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2013, 9(2): 341-363. doi: 10.3934/jimo.2013.9.341

Using emission functions in modeling environmentally sustainable traffic assignment policies

1. 

Faculty of Engineering and Technology, Galatasaray University, Çirağan Caddesi No:36 Ortaköy, 34357 Istanbul, Turkey, Turkey

2. 

Faculty of Engineering and Natural Sciences, Sabanci University, Üniversite Caddesi No:27 Tuzla, 34956 Istanbul, Turkey, Turkey

3. 

Faculty of Engineering and Natural Sciences, Sabanci University, niversite Caddesi No:27 Tuzla, 34956 Istanbul, Turkey

Received  November 2011 Revised  July 2012 Published  February 2013

Transport systems play a crucial role for sustainable development, and hence, sustainable urban transportation has recently become a major research area. Most of the existing studies propose evaluation methods that use simulation tools to assess the sustainability of different transportation policies. Although there are some recent studies, considering the sustainability dimension and the resulting policies through mathematical programming models is still an open research area. In this study, we focus on controlling the gas emissions for the environmental sustainability and propose several mathematical programming models that incorporate the measurements of gas emissions over a traffic network. We define emission functions in terms of the traffic flow so that the accumulated emission amounts can be modeled accurately, particularly in case of congestion. Using these emission functions, we introduce alternate objective functions and develop optimization models under various policies which are based on the well-known toll pricing and capacity enhancement. The proposed models both reflect the route choice decisions of the network users and the decisions of the transportation managers that aim at making the transport systems more sustainable through the policies of interest. We conduct a computational study on a well-known testing network and present numerical results to evaluate the proposed alternate models. We conclude that simultaneously applying the toll pricing and capacity enhancement policies is in general more effective in serving the travel demand and reducing the emission amounts compared to implementing these policies individually.
Citation: O. İlker Kolak, Orhan Feyzioğlu, Ş. İlker Birbil, Nilay Noyan, Semih Yalçindağ. Using emission functions in modeling environmentally sustainable traffic assignment policies. Journal of Industrial & Management Optimization, 2013, 9 (2) : 341-363. doi: 10.3934/jimo.2013.9.341
References:
[1]

M. Abdulaal and L. J. LeBlanc, Continuous equilibrium network design models,, Transportation Research Part B: Methodological, 13 (1979), 19.

[2]

R. Akçelik, "Speed-Flow Models for Uninterrupted Traffic Facilities,", Tech. Report, (2003).

[3]

R. Akçelik, "Speed-Flow and Bunching Relationships for Uninterrupted Flows,", Proceeding of the 5th International Symposium on Highway Capacity and Quality of Service, (2006).

[4]

R. Arnott and K. Small, "The Economics of Traffic Congestion,", Boston College working papers in economics, (1993).

[5]

F. Babonneau and J.-P. Vial, An efficient method to compute traffic assignment problems with elastic demands,, Transportation Science, 42 (2008), 249.

[6]

C. Benedek and L. Rilett, Equitable traffic assignment with environmental cost functions,, Journal of Transportation Engineering, 124 (1998), 16.

[7]

Ş. I. Birbil, G. Gürkan and O. Listeş, Solving stochastic mathematical programs with complementarity constraints using simulation,, Mathematics of Operations Research, 31 (2006), 739. doi: 10.1287/moor.1060.0215.

[8]

, "Traffic Assignment Manual for Application with a Large, High Speed Computer,", U.S. Dept. of Commerce, (1964).

[9]

L. Brotcorne, M. Labbe, P. Marcotte and G. Savard, A bilevel model for toll optimization on a multicommodity transportation network,, Transportation Science, 35 (2001), 345.

[10]

, "Methods to Find the Cost-Effectiveness of Funding Air Quality Projects,", Tech. Report, (2010).

[11]

A. Chen and K. Subprasom, Analysis of regulation and policy of private toll roads in a build-operate-transfer scheme under demand uncertainty,, Transportation Research Part A: Policy and Practice, 41 (2007), 537.

[12]

S.-W. Chiou, Bilevel programming for the continuous transport network design problem,, Transportation Research Part B: Methodological, 39 (2005), 361.

[13]

J. Dargay, D. Gately and M. Sommer, Vehicle ownership and income growth, worldwide: 1960-2030,, The Energy Journal, 28 (2007), 163.

[14]

G. de Ceuster, B. van Herbruggen, O. Ivanova, K. Carlier, A. Martino and D. Fiorello, "TREMOVE - Final Report,", Tech. Report, (2007).

