The Theory of Transit Assignment: Demand and Supply Phenomena

  • Guido GentileEmail author
  • Klaus Noekel
  • Jan-Dirk Schmöcker
  • Valentina Trozzi
  • Ektoras Chandakas
Part of the Springer Tracts on Transportation and Traffic book series (STTT)


This chapter addresses the modelling of various demand and supply phenomena emerging on public transport networks: passenger information, congestion at stops and on board, and service regularity.


  1. Aashtiani H, Iravani H (2002) Applications of dwell time function in transit assignment model. Transp Res Record 1887, Paper 02-3498Google Scholar
  2. Abkowitz M, Tozzi J (1987) Research contributions to managing transit service reliability. J Adv Transp 21:47–65CrossRefGoogle Scholar
  3. Adebisi O (1986) A mathematical model for headway variance of fixed-route buses. Transp Res B 20:59–70CrossRefGoogle Scholar
  4. Arentze TA (2013) Adaptive, personalized travel information systems: A Bayesian method to learn users’ personal preferences in multi-modal transport networks. IEEE Trans Intell Transp Syst 14:1957–1966CrossRefGoogle Scholar
  5. Asakura Y (1996) Reliability measures of an origin and destination pair in a deteriorated road network with variable flows. In: Bell MGH (ed) Transportation networks: recent methodological advances. Pergamon Press, Oxford, pp 273–288Google Scholar
  6. Babaei M, Schmocker J-D, Shariat-Mohaymany A (2014) The impact of irregular headways on seat availability. Transportmetrica A 10:483–501CrossRefGoogle Scholar
  7. Babazadeh A, Aashtiani ZH (2005) Algorithm for equilibrium transit assignment problem. Transp Res Rec 1923:227–235CrossRefGoogle Scholar
  8. Beckmann M, McGuire C, Winston C (1956) Studies in the economics of transportation. Yale University Press, New Haven, ConnecticutGoogle Scholar
  9. Bell MGH (1995) Stochastic user equilibrium assignment in networks with queues. Transp Res B 29:125–137CrossRefGoogle Scholar
  10. Bell MGH, Schmocker J-D (2004) A solution to the congested transit assignment problem. In: Wilson NHM, Nuzzolo A (eds) Scheduled-based dynamic transit modeling: theory and applications. Springer, New York, pp 263–280Google Scholar
  11. Bellei G, Gkoumas K (2010) Transit vehicles’ headway distribution and service irregularity. Public Transport 2:269–289CrossRefGoogle Scholar
  12. Bellei G, Gentile G, Papola N (2000) Transit assignment with variable frequencies and congestion effects. In: Proceedings of the 8th meeting of the EURO working group on transportation, Rome, ItalyGoogle Scholar
  13. Bertsekas DP (1999) Nonlinear programming, 2nd edn. Athena Scientific, Belmont, MAzbMATHGoogle Scholar
  14. Billi C, Gentile G, Nguyen S, Pallottino S (2004) Rethinking the wait model at transit stops. In: Proceedings of TRISTAN V, Guadeloupe, French West Indies. Also in Proceedings of MTIT 2003, Reggio Calabria, ItalyGoogle Scholar
  15. Bouzaiene-Ayari B, Gendreau M, Nguyen S (1998) Passenger assignment in congested transit networks: a historical perspective. In: Marcotte P, Nguyen S (eds) Equilibrium and advanced transportation modelling. Kluwer Academic Publishers, pp. 304–321Google Scholar
  16. Bouzaıene-Ayari B, Gendreau M, Nguyen S (2001) Modelling bus stops in transit networks: a survey and new formulations. Transp Sci 35:304–321CrossRefzbMATHGoogle Scholar
  17. Bowman LA, Turnquist MA (1981) Service frequency, schedule reliability and passenger wait times at transit stops. Transp Res A 15:465–471CrossRefGoogle Scholar
  18. Carey M (1999) Ax ante heuristic measures of schedule reliability. Transp Res B 33:473–494CrossRefMathSciNetGoogle Scholar
  19. Carraresi P, Malucelli F, Pallottino S (1996) Regional mass transit assignment with resource constraints. Transp Res B 30:81–89CrossRefGoogle Scholar
  20. Cats O (2011) Dynamic modeling of transit operations and passenger decisions. PhD Thesis, KTH Royal Institute of Technology, Stockholm, SwedenGoogle Scholar
  21. Ceder A (2007) Public transit planning and operation: theory, modeling and practice. Butterworth-Heinemann, OxfordGoogle Scholar
  22. Cepeda M, Cominetti R, Florian M (2006) A frequency-based assignment model for congested transit networks with strict capacity constraints: characterization and computation of equilibria. Transp Res B 40:437–459CrossRefGoogle Scholar
