Networks and Spatial Economics

, Volume 8, Issue 2–3, pp 225–240

A Stochastic Process Approach for Frequency-based Transit Assignment with Strict Capacity Constraints



Transit assignment models represent the stochastic nature of waiting times, but usually adopt a deterministic representation route flows and costs. Especially in cities where transit vehicles are small and not operating to timetables, there is a need to represent the variability in flows and costs to enable planners make more informed decisions. Stochastic process (SP) models consider the day-to-day dynamics of the transit demand-supply system, explicitly modelling passengers’ information acquisition and decision processes. A Monte Carlo simulation based SP model that includes strict capacity constraints is presented in this paper. It uses micro-simulation to constrain passenger flows to capacities and obtain realistic cost estimates. Applications of the model and its comparison with the De Cea and Fernandez (Transp Sci, 27:133–147, 1993) model are presented using a small network.


Transit assignment Stochastic process Strict capacity constraints Day-to-day dynamics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Cantarella GE, Cascetta E (1995) Dynamic processes and equilibrium in transportation networks: towards a unifying theory. Transp Sci 29:305–329CrossRefGoogle Scholar
  2. Cascetta E (1989) A stochastic process approach to the analysis of temporal dynamics in transportation networks. Transp Res Part B 23:1–17CrossRefGoogle Scholar
  3. 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 Part B 40:437–459CrossRefGoogle Scholar
  4. Cominetti R, Correa J (2001) Common lines and passenger assignment in congested transit networks. Transp Sci 35:250–267CrossRefGoogle Scholar
  5. Davis GA, Nihan NL (1993) Large population approximations of a general stochastic traffic assignment model. Oper Res 41:169–178Google Scholar
  6. De Cea J, Bunster JP, Zubieta L, Florian M (1988) Optimal strategies and optimal routes in public transit assignment models: an empirical comparison. Traffic Eng Control 49:520–526Google Scholar
  7. De Cea J, Fernandez E (1993) Transit assignment for congestion public transport networks: an equilibrium model. Transp Sci 27:133–147Google Scholar
  8. Hamdouch Y, Marcotte P, Nguyen S (2004) Capacitated transit assignment with loading priorities. Math Program B 101:205–230CrossRefGoogle Scholar
  9. Hazelton M, Watling D (2004) Computation of equilibrium distributions of Markov traffic assignment models. Transp Sci 38:331–342CrossRefGoogle Scholar
  10. Kurauchi F, Bell MGH, Schmöcker J-D (2003) capacity constrained transit assignment with common lines. J Math Model Algorithms 2:309–327CrossRefGoogle Scholar
  11. Nguyen S, Pallottino S (1988) Equilibrium traffic assignment for large scale transit networks. Eur J Oper Res 37:176–186CrossRefGoogle Scholar
  12. Sheffi Y (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice Hall, Englewood CliffsGoogle Scholar
  13. Smith MJ (1984) The stability of a dynamic model of traffic assignment: an application of a method of Lyapunov. Transp Sci 18:245–252Google Scholar
  14. Spiess H, Florian M (1989) Optimal strategies: a new assignment model for transit networks. Transp Res Part B 23:83–102CrossRefGoogle Scholar
  15. Watling D (1996) Asymmetric problems and stochastic process models of traffic assignment. Transp Res Part B 30:339–357CrossRefGoogle Scholar
  16. Wu JH, Florian M, Marcotte P (1994) Transit equilibrium assignment: a model and solution algorithms. Transp Sci 28:193–203Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Institute for Transport StudiesUniversity of LeedsLeedsUK

Personalised recommendations