[15]

E. Deakin, "Sustainable Development and Sustainable Transportation: Strategies for Economic Prosperity Environmental Quality and Equity,", Tech. Report 2001'03, (2001).

[16]

S. P. Dirkse and M. C. Ferris, Traffic modeling and variational inequalities using GAMS,, in, (1997), 136.

[17]

A. Drud, CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems,, Mathematical Programming, 31 (1985), 153. doi: 10.1007/BF02591747.

[18]

, "Major Pollutants from Petrol and Diesel Engines,", Tech. Report, (2010).

[19]

, "User's Guide to Mobile 6.1 and Mobile 6.2 - Mobile Source Emission Factor Model,", Environmental Protection Agency, (2003).

[20]

M. C. Ferris, S. P. Dirkse and A. Meeraus, Mathematical programs with equilibrium constraints: Automatic reformulation and solution via constrained optimization,, in, (2005), 67.

[21]

T. L. Friesz, R. L. Tobin, H.-J. Cho and N. J. Mehta, Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints,, Mathematical Programming, 48 (1990), 265. doi: 10.1007/BF01582259.

[22]

, "GAMS-A User's Guide,", General Algebraic Modeling System, (2010).

[23]

Z. Gao and Y. Song, A reserve capacity model of optimal signal control with user-equilibrium route choice,, Transportation Research: Part B, 36 (2002), 313.

[24]

D. Gkatzoflias, C. Kouridis, L. Ntziachristos and Z. Samaras, "Copert 5 - Computer Programme to Calculate Emissions from Road Transport, User Manual, Version 5.0,", European Environment Agency, (2007).

[25]

S. Gokhale and M. Khare, A review of deterministic, stochastic and hybrid vehicular exhaust emission models,, International Journal of Transport Management, 2 (2004), 59.

[26]

R. L. Guensler and D. Sperling, Congestion pricing and motor vehicle emissions: An initial review,, Transportation Research Board Special Report, 242 (1994), 356.

[27]

E. Gutt, V. Patton and N. Spencer, "Building on 30 Years of Clean Air Act Success: The Case for Reducing NOx Air Pollution,", Tech. Report, (2000).

[28]

D. W. Hearn and M. V. Ramana, Solving congestion toll pricing models,, in, (1998), 109.

[29]

C. M. Jeon and A. Amekudzi, Addressing sustainability in transportation systems: Definitions, indicators, and metrics,, Journal of Infrastructure Systems, 11 (2005), 31.

[30]

O. Johansson-Stenman and T. Sterner, What is the scope for environmental road pricing?,, in, (1998), 150.

[31]

M. Ketzel, P. Louka, P. Sahm, E. Guilloteau, J.-F. Sini and N. Moussiopoulos, Intercomparison of numerical urban dispersion models: Part I & II,, Water, 2 (2002), 603.

[32]

F. H. Knight, Some fallacies in the interpretation of social cost,, The Quarterly Journal of Economics, 38 (1924), 582.

[33]

M. Labbe, P. Marcotte and G. Savard, A bilevel model of taxation and its application to optimal highway pricing,, Management Science, 44 (1998), 1608.

[34]

S. Lawphongpanich and D. W. Hearn, An MPEC approach to second-best toll pricing,, Mathematical Programming, 101 (2004), 33. doi: 10.1007/s10107-004-0536-5.

[35]

T. Litman, "Well Measured: Developing Indicators for Sustainable and Livable Transport Planning,", Tech. Report, (2010).

[36]

T. Litman and D. Burwell, Issues in sustainable transportation,, International Journal of Global Environmental Issues, 6 (2006), 331.

[37]

Z.-Q. Luo, J.-S. Pang, and D. Ralph, "Mathematical Programs with Equilibrium Constraints,", Cambridge University Press, (1996). doi: 10.1017/CBO9780511983658.

[38]

D. R. Lynam and G. D. Pfeifer, Human health effects of highway-related pollutants,, in, 44 (1991), 259.

[39]

T. L. Magnanti and R. T. Wong, Network Design and Transportation Planning: Models and Algorithms,, Transportation Science, 18 (1984), 1.

[40]

P. Marcotte, Network design problem with congestion effects: A case of bilevel programming,, Mathematical Programming, 34 (1986), 142. doi: 10.1007/BF01580580.

[41]

A. Nagurney, Congested urban transportation networks and emission paradoxes,, Transportation Research Part D: Transport and Environment, 5 (2000), 145.

