Reliability-based stochastic transit assignment with capacity constraints: Formulation and solution method

W. Y. Szeto*, Yu Jiang, Ka-Io Wong, Muthu Solayappan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

49 Scopus citations


This paper proposes a Linear Complementarity Problem (LCP) formulation for the reliability-based stochastic transit assignment problem with capacity constraints and non-additive link costs, where in-vehicle travel times and waiting times are uncertain. The capacity constraints are developed via the notions of effective capacity and chance constraints. An equivalent route-based linear program (LP) for the proposed problem is formulated to determine the patronage of each line section, critical links, critical service frequencies, unmet demand and the network capacity, which considers the risk-aversive behavior of travelers. A solution method is developed, utilizing the K-shortest path algorithm, the column generation technique, and the revised simplex method, to solve the proposed LP with guaranteed finite convergence. Numerical experiments are also set up to illustrate the properties of the problem and the application of the proposed model for reliability analysis.

Original languageEnglish
Pages (from-to)286-304
Number of pages19
JournalTransportation Research Part C: Emerging Technologies
StatePublished - 1 Jan 2013


  • Capacity constraint
  • Chance constraint
  • Column generation
  • Linear Complementarity Problem
  • Reliability-based user equilibrium
  • Transit assignment

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