Integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network: A space-time-state hyper network-based assignment approach

Pan Shang, Ruimin Li, Jifu Guo, Kai Xian, Xuesong Zhou

Research output: Contribution to journalArticle

16 Scopus citations


In this study, we focus on one of practically important research problems of integrating Lagrangian and Eulerian observations for passenger flow state estimation in an urban rail transit network. The task is accomplished by using a triple of flow, density, and speed to construct a discretized passenger flow state, further constructing a space-time-state (STS) hyper network so that we can utilize a better defined three-dimensional solution space to integrate structurally heterogeneous data sources. The monitoring data include passenger transaction records and identification space-time samples observed over a possible range of a few hours from origins to destinations (Lagrangian observations), and time-dependent passenger counts collected at some key bottleneck locations (Eulerian observations). To describe the complex urban-rail passenger flow evolution, passenger traveling and fixed sensor state transition processes can be unified within a STS path representation. To estimate the consistent system internal states between two different types of observations, we formulate a hyper network-based flow assignment model in a generalized least squares estimation framework. For applications in large-scale transportation networks, we decompose the proposed model into three easy-to-solve sub-problems. The proposed model is applied to a real-world case based on the Beijing subway network with complete smart card data for each passenger at his/her origin and destination and time-dependent passenger counts in several key transfer corridors, while the specific space-time trajectories of all passengers and high-resolution time-dependent congestion levels at platforms, in trains, and in transfer corridors are estimated. This proposed passenger flow state inference method can provide a rich set of state inferences for advanced transit planning and management applications, for instance, passenger flow control, adaptive travel demand management, and real-time train scheduling.

Original languageEnglish (US)
Pages (from-to)135-167
Number of pages33
JournalTransportation Research Part B: Methodological
StatePublished - Mar 1 2019



  • Decomposition solution framework
  • Discretized passenger flow state
  • Lagrangian and Eulerian observations
  • Space-time-state network
  • Urban rail transit network

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Transportation

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