[42]

A. Nagurney, "Sustainable Transportation Networks,", Edward Elgar Publishing, (2000).

[43]

A. Nagurney, Paradoxes in networks with zero emission links: Implications for telecommunications versus transportation,, Transportation Research Part D: Transport and Environment, 6 (2001), 283.

[44]

M. Patriksson, "The Traffic Assignment Problem: Models and Methods,", V.S.P. International Science, (1994).

[45]

M. Patriksson and R. T. Rockafellar, A mathematical model and descent algorithm for bilevel traffic management,, Transportation Science, 36 (2002), 271.

[46]

V. Patton, Opportunity NOx,, The Environmental Forum, 18 (2001), 30.

[47]

A. Pigou, "Wealth and Welfare,", Macmillan, (1920).

[48]

A. Rahman and R. V. Grol, "SUMMA Final Publishable Report Version 2.0,", Tech. Report, (2005).

[49]

L. Rilett and C. Benedek, Traffic assignment under environmental and equity objectives,, Transportation Research Record, 1443 (1994), 92.

[50]

J. Rouwendal and E. T. Verhoef, Basic economic principles of road pricing: From theory to applications,, Transport Policy, 13 (2006), 106.

[51]

Y. Sheffi, "Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods,", Prentice Hall, (1985).

[52]

S. Sugawara and D. A. Niemeier, How much can vehicle emissions be reduced? Exploratory analysis of an upper boundary using an emissions-optimized trip assignment,, Transportation Research Record, 1815 (2002), 29.

[53]

L. Sun, Z. Gao and Y. Wang, A Stackelberg game management model of the urban public transport,, Journal of Industrial and Management Optimization, 8 (2012), 507. doi: 10.3934/jimo.2012.8.507.

[54]

G. H. Tzeng and C. H. Chen, Multiobjective decision making for traffic assignment,, IEEE Transactions on Engineering Management, 40 (1993), 180.

[55]

, "World Urbanization Prospects: The 2009 Revision,", Tech. Report, (2009).

[56]

W. S. Vickrey, Congestion theory and transport investment,, American Economic Review, 59 (1969), 251.

[57]

J. G. Wardrop, Some theoretical aspects of road traffic research,, ICE Proceedings: Engineering Divisions, 1 (1952), 325.

[58]

H. Yang and M. G. H. Bell, Models and algorithms for road network design: A review and some new developments,, Transport Reviews: A Transnational Transdisciplinary Journal, 18 (1998), 257.

[59]

H. Yang and Q. Meng, Highway pricing and capacity choice in a road network under a build-operate-transfer scheme,, Transportation Research Part A: Policy and Practice, 34 (2000), 207.

[60]

H. Yang and Q. Meng, A note on highway pricing and capacity choice in a road network under a build-operate-transfer scheme,, Transportation Research Part A: Policy and Practice, 36 (2002), 659.

[61]

Y. Yin and S. Lawphongpanich, Internalizing emission externality on road networks,, Transportation Research Part D: Transport and Environment, 11 (2006), 292.

[62]

H. Zhang and Z. Gao, Bilevel programming model and solution method for mixed transportation network design problem,, Journal of Systems Science and Complexity, 22 (2009), 446. doi: 10.1007/s11424-009-9177-3.

show all references

References:
[1]

M. Abdulaal and L. J. LeBlanc, Continuous equilibrium network design models,, Transportation Research Part B: Methodological, 13 (1979), 19.

[2]

R. Akçelik, "Speed-Flow Models for Uninterrupted Traffic Facilities,", Tech. Report, (2003).

[3]

R. Akçelik, "Speed-Flow and Bunching Relationships for Uninterrupted Flows,", Proceeding of the 5th International Symposium on Highway Capacity and Quality of Service, (2006).

[4]

R. Arnott and K. Small, "The Economics of Traffic Congestion,", Boston College working papers in economics, (1993).

[5]

F. Babonneau and J.-P. Vial, An efficient method to compute traffic assignment problems with elastic demands,, Transportation Science, 42 (2008), 249.

[6]

C. Benedek and L. Rilett, Equitable traffic assignment with environmental cost functions,, Journal of Transportation Engineering, 124 (1998), 16.

[7]

Ş. I. Birbil, G. Gürkan and O. Listeş, Solving stochastic mathematical programs with complementarity constraints using simulation,, Mathematics of Operations Research, 31 (2006), 739. doi: 10.1287/moor.1060.0215.

