Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
권호 표지

First- and Second-best Pricing in Stable Dynamic Models

안정동력학 모형에서 최선 통행료 및 차선 통행료

  • 박구현 (홍익대학교 산업공학과)
  • Published : 2009.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

This study examined the first- and second-best pricing by stable dynamics in congested transportation networks. Stable dynamics, suggested by Nesterov and de Palma (2003), is a new model which describes and provides a stable state of congestion in urban transportation networks. The first-best pricing in user equilibrium models introduces user-equilibrium in the system-equilibrium by tolling the difference between the marginal social cost and the marginal private cost on each link. Nevertheless, the second-best pricing, which levies the toll on some, but not all, links, is relevant from the practical point of view. In comparison with the user equilibrium model, the stable dynamic model provides a solution equivalent to system-equilibrium if it is focused on link flows. Therefore the toll interval on each link, which keeps up the system-equilibrium, is more meaningful than the first-best pricing. In addition, the second-best pricing in stable dynamic models is the same as the first-best pricing since the toll interval is separately given by each link. As an effect of congestion pricing in stable dynamic models, we can remove the inefficiency of the network with inefficient Braess links by levying a toll on the Braess link. We present a numerical example applied to the network with 6 nodes and 9 links, including 2 Braess links.

Keywords

References

  1. 권용석, 박창호, '통행료체계에서의 경로기반 통행배정모형 개발', '대한교통학회지', 제18권, 제6호(2000), pp.77-88
  2. 김병관, 임용택, 임강원, '민감도 분석을 이용한 혼잡통행료 산정 모형 개발', '대한교통학회지', 제22권, 제5호(2004), pp.139-149
  3. 문용주, '일반균형에서 최적 혼잡통행료', '대한교통학회지', 제18권, 제2호(2000), pp.91-101
  4. 박구현, '교통망에서 다차종 통행을 고려하는 통행배정모형 수립', '한국경영과학회지', 제32권, 제3호(2007), pp.63-80
  5. 박구현, '안정동력학에 의한 가변수요 통행배정 모형', '한국경영과학회지', 제34권, 제1호(2009), pp.61-83
  6. 임용택, 김병관, '혼잡통행료 산정모형의 개발 및 계층간 형평성 연구', '대한교통학회지', 제25권, 제5호(2007), pp.183-193
  7. 황기연, 김익기, 이우철, '교통수요관리 정책의 효과분석을 위한 다항로짓 모형의 적용' '대한교통학회지', 제16권, 제4호(1998), pp.53-63
  8. Daganzo, C.F. and Y. Sheffi, 'On stochastic models of traffic assignment,' Transportation Science, Vol.11, No.3(1977), pp.253-274 https://doi.org/10.1287/trsc.11.3.253
  9. Dial, R.B., 'A model and algorithm for multicriteria route-mode choice,' Transportation Research B, Vol.13(1979), pp.311-316 https://doi.org/10.1016/0191-2615(79)90024-9
  10. Leurent, F., 'Cost versus time equilibrium over a network,' European Journal of Operational Research, Vol.71, No.2(1993), pp.205-221 https://doi.org/10.1016/0377-2217(93)90049-S
  11. Hensher, D.A. and T.P. Truong, 'Valuation of travel savings,' Journal of Transport Economics and Policy, (1985), pp.237-260
  12. Gabriel, S.A. and D. Bernstein, 'The traffic equilibrium problem with nonadditive path costs,' Transportation Science, Vol.31(1997), pp.337-348 https://doi.org/10.1287/trsc.31.4.337
  13. Larsson, T., P.O. Lindberg, M. Patriksson, and C. Rydergren, 'On traffic equilibrium models with a nonlinear time/money relation,' Chapter 2 of Transportation Planning, Applied Optimization, Vol.64(2002), pp.19-31 https://doi.org/10.1007/b101966
  14. Nesterov, Y. and A. de Palma, 'Stationary dynamic solutions in congested transportation networks : Summary and perspectives,' Networks and Spatial Economics, Vol.3(2003), pp.371-395 https://doi.org/10.1023/A:1025350419398
  15. Nesterov, Y. and A. de Palma, 'Park and ride for the day period and morning-evening commute,' Mathematical and Computational Models for Congestion Charging, Applied Optimization 101, Springer US, (2006), pp.143-157
  16. Park, K., 'Detecting Braess paradox based on stable dynamics in general congested transportation networks,' Networks and Spatial Economics, (2009), doi : 10.1007/s11007-009-9101-3
  17. Sheffi, Y., Urban Transportation Networks : Equilibrium Analysis with Mathematical Programming Methods, Prentice-Hall, Inc., Englewood Cliffs, (1985), New Jersey
  18. Yang, H. and H.-J. Huang, 'Principle of marginal-cost pricing: How does it work in a general road network',' Transportation Re-search A, Vol.32, No.1(1998), pp.45-54 https://doi.org/10.1016/S0965-8564(97)00018-9
  19. Yang, H. and H. -J. Huang, Mathematical and Economic Theory of Road Pricing, Elsevier, Amsterdam, 2005