  23. Chen X, Yu L, Zhang Y, Guo J (2009) Analyzing urban bus reliability at the stop, route and network levels. Transp Res A 43:722–734Google Scholar
  24. Cicerone S, D’Angelo G, Di Stefano G, Frigioni D, Navarra A, Schachtebeck M, Schöbel A (2009) Recoverable robustness in shunting and timetabling. In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization: models and techniques for transportation systems, Lecture Notes in Computer Science, pp 28–60Google Scholar
  25. Cominetti R, Correa J (2001) Common lines and passenger assignment in congested transit networks. Transp Sci 35:250–267CrossRefzbMATHGoogle Scholar
  26. Constantin I, Florian D (2015) Integrated fare modelling with strategy-based transit assignment. In: Proceedings of CASPT15, RotterdamGoogle Scholar
  27. Cortés CE, Jara-Moroni P, Moreno E, Pineda C (2013) Stochastic transit equilibrium. Transp Res B 51:29–44CrossRefGoogle Scholar
  28. Crisalli U, Rosati L (2005) Transit services and user information: an application of schedule-based path choice and assignment models. In: Proceedings of European Transportation Forum 2005, StrasbourgGoogle Scholar
  29. De Cea J, Fernandez JE (1993) Transit assignment for congested public transport systems: an equilibrium model. Transp Sci 27:133–147CrossRefzbMATHGoogle Scholar
  30. Dewilde T, Sels P, Cattrysse D, Vansteenwegen P (2011) Defining robustness of a railway timetable. In: Proceedings of 4th international seminar on railway operations modelling and analysis, Rome, Italy, pp 1–20Google Scholar
  31. Dewilde T, Sels P, Cattrysse D, Vansteenwegen P (2014) Improving the robustness in railway station areas. Eur J Oper Res 235:276–286CrossRefMathSciNetzbMATHGoogle Scholar
  32. DfT (2007) Model structures and traveller responses for public transport schemes. Transport Analysis Guidance 3.11.1. UK Department for Transport, London, UKGoogle Scholar
  33. Dial R (2006) A path-based user-equilibrium traffic assignment algorithm that obviates path storage and enumeration. Transp Res B 40:917–936CrossRefGoogle Scholar
  34. Dziekan K, Kottenhoff K (2007) Dynamic at-stop real-time information displays for public transport: effects on customers. Transp Res A 41:489–501Google Scholar
  35. El-Geneidy AM, Horning J, Krizek KJ (2011) Analyzing transit service reliability using detailed data from automatic vehicular locator systems. J Adv Transp 45:66–79CrossRefGoogle Scholar
  36. Fernandez R (2011) Experimental study of bus boarding and alighting times. Proceeding of ETC 2011, GlasgowGoogle Scholar
  37. Fernandez R, Zegers P, Weber G, Tyler N (2010) Influence of platform height, door width and fare collection on bus dwell time: laboratory evidence from Santiago de Chile. In: Proceedings of TRB annual meeting, Washington, DCGoogle Scholar
  38. Fritz M (1983) Effect of crowding on light rail passenger boarding times. Transp Res Rec 908:43–50Google Scholar
  39. Garcia R, Marin A (2005) Network equilibrium with combined modes: models and solution algorithms. Transp Res B 39:223–254CrossRefGoogle Scholar
  40. Gendreau M (1984) Une etude approfondie d’un modele d’equilibre pour l’affectation des passagers dans les reseaux de transport en commun. PhD thesis, Departement d’informatique et de recherche operationnelle, Universite de Montreal, CanadaGoogle Scholar
  41. Gentile G (2014) Local user cost equilibrium: a bush-based algorithm for traffic assignment. Transp A 10:15–54Google Scholar
  42. Gentile G, Nguyen S, Pallottino S (2005) Route choice on transit networks with online information at stops. Transp Sci 39, 289–297 (Also in Proceedings of the VI Congresso SIMAI 2002, Chia Laguna, Italy)Google Scholar
  43. Goverde RMP (2005) Punctuality of railway operations and timetable stability analysis. Ph.D. thesis, Delft University of Technology, DelftGoogle Scholar
  44. Hamdouch Y, Lawphongpanich S (2008) Schedule-based transit assignment model with travel strategies and capacity constraints. Transp Res B 42:663–684CrossRefGoogle Scholar
  45. Hamdouch Y, Florian M, Hearn DW, Lawphongpanich S (2007) Congestion pricing for multi-modal transportation systems. Transp Res B 41:275–291CrossRefGoogle Scholar