[8]

, "Traffic Assignment Manual for Application with a Large, High Speed Computer,", U.S. Dept. of Commerce, (1964).

[9]

L. Brotcorne, M. Labbe, P. Marcotte and G. Savard, A bilevel model for toll optimization on a multicommodity transportation network,, Transportation Science, 35 (2001), 345.

[10]

, "Methods to Find the Cost-Effectiveness of Funding Air Quality Projects,", Tech. Report, (2010).

[11]

A. Chen and K. Subprasom, Analysis of regulation and policy of private toll roads in a build-operate-transfer scheme under demand uncertainty,, Transportation Research Part A: Policy and Practice, 41 (2007), 537.

[12]

S.-W. Chiou, Bilevel programming for the continuous transport network design problem,, Transportation Research Part B: Methodological, 39 (2005), 361.

[13]

J. Dargay, D. Gately and M. Sommer, Vehicle ownership and income growth, worldwide: 1960-2030,, The Energy Journal, 28 (2007), 163.

[14]

G. de Ceuster, B. van Herbruggen, O. Ivanova, K. Carlier, A. Martino and D. Fiorello, "TREMOVE - Final Report,", Tech. Report, (2007).

[15]

E. Deakin, "Sustainable Development and Sustainable Transportation: Strategies for Economic Prosperity Environmental Quality and Equity,", Tech. Report 2001'03, (2001).

[16]

S. P. Dirkse and M. C. Ferris, Traffic modeling and variational inequalities using GAMS,, in, (1997), 136.

[17]

A. Drud, CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems,, Mathematical Programming, 31 (1985), 153. doi: 10.1007/BF02591747.

[18]

, "Major Pollutants from Petrol and Diesel Engines,", Tech. Report, (2010).

[19]

, "User's Guide to Mobile 6.1 and Mobile 6.2 - Mobile Source Emission Factor Model,", Environmental Protection Agency, (2003).

[20]

M. C. Ferris, S. P. Dirkse and A. Meeraus, Mathematical programs with equilibrium constraints: Automatic reformulation and solution via constrained optimization,, in, (2005), 67.

[21]

T. L. Friesz, R. L. Tobin, H.-J. Cho and N. J. Mehta, Sensitivity analysis based heuristic algorithms for mathematical programs with variational inequality constraints,, Mathematical Programming, 48 (1990), 265. doi: 10.1007/BF01582259.

[22]

, "GAMS-A User's Guide,", General Algebraic Modeling System, (2010).

[23]

Z. Gao and Y. Song, A reserve capacity model of optimal signal control with user-equilibrium route choice,, Transportation Research: Part B, 36 (2002), 313.

[24]

D. Gkatzoflias, C. Kouridis, L. Ntziachristos and Z. Samaras, "Copert 5 - Computer Programme to Calculate Emissions from Road Transport, User Manual, Version 5.0,", European Environment Agency, (2007).

[25]

S. Gokhale and M. Khare, A review of deterministic, stochastic and hybrid vehicular exhaust emission models,, International Journal of Transport Management, 2 (2004), 59.

[26]

R. L. Guensler and D. Sperling, Congestion pricing and motor vehicle emissions: An initial review,, Transportation Research Board Special Report, 242 (1994), 356.

[27]

E. Gutt, V. Patton and N. Spencer, "Building on 30 Years of Clean Air Act Success: The Case for Reducing NOx Air Pollution,", Tech. Report, (2000).

[28]

D. W. Hearn and M. V. Ramana, Solving congestion toll pricing models,, in, (1998), 109.

[29]

C. M. Jeon and A. Amekudzi, Addressing sustainability in transportation systems: Definitions, indicators, and metrics,, Journal of Infrastructure Systems, 11 (2005), 31.

[30]

O. Johansson-Stenman and T. Sterner, What is the scope for environmental road pricing?,, in, (1998), 150.

[31]

M. Ketzel, P. Louka, P. Sahm, E. Guilloteau, J.-F. Sini and N. Moussiopoulos, Intercomparison of numerical urban dispersion models: Part I & II,, Water, 2 (2002), 603.

[32]

F. H. Knight, Some fallacies in the interpretation of social cost,, The Quarterly Journal of Economics, 38 (1924), 582.

[33]

M. Labbe, P. Marcotte and G. Savard, A bilevel model of taxation and its application to optimal highway pricing,, Management Science, 44 (1998), 1608.

