##
**Stochastic congestion pricing among multiple regions: competition and cooperation.**
*(English)*
Zbl 1266.90065

Summary: Previous studies of road congestion pricing problem assume that transportation networks are managed by a central administrative authority with an objective of improving the performance of the whole network. In practice, a transportation network may be comprised of multiple independent local regions with relative independent objectives. In this paper, we investigate the cooperative and competitive behaviors among multiple regions in congestion pricing considering stochastic conditions; especially demand uncertainty is taken into account in transportation modelling. The corresponding congestion pricing models are formulated as a bilevel programming problem. In the upper level, congestion pricing model either aims to maximize the regional social welfare in competitive schemes or attempts to maximize the total social welfare of multiple regions in cooperative schemes. In the lower level, travellers are assumed to follow a reliability-based stochastic user equilibrium principle considering risks of late arrival under uncertain conditions. Numerical examples are carried out to compare the effects of different pricing schemes and to analyze the impact of travel time reliability. It is found that cooperative pricing strategy performs better than competitive strategy in improving network performance, and the pricing effects of both schemes are quite sensitive to travel time reliability.

### MSC:

90B20 | Traffic problems in operations research |

### Software:

fminsearch
PDF
BibTeX
XML
Cite

\textit{H. Wang} et al., J. Appl. Math. 2013, Article ID 696481, 11 p. (2013; Zbl 1266.90065)

Full Text:
DOI

### References:

[1] | H. Yang and H. J. Huang, Mathematical and Economic Theory of Road Pricing, Elsevier, 2005. |

[2] | H. Yang and X. Zhang, “Multiclass network toll design problem with social and spatial equity constraints,” Journal of Transportation Engineering, vol. 128, no. 5, pp. 420-428, 2002. |

[3] | H. Yang and X. Zhang, “Optimal toll design in second-best link-based congestion pricing,” Transportation Research Record, no. 1857, pp. 85-92, 2003. |

[4] | H. Yang, X. Zhang, and Q. Meng, “Modeling private highways in networks with entry-exit based toll charges,” Transportation Research Part B, vol. 38, no. 3, pp. 191-213, 2004. |

[5] | X. Zhang and H. Yang, “The optimal cordon-based network congestion pricing problem,” Transportation Research Part B, vol. 38, no. 6, pp. 517-537, 2004. |

[6] | X. Zhang, H. J. Huang, and H. M. Zhang, “Integrated daily commuting patterns and optimal road tolls and parking fees in a linear city,” Transportation Research Part B, vol. 42, no. 1, pp. 38-56, 2008. |

[7] | X. Zhang, H. Yang, and H. J. Huang, “Multiclass multicriteria mixed equilibrium on networks and uniform link tolls for system optimum,” European Journal of Operational Research, vol. 189, no. 1, pp. 146-158, 2008. · Zbl 1152.91644 |

[8] | X. Zhang and B. van Wee, “Enhancing transportation network capacity by congestion pricing with simultaneous toll location and toll level optimization,” Engineering Optimization, vol. 44, no. 4, pp. 477-488, 2012. |

[9] | X. N. Zhang, H. M. Zhang, H. J. Huang, L. J. Sun, and T. Q. Tang, “Competitive, cooperative and Stackelberg congestion pricing for multiple regions in transportation networks,” Transportmetrica, vol. 7, no. 4, pp. 297-320, 2011. |

[10] | X. Zhang and B. van Wee, “Efficiency comparison of various parking charge schemes considering daily travel cost in a linear city,” European Journal of Transport and Infrastructure Research, vol. 11, no. 2, pp. 234-255, 2011. |

[11] | X. N. Zhang, H. Yang, and H. J. Huang, “Improving travel efficiency by parking permits distribution and trading,” Transportation Research Part B, vol. 45, no. 7, pp. 1018-1034, 2011. |

[12] | A. De Palma and R. Lindsey, “Private toll roads: competition under various ownership regimes,” Annals of Regional Science, vol. 34, no. 1, pp. 13-35, 2000. |

[13] | B. Ubbels and E. T. Verhoef, “Governmental competition in road charging and capacity choice,” Regional Science and Urban Economics, vol. 38, no. 2, pp. 174-190, 2008. |

[14] | A. Yuen, L. J. Basso, and A. Zhang, “Effects of gateway congestion pricing on optimal road pricing and hinterland,” Journal of Transport Economics and Policy, vol. 42, no. 3, pp. 495-526, 2008. |

[15] | A. Sumalee and W. Xu, “First-best marginal cost toll for a traffic network with stochastic demand,” Transportation Research Part B, vol. 45, no. 1, pp. 41-59, 2011. |

