econometrica 56 (1988) 295–316. [63] K. Small, W. Clifford, E. Carol, Road Work, A New Highway Pricing and Investment Policy, The Brookings Institution, 1989. [64] G. Lindberg, Marginal Cost of Road Maintenance For Heavy Goods Vehicles on Swedish roads, Infrastructure Cost, Unification of Accounts and Marginal Costs For Transport Efficiency (UNITE), University of Leeds, 2002. [65] A. Ahmed, Q. Bai, S. Labi, Pavement Damage Cost estimation: a Synthesis of Past Research, ICE, Institution of Civil Engineers, 2013. [66] A. Ahmed, Q. Bai, S. Lavrenz, S. Labi, Estimating the marginal cost of pavement damage by highway users on the basis of practica schedules for pavement maintenance, rehabilitation and reconstruction, Struct. Infrastruct. Eng. 11 (8) (2015) 1069–1082. [67] Z. Li, K. Sinha, A methodology to determine the load and non-load shares of pavement repair expenditure, Joint Transportation Research Program, Program Purdue University, 2000. [68] ANIFExigencias De Basilea III y Concesiones 4G, Bancolombia, Bogotá, 2017. [69] Banco de la República, representative market rate, http://www.banrep.gov.co/es/trm, 2018 (accessed may 2018). [70] H. Ye, W. Luo, Z. Li, Convergence analysis of particle swarm optimiser and its improved algorithm based on velocity differential evolution, Comput. Intell. Neurosci. 2013 (2013) 1–7.
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spelling	Fuentes, RicardoCantillo, VíctorLópez-Ospina, Héctor2022-06-15T18:58:01Z20242022-06-15T18:58:01Z2022Ricardo Fuentes, Víctor Cantillo, Héctor López-Ospina, A road pricing model involving social costs and infrastructure financing policies, Applied Mathematical Modelling, Volume 105, 2022, Pages 729-750, ISSN 0307-904X, https://doi.org/10.1016/j.apm.2022.01.0130307-904Xhttps://hdl.handle.net/11323/9255https://doi.org/10.1016/j.apm.2022.01.01310.1016/j.apm.2022.01.013Corporación Universidad de la CostaREDICUC - Repositorio CUChttps://repositorio.cuc.edu.co/This research develops a non-linear continuous optimisation model to estimate tolls for multi-class and multi-period traffic considering integral social costs such as congestion externalities, pavement damage, environmental emissions, operational travel costs, and user travel time cost, in addition to maintenance and construction of road infrastructure costs. The approach uses social welfare principles, formulating a function to calculate the social welfare of a multi-class flow that moves in multiple periods based on a stochastic discrete choice model and considering infrastructure financing constraints. A case study was conducted applying the model to a road in the Colombian Caribbean region and estimated the value of tolls using the particle swarm optimisation heuristic. Results showed that infrastructure policies considering partial financing resulted in higher social welfare values. Scenarios requiring toll revenue to be higher than infrastructure cost can shrink demand and cause distributive issues.22 páginasapplication/pdfengElsevier Inc.United States© 2022 Elsevier Inc. All rights reserved.Atribución-NoComercial-SinDerivadas 4.0 Internacional (CC BY-NC-ND 4.0)https://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/embargoedAccesshttp://purl.org/coar/access_right/c_f1cfA road pricing model involving social costs and infrastructure financing policiesArtículo de revistahttp://purl.org/coar/resource_type/c_6501http://purl.org/coar/resource_type/c_2df8fbb1Textinfo:eu-repo/semantics/articlehttp://purl.org/redcol/resource_type/ARThttp://purl.org/coar/version/c_970fb48d4fbd8a85https://www.sciencedirect.com/science/article/pii/S0307904X22000269#!Applied Mathematical Modelling[1] G. De Rus, J. Campos, G. Nombela, Economia Del Transporte, Antoni Bosch, Barcelona, 2003.[2] K. Ozbay, B. Bartin, Estimation and evaluation of full marginal costs of highway transportation in New Jersey, J. Transp. Stat. 4 (1) (2001) 81–103.[3] Y. Nie, Y. Liu, Existence of self-financing and Pareto-improving congestion pricing: impact of value of time distribution, Transp. Res. Part A 44 (1) (2010) 39–51.[4] S. Jara-Díaz, Transport Economic Theory, Elsevier, 2007.[5] P. Cantos-Sánchez, R. Moner-Colonques, J. Sempere-Monerris, O. Álvarez-SanJaime, Alternative pricing regimes in interurban passenger transport with externalities and modal competition, Reg. Sci. Urban Econ. 39 (2) (2009) 128–137.[6] P. Samuel, The Role of Tolls in Financing 21st Century Highways, Reason Foundation, 2007.[7] X. Chen, L. Zhang, X. He, C. Xiong, Z. Zhu, Simulation-based pricing optimisation for improving network-wide travel time reliability, Transportmetr. A Transp. Sci. 14 (1–2) (2018) 155–176.[8] K.A. Small, E.T. Verhoef, The Economics of Urban Transportation, Routledge, New York, 2007.[9] W. Nicholson, C. Snyder, Microeconomic Theory: Basic Principles and Extensions, Thomson Higher Education, Mason, 2008.[10] J. Holguín-Veras, M. Cetin, Optimal tolls for multi-class traffic: analytical formulations and policy implications, Transp. Res. Part A 43 (4) (2009) 445–467.[11] J. Oh, S. Labi, K. Sinha, Implementation and evaluation of self-financing highway pricing schemes, Transp. Res. Rec. 1996 (1) (2007) 25–33.