Real-Time Train Scheduling With Uncertain Passenger Flows: A Scenario-Based Distributed Model Predictive Control Approach

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Real-time train scheduling is essential for passenger satisfaction in urban rail transit networks. This paper focuses on real-time train scheduling for urban rail transit networks considering uncertain time-dependent passenger origin-destination demands. First, a macroscopic passenger flow model we proposed before is extended to include rolling stock availability. Then, a distributed-knowledgeable-reduced-horizon (DKRH) algorithm is developed to deal with the computational burden and the communication restrictions of the train scheduling problem in urban rail transit networks. For the DKRH algorithm, a cost-to-go function is designed to reduce the prediction horizon of the original model predictive control approach while taking into account the control performance. By applying a scenario reduction approach, a scenario-based distributed-knowledgeable-reduced-horizon (S-DKRH) algorithm is proposed to handle the uncertain passenger flows with an acceptable increase in computation time. Numerical experiments are conducted to evaluate the effectiveness of the developed DKRH and S-DKRH algorithms based on real-life data from the Beijing urban rail transit network. The simulation results indicate that DKRH can be used to achieve real-time train scheduling for the urban rail transit network, while S-DKRH can handle the uncertainty in the passenger flows with an acceptable sacrifice in computation time.

Original languageEnglish
Pages (from-to)4219-4232
Number of pages14
JournalIEEE Transactions on Intelligent Transportation Systems
Issue number5
Publication statusPublished - 2023


  • distributed model predictive control
  • Prediction algorithms
  • Predictive control
  • Processor scheduling
  • Rail transportation
  • Rails
  • Real-time systems
  • scenario approach
  • time-dependent passenger origin-destination demands
  • uncertain passenger flows
  • Uncertainty
  • Urban rail transit networks


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