  46. Harris NG (2005) Train boarding and alighting rates at high passenger loads. J Adv Transp 40:249–263CrossRefGoogle Scholar
  47. Harris NG, Anderson RJ (2007) An international comparison of urban rail boarding and alighting rates. In: Proceedings of the institution of mechanical engineers. Journal of Rail and Rapid Transit 221, 521–526Google Scholar
  48. Hasseltroem D (1981) Public transportation planning—A mathematical programming approach. PhD thesis, Department of Business Administration, University of Gothenburg, SwedenGoogle Scholar
  49. Hickman MD, Wilson NHM (1995) Passenger travel time and path choice implications of real-time transit information. Transp Res C 3:211–226CrossRefGoogle Scholar
  50. Holroyd EM, Scraggs DA (1966) Waiting times for buses in Central London. Traffic Eng Control 8:158–160Google Scholar
  51. Horn MET (2003) An extended model and procedural framework for planning multi-modal passenger journeys. Transp Res B 37:641–660CrossRefGoogle Scholar
  52. Huang R, Peng ZR (2002) Schedule-based path-finding algorithms for transit trip-planning systems. Transp Res Rec 1783:142–148CrossRefGoogle Scholar
  53. Iida Y, Wakabayashi H (1990) An approximation method of terminal reliability of road network using partial minimal path and cut set. In: Proceedings of the 5th WCTR, pp 367–380Google Scholar
  54. Jansson K, Ridderstolpe B (1992) A method for the route-choice problem in public transport systems. Transp Sci 26:246–251CrossRefzbMATHGoogle Scholar
  55. Kato H, Kaneko Y, Inoue M (2010) Comparative analysis of transit assignment: evidence from urban railway system in the Tokyo Metropolitan Area. Transportation 37:775–799CrossRefGoogle Scholar
  56. Kroon L, Maroti G, Retel Helmrich M, Vromans MJCM, Dekker R (2008) Stochastic improvement of cyclic railway timetables. Transp Res B 42:553–570CrossRefGoogle Scholar
  57. Kurauchi F, Bell MGH, Schmöcker J-D (2003) Capacity constrained transit assignment with common lines. J Math Modell Algorithms 2–4:309–327CrossRefGoogle Scholar
  58. Lai YC, Wang SH, Jong JC (2011) Development of analytical capacity models for commuter rail operations with advanced signaling systems. In: Proceedings of the 90th annual meeting of transportation research board, Washington, DCGoogle Scholar
  59. Lam WHK, Gao ZY, Chan KS, Yang N (1999) A stochastic user equilibrium assignment model for congested transit networks. Transp Res B 33:351–368CrossRefGoogle Scholar
  60. Lam WHK, Zhou J, Sheng Z-H (2002) A capacity restraint transit assignment with elastic line frequency. Transp Res B 36:919–938CrossRefGoogle Scholar
  61. Leurent F (2012) On seat capacity in traffic assignment to a transit network. J Adv Transp 46:112–138CrossRefGoogle Scholar
  62. Leurent F, Liu K (2009) On seat congestion, passenger comfort and route choice in urban transit: a network equilibrium assignment model with application to Paris. In: Proceedings of the 88th annual transportation research board meeting, Washington, DCGoogle Scholar
  63. Leurent F, Chandakas E, Poulhes A (2011) User and service equilibrium in a structural model of traffic assignment to a transit network. In: Procedia—social and behavioral sciences 20, Proceedings of EWGT2011, pp 495–505Google Scholar
  64. Leurent F, Chandakas E, Poulhès A (2012) A passenger traffic assignment model with capacity constraints for transit networks. In: Procedia—Social and Behavioral Sciences vol 54, Proceedings of EWGT2012, pp 772–784Google Scholar
  65. Lin T-M, Wilson NHM (1992) Dwell time relationships for light rail systems. Transp Res Rec 1361:287–295Google Scholar
  66. Lo HK, Chen A (2000) Traffic equilibrium problem with route-specific costs: formulation and algorithms. Transp Res B: Methodol 34:493–513CrossRefGoogle Scholar
  67. Lo HK, Yip CW, Wan KH (2003) Modeling transfer and non-linear fare structure in multi-modal network. Transp Res B 37:149–170CrossRefGoogle Scholar
  68. Lo HK, Yip CW, Wan QK (2004) Modeling competitive multi-modal transit services: a nested logit approach. Transp Res C 12:251–272CrossRefGoogle Scholar