[12] G. De Rus, M. Romero, Private financing of roads and optimal pricing: is it possible to get both? Ann. Reg. Sci. 38 (3) (2004) 485–497.[13] T. Light, Optimal highway design and user welfare under value pricing, J. Urban Econ. 66 (2) (2009) 116–124.[14] E. Verhoef, Second-best congestion pricing in general networks. Heuristic algorithms for finding second-best optimal toll levels and toll points, Transp. Res. Part B 36 (8) (2002) 707–729.[15] D. Watling, S. Shepherd, A. Koh, Cordon toll competition in a network of two cities: formulation and sensitivity to traveller route and demand responses, Transp. Res. Part B 76 (2015) 93–116.[16] A. De Palma, M. Kilani, R. Linsey, Congestion pricing on a road network: a study using the dynamic equilibrium simulator METROPOLIS, Transp. Res. Part A Policy Pract. 39 (7–9) (2005) 588–611.[17] H. Iseki, Q. Li, An Empirical Analysis of the Pricing Structure of Toll Facilities Based on Social Costs of Driving by Vehicle Class and Its Effects on Traffic, Toll Revenue, Emission, and ESAL. Transportation Research Board 93rd Annual Meeting. Washington DC (No. 14-5275), https://trid.trb.org/view/1289850, 2014.[18] H. Williams, On the formation of travel demand models and economic evaluation measures of user benefit, Environ. Plan. A Econ. Space 9 (3) (1997) 285–344.[19] Z.C. Li, W.H. Lam, S.C. Wong, Modeling intermodal equilibrium for bimodal transportation system design problems in a linear monocentric city, Transp. Res. Part B Methodol. 46 (1) (2012) 30–49.[20] A.Y. Bigazzi, M.A. Figliozzi, Marginal costs of freeway traffic congestion with on-road pollution exposure externality, Transp. Res. Part A Policy Pract. 57 (2013) 12–24.[21] M. Miralinaghi, S. Peeta, Promoting zero-emissions vehicles using robust multi-period tradable credit scheme, Transp. Res. Part D Transp. Environ. 75 (2019) 265–285.[22] X. Guo, D. Xu, Profit maximisation by a private toll road with cars and trucks, Transp. Res. Part B Method 91 (2016) 113–129.[23] J. Wang, X. Hu, C. Li, Optimisation of the freeway truck toll by weight policy, including external environmental costs, J. Clean. Prod. 184 (2018) 220–226.[24] A. Beziat, M. Koning, F. Toilier, Marginal congestion costs in the case of multi-class traffic: a macroscopic assessment for the Paris Region, Transp. Policy 60 (2017) 87–98.[25] X. Fu, V.A. Van Den Berg, E.T. Verhoef, Private road supply in networks with heterogeneous users, Transp. Res. Part A Policy Pract. 118 (2018) (2018) 430–443.[26] H. López-Ospina, A. Agudelo-Bernal, L. Reyes-Muñoz, G. Zambrano-Rey, J. Pérez, Design of a location and transportation optimization model including quality of service using constrained multinomial logit, Appl. Math. Model. 89 (2021) 428–453.[27] J. Holguín-Veras, M. Silas, J. Polimeni, B. Cruz, An investigation on the effectiveness of joint receiver-carrier policies to increase truck traffic in the off-peak hours, Netw. Spat. Econ. 8 (1) (2008) 327–354.[28] M. Adnan, Passenger car equivalent factors in heterogenous traffic environment-are we using the right numbers? Procedia Eng. 77 (2014) 106–113.[29] A. Kudhiaer, Estimation of free flow speeds and passenger car equivalent factors for multilane highways, Int. J. Sci. Eng. Res. 7 (6) (2016) 721–727.[30] INVIASManual de Diseño Geometrico de Carreteras, Ministerio de Transporte de Colombia, Bogotá, 2008.[31] Transportation Research BoardHighway Capacity Manual, TRB, 2010.[32] B.Q. Liu, C.C. Huang, Multi-class time reliability-based congestion pricing model based on a degradable transportation network, Appl. 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Neurosci. 2013 (2013) 1–7.750729105Social welfareParticle swarm optimisationTollingRoad-financing policiesPublicationORIGINALA road pricing model involving social costs and infrastructure financing policies.pdfA road pricing model involving social costs and infrastructure financing policies.pdfapplication/pdf2284361https://repositorio.cuc.edu.co/bitstreams/eb3f9ca9-c542-4b24-b620-0bdbe2202f5c/download900eb39dcd94a0f80d937216a9af71e6MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-83196https://repositorio.cuc.edu.co/bitstreams/c8f32d0b-3e5e-4917-8969-52886dd26792/downloade30e9215131d99561d40d6b0abbe9badMD52TEXTA road pricing model involving social costs and infrastructure financing policies.pdf.txtA road pricing model involving social costs and infrastructure financing policies.pdf.txttext/plain92771https://repositorio.cuc.edu.co/bitstreams/96fcaa29-9d2b-4d8d-b9c8-0726224367b8/download2b89f71a5a3141682b3ed04bbbc4ed34MD53THUMBNAILA road pricing model involving social costs and infrastructure financing policies.pdf.jpgA road pricing model involving social costs and infrastructure financing policies.pdf.jpgimage/jpeg14731https://repositorio.cuc.edu.co/bitstreams/e6a099f2-a54e-4b89-a8fe-d8de2c69416c/download385eb32a5f1a62dd26ccee5eae513e64MD5411323/9255oai:repositorio.cuc.edu.co:11323/92552024-09-17 12:48:14.522https://creativecommons.org/licenses/by-nc-nd/4.0/© 2022 Elsevier Inc. 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A road pricing model involving social costs and infrastructure financing policies

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