Cluster Computing

, Volume 20, Issue 4, pp 3023–3036 | Cite as

The model and algorithm of distributing cooperation profits among operators of urban rail transit under PPP pattern

  • Li JiaEmail author
  • Dingyou Lei
  • Yinggui ZhangEmail author
  • Qiongfang Zeng
  • Juan Wang


The financing channels, investors and operators of urban rail transit are becoming more and more diversified, and public private partnership pattern has been increasingly suggested in financing and investment field of urban rail transit in China. The diversification of investors of urban rail transit will no doubt lead to the diversification of operators of urban rail transit network. To legitimately distribute the cooperation profits among operators, a model is developed based on passenger’s path choice behavior by considering travel period, travel time, transfer convenience and the comprehensive proportion of different service types provided by operators. In accordance with the features of urban rail transit network and origin-destination (OD) pairs of transferring among lines of different operators, a scheme of improved rail transit network is proposed. On the basis of the algorithm of breadth-first search and depth-first search, an algorithm of searching effective paths based on backtracking and traversing along the shortest path is established by considering the factor of transfer. Taking the example of Shenzhen’s rail transit network, three typical OD pairs are selected to measure and calculate, compare and analyze by six different conditions. The result shows that travel period, travel time, transfer convenience, and service types provided by operators exert great influence on the distribution of cooperation profits. Therefore, it is advisable to comprehensively consider all of these factors to improve the accuracy of cooperation profits distribution. Moreover, the proposed algorithm can search effective paths efficiently.


Urban rail transit PPP pattern Cooperation profits distribution Passenger’s path choice behavior Improvement of rail transit network Effective path search 


  1. 1.
    Carbonara, N., Costantino, N., Pellegrino, R.: Concession period for PPPs: a win-win model for a fair risk sharing. Int. J. Proj. Manag. 32(7), 1223–1232 (2014)CrossRefGoogle Scholar
  2. 2.
    Tang, L., Shen, Q.: Factors affecting effectiveness and efficiency of analyzing stakeholders’ needs at the briefing stage of public private partnership projects. Int. J. Proj. Manag. 31(4), 513–521 (2013)CrossRefGoogle Scholar
  3. 3.
    Qi, X., Yi, C., Li, J.: The study on the barrier of implementation of PPP project’s assessment system based on VFM in China. Appl. Mech. Mater. 409–410, 1543–1546 (2013)CrossRefGoogle Scholar
  4. 4.
    Javed, A.A., Lam, P.T.I., Chan, A.P.C.: Change negotiation in public-private partnership projects through output specifications: an experimental approach based on game theory. Constr. Manag. Econ. 32(4), 323–348 (2014)CrossRefGoogle Scholar
  5. 5.
    Engel, E., Fischer, R.D., Galetovic, A.: Renegotiation in public-private partnerships: theory and evidence. Int. Transp. Forum Discuss. Pap. 17, 1–24 (2014)Google Scholar
  6. 6.
    Francesconi, M., Muthoo, A.: Control rights in public-private partnerships. IZA Discuss. Pap. 2143, 1–37 (2006)Google Scholar
  7. 7.
    Chan, A.P.C., Yeung, J.F.Y., Yu, C.C.P., Wang, S.Q., Ke, Y.J.: Empirical study of risk assessment and allocation of public-private partnership projects in China. J. Manag. Eng. 27(3), 136–148 (2011)CrossRefGoogle Scholar
  8. 8.
    Ebrahimnejad, S., Mousavi, S.M., Seyrafianpour, H.: Risk identification and assessment for build-operate-transfer projects: a fuzzy multi attribute decision making model. Exp. Syst. Appl. 37(1), 575–586 (2010)CrossRefGoogle Scholar
  9. 9.
    Hwang, B.G., Zhao, X.B., Gay, M.J.S.: Public private partnership projects in Singapore: factors, critical risks and preferred risk allocation from the perspective of contractors. Int. J. Proj. Manag. 31(3), 424–433 (2013)CrossRefGoogle Scholar
  10. 10.
    Macario, R.: Future challenges for transport infrastructure pricing in PPP arrangements. Res. Transp. Econ. 30(1), 145–154 (2010)CrossRefGoogle Scholar
  11. 11.
    Smyth, H., Edkins, A.: Relationship management in the management of PFI/PPP projects in the UK. Int. J. Proj. Manag. 25(3), 232–240 (2007)CrossRefGoogle Scholar
  12. 12.
    Carmona, M.: The regulatory function in public-private partnerships for the provision of transport infrastructure. Res. Transp. Econ. 30(1), 110–125 (2010)CrossRefGoogle Scholar
  13. 13.
    Scharle, P.: Public-private partnership (PPP) as a social game. Innov. Eur. J. Soc. Sci. Res. 15(3), 227–252 (2002)CrossRefGoogle Scholar
  14. 14.
    Lossa, E., Martimort, D.: Risk allocation and the costs and benefits of public-private partnerships. RAND J. Econ. 43(3), 442–474 (2012)CrossRefGoogle Scholar
  15. 15.
    Shi, F., Zhou, Z., Yao, J., Huang, H.L.: Incorporating transfer reliability into equilibrium analysis of railway passenger flow. Eur. J. Oper. Res. 220(2012), 378–385 (2012)CrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Hung, R., Jiang, Y.K., Liu, Z.L., Yang, Y.Z., Jiang, W.: Algorithm and implementation of urban rail transit network based on joint operation. J. Transp. Syst. Eng. Inf. Technol. 10(2), 130–135 (2010)Google Scholar
  17. 17.
    Si, B.F., Zhong, M., Liu, J.F., Gao, Z.Y., Wu, J.J.: Development of a transfer-cost-based Logit assignment model for the Beijing rail transit network using automated fare collection data. J. Adv. Transp. 47(3), 297–318 (2013)CrossRefGoogle Scholar
  18. 18.
    Kusakabe, T., Iryo, T., Asakura, Y.: Estimation method for railway passengers’ train choice behavior with smart card transaction data. Transportation 37(5), 731–749 (2010)CrossRefGoogle Scholar
  19. 19.
    Guo, Z., Wilson, N.H.M.: Assessment of the transfer penalty for transit trips: a geographic information system-based disaggregate modeling approach. Transp. Res. Rec. 1872(2004), 10–18 (2004)Google Scholar
  20. 20.
    Guo, Z., Wilson, N.H.M.: Modeling effects of transit system transfers on travel behavior: case of commuter rail and subway in Downtown Boston, Massachusetts. Transp. Res. Rec. 2006(2007), 11–20 (2007)CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of Traffic and Transportation EngineeringCentral South UniversityChangshaChina

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