[16] | A. C. Pigou, The Economics of Welfare, MacMillan, London, UK, 1920. |

[17] | F. H. Knight, “Some fallacies in the interpretation of social costs,” Quarterly Journal of Economics, vol. 38, pp. 582-606, 1924. |

[18] | H. Yang and H. J. Huang, “Principle of marginal-cost pricing: how does it work in a general road network?” Transportation Research Part A, vol. 32, no. 1, pp. 45-54, 1998. |

[19] | H. Yang, “System optimum, stochastic user equilibrium, and optimal link tolls,” Transportation Science, vol. 33, no. 4, pp. 354-360, 1999. · Zbl 0960.90009 |

[20] | S. T. Waller and A. K. Ziliaskopoulos, “Stochastic dynamic network design problem,” Transportation Research Record, no. 1771, pp. 106-113, 2001. |

[21] | G. R. Patil and S. V. Ukkusuri, “System-optimal stochastic transportation network design,” Transportation Research Record, no. 2029, pp. 80-86, 2007. |

[22] | A. Chen, Z. Ji, and W. Recker, “Travel time reliability with risk-sensitive travelers,” Transportation Research Record, no. 1783, pp. 27-33, 2002. |

[23] | S. Nakayama and J. Takayama, “A traffic network equilibrium model for uncertain demands,” in Proceedings of the 82nd Transportation Research Board Annual Meeting, 2003. |

[24] | S. Clark and D. Watling, “Modelling network travel time reliability under stochastic demand,” Transportation Research Part B, vol. 39, no. 2, pp. 119-140, 2005. |

[25] | H. Shao, W. H. K. Lam, Q. Meng, and M. L. Tam, “Demand-driven traffic assignment problem based on travel time reliability,” Transportation Research Record, no. 1985, pp. 220-230, 2006. |

[26] | H. Shao, W. H. K. Lam, and M. L. Tam, “A reliability-based stochastic traffic assignment model for network with multiple user classes under uncertainty in demand,” Networks and Spatial Economics, vol. 6, no. 3-4, pp. 173-204, 2006. · Zbl 1138.90358 |

[27] | W. H. K. Lam, H. Shao, and A. Sumalee, “Modeling impacts of adverse weather conditions on a road network with uncertainties in demand and supply,” Transportation Research Part B, vol. 42, no. 10, pp. 890-910, 2008. |

[28] | B. Y. Chen, W. H. K. Lam, A. Sumalee, and H. Shao, “An efficient solution algorithm for solving multi-class reliability-based traffic assignment problem,” Mathematical and Computer Modelling, vol. 54, no. 5-6, pp. 1428-1439, 2011. · Zbl 1228.90024 |

[29] | H. Li, M. C. J. Bliemer, and P. H. L. Bovy, “Network reliability-based optimal toll design,” Journal of Advanced Transportation, vol. 42, no. 3, pp. 311-332, 2008. |

[30] | S. D. Boyles, K. M. Kockelman, and S. T. Waller, “Congestion pricing under operational, supply-side uncertainty,” Transportation Research Part C, vol. 18, no. 4, pp. 519-535, 2010. |

[31] | L. M. Gardner, S. D. Boyles, and S. T. Waller, “Quantifying the benefit of responsive pricing and travel information in the stochastic congestion pricing problem,” Transportation Research Part A, vol. 45, no. 3, pp. 202-218, 2011. |

[32] | R. W. Hall, “Travel outcome and performance: the effect of uncertainty on accessibility,” Transportation Research Part B, vol. 17, no. 4, pp. 275-290, 1983. |

[33] | Y. Sheffi, Urban Transportation Networks: Equilibrium Analysis with Mathematical Programming Methods, Prentice Hall, Englewood Cliff, NJ, USA, 1985. |

[34] | J. C. Lagarias, J. A. Reeds, M. H. Wright, and P. E. Wright, “Convergence properties of the Nelder-Mead simplex method in low dimensions,” SIAM Journal on Optimization, vol. 9, no. 1, pp. 112-147, 1999. · Zbl 1005.90056 |

[35] | V. Torczon, “On the convergence of pattern search algorithms,” SIAM Journal on Optimization, vol. 7, no. 1, pp. 1-25, 1997. · Zbl 0884.65053 |

[36] | C. Audet and J. E. Dennis, “Analysis of generalized pattern searches,” SIAM Journal on Optimization, vol. 13, no. 3, pp. 889-903, 2003. · Zbl 1053.90118 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.