A general formulation for multi-modal dynamic traffic assignment considering multi-class vehicles, public transit and parking

Xidong Pi, Wei Ma, Zhen (Sean) Qian

Research output: Journal article publicationJournal articleAcademic researchpeer-review

32 Citations (Scopus)


Travel behavior and travel cost in modern urban transportation systems are impacted by many aspects including heterogeneous traffic (private cars, freight trucks, buses, etc.) on roads, parking availability near destinations, and travel modes available in the network, such as solo-driving, carpooling, ride-hailing, public transit, and park-and-ride. Managing such a complex multi-modal system requires a holistic modeling framework of transportation network flow in terms of both passenger flow and vehicular flow. In this paper, we formulate and solve for spatio-temporal passenger and vehicular flows in a general multi-modal network explicitly considering multi-class vehicles, parking facilities, and various travel modes. Vehicular flows, namely cars, trucks, and buses, are integrated into a holistic dynamic network loading (DNL) model. Travel behavior of passenger demand on modes and routes choices is encapsulated by a multi-layer nested logit model. We formulate the multi-modal dynamic user equilibrium (MMDUE) that can be cast into a Variational Inequality (VI) problem. A simple flow solution performed at the origin-destination level and based on the gradient projection is derived from the KKT conditions and shown to efficiently solve for the VI problem on large-scale networks. Numerical experiments are conducted on a multi-modal network in the Pittsburgh region along with sensitivity analysis with respect to demand and management strategies. We show that many factors including the total passenger demand, parking prices, transit fare, and ride-sharing impedance can effectively impact the system performance and individual user costs. Experiments on a large-scale multi-modal network in Fresno, California also show our model and solution algorithm have satisfactory convergence performance and computational efficiency.

Original languageEnglish
Pages (from-to)369-389
Number of pages21
JournalTransportation Research Part C: Emerging Technologies
Publication statusPublished - Jul 2019
Externally publishedYes


  • Dynamic traffic assignment
  • Heterogeneous traffic simulation
  • Multi-modal dynamic user equilibrium
  • Nested logit model
  • Parking
  • Public transit

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Automotive Engineering
  • Transportation
  • Computer Science Applications


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