Traffic&Transportation Journal
Sign In / Sign Up


Over-supply in Public Transportation: Case Study of Bus and Metro Lines in Harbin City, China
Shumin Feng, Xianghao Shen, Baoyu Hu
Keywords:public transportation, supply competition, Nash equilibrium, over-supply, game theory, China,


As the two most important modes in public transportation, the coordinated development of bus and metro networks significantly influences the efficiency of public transportation. However, two parallel bus and metro lines belonging to different operators may lead to supply competition and consequently yield over-supply. Taking two parallel bus and metro lines in Harbin city, China as a case study, this paper, drawing on game theory, establishes a utility model based on the two lines’ frequencies, and reveals and explains the fundamental reason for the over-supply problem using a Nash equilibrium. In an attempt to resolve this issue, the study proposes a new operation mode: integrating frequencies of the two modes to obtain larger total profits then reallocating the total profits to the two modes. The case study shows that this new operation mode can effectively solve the over-supply problem while satisfying both operators of the two modes, and hence having practical value.


China Association of Metros. Urban metro annual statistical analysis report; 2014. Available from:

Sun Y, Sun X, Kong Q, Song R, He S. Methodology of bus network optimization and adjustment under operation of new urban rail transit line [in Chinese]. Journal of the China Railway Society. 2014;36(3):1-8.

Chen X, Lin G, Yu L. Modeling operation scheduling coordination between urban rail system and bus system [in Chinese]. Systems Engineering-Theory & Practice. 2009;29(10):165-173.

Chen J. Research on urban rail transit and bus prices coordination [MS thesis] [in Chinese]. Harbin, China: Harbin Institute of Technology; 2010.

Jin JG, Tang CL, Sun L, Lee D. Enhancing metro network resilience via localized integration with bus service. Transportation Res E-Log. 2014;63:17-30.

Ma C, Wang Y, Chen K. Competition model between urban rail and bus transit [in Chinese]. J Transp Syst Eng Inf Technol. 2007;7(3):140-145.

Van der Weijde AH, Verhoef ET, van den Berg VAC. Competition in multi-modal transport networks: a dynamic approach. Transport Res B-Meth. 2013;53:31-44.

Hu X. Research on participators’ economic decision-making model of urban passenger transportation system [PhD thesis] [in Chinese]. Harbin, China: Harbin Institute of Technology; 2013. p. 63-80.

Li L. Study of competitive theory and method of urban rail transit passenger flow [PhD thesis] [in Chinese]. Wuxi, China: Jiangsu University; 2012. p. 63-92.

Wu G, Lv ZZhouyang L. Principles and application of game theory [in Chinese]. 1st ed. Nanjing, China: Southeast University Press; 2009. p. 22-59.

Soora R, Harry T. Applications of theories and models of choice and decision-making under conditions of uncertainty in travel behavior research. Travel Behaviour and Society. 2014;1(9):79-90.

Copyright (c) 2023 Shumin Feng, Xianghao Shen, Baoyu Hu

Published by
University of Zagreb, Faculty of Transport and Traffic Sciences
Online ISSN
Print ISSN
SCImago Journal & Country Rank
Publons logo
© Traffic&Transportation Journal