  69. Marguier PHJ (1981) Optimal strategies in waiting for common bus lines. Master’s thesis, Department of Civil Engineering, MIT, CambridgeGoogle Scholar
  70. Marguier PHJ, Ceder A (1984) Passenger waiting strategies for overlapping bus route. Transp Sci 18:207–230CrossRefGoogle Scholar
  71. Meschini L, Gentile G, Papola N (2007) A frequency based transit model for dynamic traffic assignment to multimodal networks. In: Allsop R, Bell MGH, Heydecker BG (eds) Proceedings of the 17th international symposium on transportation and traffic theory (ISTTT). Elsevier, London, pp 407–436Google Scholar
  72. Morichi S, Iwakura S, Morishige S, Itoh M, Hayasaki S (2001) Tokyo metropolitan rail network long-range plan for the 21st century. In: Proceedings of the 80th annual meeting of transportation research board, Washington, DCGoogle Scholar
  73. Morosan CD, Florian M (2015) A network model for capped link-based tolls. EURO J Transp Logistics 4:223–236CrossRefGoogle Scholar
  74. Nguyen S, Pallottino S (1988) Equilibrium traffic assignment for large scale transit networks. Eur J Oper Res 37:176–186CrossRefMathSciNetzbMATHGoogle Scholar
  75. Nguyen S, Pallottino S, Gendreau M (1998) Implicit enumeration of hyperpaths in a logit model for transit networks. Transp Sci 32:54–64CrossRefzbMATHGoogle Scholar
  76. Nielsen OA (2000) A stochastic transit assignment model considering differences in passenger utility functions. Transp Res B 34:377–402CrossRefGoogle Scholar
  77. Nielsen OA (2004) A large-scale stochastic multi-class schedule-based transit model with random coefficients. In: Wilson NHM, Nuzzolo A (eds) Schedule-based dynamic transit modeling: theory and applications. Kluwer Academic Publisher, pp 53–78Google Scholar
  78. Noekel K, Wekeck S (2009) Boarding and alighting in frequency-based transit assignment. Transp Res Rec 2111:60–67CrossRefGoogle Scholar
  79. Nuzzolo A, Russo F, Crisalli U (2001) A doubly dynamic schedule-based assignment model for transit networks. Transp Sci 35:268–285CrossRefzbMATHGoogle Scholar
  80. Nuzzolo A, Crisalli U, Rosati L (2012) A schedule-based assignment model with explicit capacity constraints for congested transit networks. Transp Res C 20:16–33CrossRefGoogle Scholar
  81. Nuzzolo A, Crisalli U, Comi A, Rosati L (2013) An advanced pre-trip planner with personalized information on transit networks with ATIS. In: Proceedings of 16th international ieee conference on intelligent transportation systems, The Hague, pp 2146–2151Google Scholar
  82. Okrent MM (1974) Effects of transit service characteristics on passenger waiting time. Master Thesis, Northwestern University, Department of Civil Engineering, Evanston, ILGoogle Scholar
  83. Osuna EE, Newell GF (1972) Control strategies for an idealized public transportation system. Transp Sci 6:52–72CrossRefGoogle Scholar
  84. Owen AD, Phillips GDA (1987) The characteristics of railway passenger demand: an econometric investigation. J Transp Econ Policy 21:231–253Google Scholar
  85. Papola N, Filippi F, Gentile G, Meschini L (2007) Schedule-based transit assignment: a new dynamic equilibrium model with vehicle capacity constraints. In: Wilson NHM, Nuzzolo A (eds) Schedule-based modeling of transportation networks. Theory and applications. Springer, Berlin, pp 145–171Google Scholar
  86. Poon MH, Wong SC, Tong CO (2004) A dynamic schedule-based model for congested transit networks. Transp Res B 38:343–368CrossRefGoogle Scholar
  87. PTV AG (2003) VISUM 9.0 Manual, available from PTV Group, KarlsruheGoogle Scholar
  88. Rajbhandari R, Chien S, Daniel J (2003) Estimation of bus dwell time with automatic passenger counter information. Transp Res Record 1841, 120–127Google Scholar
  89. Ren H, Gao Z, Lam WHK, Long J (2009) Assessing the benefits of integrated en-route transit information systems and time-varying transit pricing systems in a congested transit network. Transp Plann Technol 32:215–237CrossRefGoogle Scholar
  90. Schmöcker J-D, Fonzone A, Shimamoto H, Kurauchi F, Bell MGH (2011) Frequency-based transit assignment considering seat capacities. Transp Res B 45:392–408CrossRefGoogle Scholar
  91. Schmoeker J-D, Bell MGH, Kurauchi F (2008) A quasi-dynamic capacity constrained frequency-based transit assignment model. Transp Res B 42:925–945CrossRefGoogle Scholar