[34]

S. Lawphongpanich and D. W. Hearn, An MPEC approach to second-best toll pricing,, Mathematical Programming, 101 (2004), 33. doi: 10.1007/s10107-004-0536-5.

[35]

T. Litman, "Well Measured: Developing Indicators for Sustainable and Livable Transport Planning,", Tech. Report, (2010).

[36]

T. Litman and D. Burwell, Issues in sustainable transportation,, International Journal of Global Environmental Issues, 6 (2006), 331.

[37]

Z.-Q. Luo, J.-S. Pang, and D. Ralph, "Mathematical Programs with Equilibrium Constraints,", Cambridge University Press, (1996). doi: 10.1017/CBO9780511983658.

[38]

D. R. Lynam and G. D. Pfeifer, Human health effects of highway-related pollutants,, in, 44 (1991), 259.

[39]

T. L. Magnanti and R. T. Wong, Network Design and Transportation Planning: Models and Algorithms,, Transportation Science, 18 (1984), 1.

[40]

P. Marcotte, Network design problem with congestion effects: A case of bilevel programming,, Mathematical Programming, 34 (1986), 142. doi: 10.1007/BF01580580.

[41]

A. Nagurney, Congested urban transportation networks and emission paradoxes,, Transportation Research Part D: Transport and Environment, 5 (2000), 145.

[42]

A. Nagurney, "Sustainable Transportation Networks,", Edward Elgar Publishing, (2000).

[43]

A. Nagurney, Paradoxes in networks with zero emission links: Implications for telecommunications versus transportation,, Transportation Research Part D: Transport and Environment, 6 (2001), 283.

[44]

M. Patriksson, "The Traffic Assignment Problem: Models and Methods,", V.S.P. International Science, (1994).

[45]

M. Patriksson and R. T. Rockafellar, A mathematical model and descent algorithm for bilevel traffic management,, Transportation Science, 36 (2002), 271.

[46]

V. Patton, Opportunity NOx,, The Environmental Forum, 18 (2001), 30.

[47]

A. Pigou, "Wealth and Welfare,", Macmillan, (1920).

[48]

A. Rahman and R. V. Grol, "SUMMA Final Publishable Report Version 2.0,", Tech. Report, (2005).

[49]

L. Rilett and C. Benedek, Traffic assignment under environmental and equity objectives,, Transportation Research Record, 1443 (1994), 92.

[50]

J. Rouwendal and E. T. Verhoef, Basic economic principles of road pricing: From theory to applications,, Transport Policy, 13 (2006), 106.

[51]

Y. Sheffi, "Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods,", Prentice Hall, (1985).

[52]

S. Sugawara and D. A. Niemeier, How much can vehicle emissions be reduced? Exploratory analysis of an upper boundary using an emissions-optimized trip assignment,, Transportation Research Record, 1815 (2002), 29.

[53]

L. Sun, Z. Gao and Y. Wang, A Stackelberg game management model of the urban public transport,, Journal of Industrial and Management Optimization, 8 (2012), 507. doi: 10.3934/jimo.2012.8.507.

[54]

G. H. Tzeng and C. H. Chen, Multiobjective decision making for traffic assignment,, IEEE Transactions on Engineering Management, 40 (1993), 180.

[55]

, "World Urbanization Prospects: The 2009 Revision,", Tech. Report, (2009).

[56]

W. S. Vickrey, Congestion theory and transport investment,, American Economic Review, 59 (1969), 251.

[57]

J. G. Wardrop, Some theoretical aspects of road traffic research,, ICE Proceedings: Engineering Divisions, 1 (1952), 325.

[58]

H. Yang and M. G. H. Bell, Models and algorithms for road network design: A review and some new developments,, Transport Reviews: A Transnational Transdisciplinary Journal, 18 (1998), 257.

[59]

H. Yang and Q. Meng, Highway pricing and capacity choice in a road network under a build-operate-transfer scheme,, Transportation Research Part A: Policy and Practice, 34 (2000), 207.

[60]

H. Yang and Q. Meng, A note on highway pricing and capacity choice in a road network under a build-operate-transfer scheme,, Transportation Research Part A: Policy and Practice, 36 (2002), 659.

[61]

Y. Yin and S. Lawphongpanich, Internalizing emission externality on road networks,, Transportation Research Part D: Transport and Environment, 11 (2006), 292.

[62]

H. Zhang and Z. Gao, Bilevel programming model and solution method for mixed transportation network design problem,, Journal of Systems Science and Complexity, 22 (2009), 446. doi: 10.1007/s11424-009-9177-3.

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