Journal of Applied Mathematics

The Optimal Taxi Fleet Size Structure under Various Market Regimes When Charging Taxis with Link-Based Toll

Jincheng Zhu, Bin Shuai, Zhengfeng Huang, and Chaoyuan Sun

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

This paper investigates the optimal taxi fleet size structure under monopoly and oligopoly market regimes when taxis are charged with the link-based toll. We proposed a bilevel programming model to take account of the interaction between taxi fleet size and different traffic modes in the network. The upper level is to determine the optimal taxi fleet structure so as to maximize the profit of each taxi firm. The lower-level is a combined network equilibrium model (CNEM) representing the travelers’ response to the equilibrium taxi fleet size structure when congestion toll is imposed on taxis. We show that the lower level problem can be formulated as an equivalent variational inequality formulation, which considers the hierarchical logit-based mode split, route choice, elastic demand, and vacant taxi distributions. The bilevel problem can be solved by an iterative heuristic solution algorithm, whereas the lower level model is solved by the block Gauss-Seidel decomposition approach together with method of successive averages. An application with numerical examples is presented to illustrate the effectiveness of the proposed model and algorithm, and some interesting findings are also provided.

Article information

Source
J. Appl. Math. Volume 2013 (2013), Article ID 535878, 11 pages.

Dates
First available in Project Euclid: 14 March 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1394808267

Digital Object Identifier
doi:10.1155/2013/535878

Citation

Zhu, Jincheng; Shuai, Bin; Huang, Zhengfeng; Sun, Chaoyuan. The Optimal Taxi Fleet Size Structure under Various Market Regimes When Charging Taxis with Link-Based Toll. J. Appl. Math. 2013 (2013), Article ID 535878, 11 pages. doi:10.1155/2013/535878. https://projecteuclid.org/euclid.jam/1394808267


Export citation

References

  • A. C. Pigou, Wealth and Welfare, Macmillan, London, UK, 1920.
  • D. A. King and J. R. Peters, “Slow down, you move too fast: the use of tolls by taxicabs in New York city,” in Proceedings of the 91st Annual Meeting of the Transportation Research Board, (Compendium of Papers, CD-ROM), 2012.
  • R. D. Cairns and C. Liston-Heyes, “Competition and regulation in the taxi industry,” Journal of Public Economics, vol. 59, no. 1, pp. 1–15, 1996.
  • H. Yang and S. C. Wong, “A network model of urban taxi services,” Transportation Research B, vol. 32, no. 4, pp. 235–246, 1998.
  • S. C. Wong and H. Yang, “Network model of urban taxi services: improved algorithm,” Transportation Research Record, no. 1623, pp. 27–30, 1998.
  • H. Yang, Y. W. Lau, S. C. Wong, and H. K. Lo, “A macroscopic taxi model for passenger demand, taxi utilization and level of services,” Transportation, vol. 27, no. 3, pp. 317–340, 2000.
  • J. M. Xu, S. C. Wong, H. Yang, and C. O. Tong, “Modeling level of urban taxi services using neural network,” Journal of Transportation Engineering, vol. 125, no. 3, pp. 216–223, 1999.
  • K. I. Wong, S. C. Wong, and H. Yang, “Modeling urban taxi services in congested road networks with elastic demand,” Transportation Research B, vol. 35, no. 9, pp. 819–842, 2001.
  • H. Yang, S. C. Wong, and K. I. Wong, “Demand-supply equilibrium of taxi services in a network under competition and regulation,” Transportation Research B, vol. 36, no. 9, pp. 799–819, 2002.
  • H. Yang, M. Ye, W. H. Tang, and S. C. Wong, “Regulating taxi services in the presence of congestion externality,” Transportation Research A, vol. 39, no. 1, pp. 17–40, 2005.
  • K. I. Wong, S. C. Wong, H. Yang, and J. H. Wu, “Modeling urban taxi services with multiple user classes and vehicle modes,” Transportation Research B, vol. 42, no. 10, pp. 985–1007, 2008.
  • R. Shi and Z. Li, “Pricing of multimodal transportation networks under different market regimes,” Journal of Transportation Systems Engineering and Information Technology, vol. 10, no. 5, pp. 91–97, 2010.
  • J. D. Ortuzar and L. G. Willumsen, Modeling Transport, John Wiley & Sons, New York, NY, USA, 2nd edition, 1996.
  • E. Cavazzuti, M. Pappalardo, and M. Passacantando, “Nash equilibria, variational inequalities, and dynamical systems,” Journal of Optimization Theory and Applications, vol. 114, no. 3, pp. 491–506, 2002.
  • M. Florian, J. H. Wu, and S. He, “A multi-class multi-mode variable demand network equilibrium model with hierarchical logit structures,” in Transportation and Network Analysis: Current Trends–-Miscellanea in Honor of Michael Florian, P. Marcotte and M. Gendreau, Eds., vol. 63 of Applied Optimization, pp. 119–133, Kluwer Academic, London, UK, 2002.
  • P. T. Harker, “A variational inequality approach for the determination of oligopolistic market equilibrium,” Mathematical Programming, vol. 30, no. 1, pp. 105–111, 1984.
  • J. Zhou, W. H. K. Lam, and B. G. Heydecker, “The generalized Nash equilibrium model for oligopolistic transit market with elastic demand,” Transportation Research B, vol. 39, no. 6, pp. 519–544, 2005.
  • J. C. Zhu, F. Xiao, and X. B. Liu, “Taxis in road pricing zone: should they pay the congestion charge?” submitted to Journal of Advanced Transportation.
  • H. J. Huang, “Pricing and logit-based mode choice models of a transit and highway system with elastic demand,” European Journal of Operational Research, vol. 140, no. 3, pp. 562–570, 2002. \endinput