  92. Schobel A, Kratz A (2009) A bicriteria approach for robust timetabling. In: Ahuja RK, Möhring RH, Zaroliagis CD (eds) Robust and online large-scale optimization: models and techniques for transportation systems, Lecture Notes in Computer Science, pp 119–144Google Scholar
  93. Shimamoto H, Kurauchi F, Iida Y (2005) Evaluation on effect of arrival time information provision using transit assignment model. Int J ITS Res 3:11–18Google Scholar
  94. Shimamoto H, Kurauchi F, Schmöcker J-D (2010) Transit assignment model incorporating the bus bunching effect. In: Proceeding of 12th world congress on transport research, Lisbon, PortugalGoogle Scholar
  95. Spiess H, Florian M (1989) Optimal strategies: a new assignment model for transit networks. Transp Res B 23:83–102CrossRefGoogle Scholar
  96. Sumalee A, Tan ZJ, Lam WHK (2009) Dynamic stochastic transit assignment with explicit seat allocation model. Transp Res B 43:895–912CrossRefGoogle Scholar
  97. Szeto WY, Solayappan M, Jiang Y (2011) Reliability-based transit assignment for congested stochastic transit networks. Comput-Aided Civil Infrastruct Eng 26:311–326CrossRefGoogle Scholar
  98. Szplett D, Wirasinghe SC (1984) An investigation of passenger interchange and train standing time at LRT Stations: alighting, boarding and platform distribution of passengers. J Adv Transp 18:1–12CrossRefGoogle Scholar
  99. Teklu F (2008) A stochastic process approach for frequency-based transit assignment with strict capacity constraints. Netw Spatial Econ 8:225–240CrossRefzbMATHGoogle Scholar
  100. Tian Q, Huang H-J, Yang H (2007) Commuting equilibria on a mass transit system with capacity constraints. In: Allsop R, Bell MGH, Heydecker BG (eds) Proceedings of the 17th international symposium on transportation and traffic theory (ISTTT). Elsevier, London, pp 261–384Google Scholar
  101. TRB (2003) Transit capacity and quality of service manual. On-line report prepared for the Transit Cooperative Research ProgramGoogle Scholar
  102. Trozzi V, Gentile G, Bell MGH, Kaparias I (2013a) Dynamic User Equilibrium in public transport networks with passenger congestion and hyperpaths. Transp Res B 57:266–285CrossRefGoogle Scholar
  103. Trozzi V, Gentile G, Bell MGH, Kaparias I (2013b) Effects of countdown displays in public transport route choice under severe overcrowding. Networks and Spatial Economics (published on-line)Google Scholar
  104. Van Oort N (2011) Service reliability and urban public transport design. Ph.D. thesis. Netherlands TRAIL Research School, DelftGoogle Scholar
  105. Van Oort N, Van Nes R (2009) Regularity analysis for optimizing urban transit network design. Public Transport 1:155–168CrossRefGoogle Scholar
  106. Vuchic VR (2006) Urban transit: operations, planning and economics. Wiley, New YorkGoogle Scholar
  107. Whelan G, Johnson D (2004) Modelling the impact of alternative fare structures on train overcrowding. Int J Transp Manage 2:51–58CrossRefGoogle Scholar
  108. Wu JH, Florian M, Marcotte P (1994) Transit equilibrium assignment: a model and solution algorithms. Transp Sci 28:193–203CrossRefzbMATHGoogle Scholar
  109. Yang L, Lam WHK (2006) Probit-type reliability-based transit network assignment. Transp Res Rec 1977:154–163CrossRefGoogle Scholar
  110. Yin Y, Lam WHK, Miller MA (2004) A simulation-based reliability assessment approach for congested transit network. J Adv Transp 38:27–44CrossRefGoogle Scholar
  111. Zhang Q, Han B, Li D (2008) Modeling and simulation of passenger alighting and boarding movement in Beijing metro stations. Transp Res C 16:635–649CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Guido Gentile
    • 1
    Email author
  • Klaus Noekel
    • 2
  • Jan-Dirk Schmöcker
    • 3
  • Valentina Trozzi
    • 4
  • Ektoras Chandakas
    • 5
  1. 1.DICEA—Dipartimento di Ingegneria Civile, Edile e AmbientaleSapienza University of RomeRomeItaly
  2. 2.PTV AGKarlsruheGermany
  3. 3.Department of Urban ManagementKyoto UniversityKyotoJapan
  4. 4.Strategy and Service DevelopmentTransport for LondonLondonUK
  5. 5.Transamo, Transdev GroupParisFrance

Personalised recommendations