Remote park-and-ride network equilibrium model and its applications

Zhiyuan Liu, Xinyuan Chen, Qiang Meng, Inhi Kim

Research output: Contribution to journalArticleResearchpeer-review

46 Citations (Scopus)


Existing park-and-ride (P&R) sites are usually located near a train/bus station where construction and operation costs are considerably high. Thus, this paper proposes a new P&R service mode, “Remote P&R (RPR)”, where the car park locates in a suburban area with lower land value. Dedicated express bus service is used to connect this site and a nearby train station. To quantitatively evaluate the impacts of RPR on the network flows, a combined modal split and traffic assignment model (CMSTA) is developed, where a cross-nested logit (CNL) model is adopted to cope with the mode similarity. The problem is formulated as a convex programming model and solved by the Evans algorithm, and then extended to asymmetric path-based cases, where a variational inequality (VI) model is built and solved by a self-adaptive gradient projection (SAGP) algorithm. Taking the CMSTA as the lower level and multimodal stochastic system optimum (MSSO) as the objective, we further develop a mathematical programming model with equilibrium constraints (MPEC) for the optimal network design of RPR. Based on an origin-based reformulation of the MPEC model, an exact solution method based on the nonlinear valid inequalities (NVI) is applied. Numerical examples demonstrate that the RPR services can significantly influence network users’ travel decisions, promote the usage of public transportation and mitigate traffic congestion in the congested area of metropolitan cities.

Original languageEnglish
Pages (from-to)37-62
Number of pages26
JournalTransportation Research Part B: Methodological
Publication statusPublished - 1 Nov 2018


  • Combined modal split and traffic assignment
  • Cross-nested logit
  • Multimodal network design
  • Remote park-and-ride

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