A multi-hop control scheme for traffic management

Hossein Rahimi Farahani, Amir Abbas Rassafi, Kenan Zhang, Yu (Marco) Nie*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We propose a multi-hop control scheme (MHCS) that aims to route traffic through a set of designated intermediate checkpoints (ICs). Because travelers are allowed to freely choose routes for each “hop” that connects real (origin and destination) and ICs, MHCS promises to keep intervention at a more tolerable level, compared to conventional route-based control schemes. The MHCS problem has a natural bi-level structure: the upper level attempts to minimize congestion by adjusting the hopping ratios, which are then used in the lower level problem to route travelers according to user equilibrium conditions. Accordingly, we formulate the problem as a mathematical program with equilibrium constraints (MPEC), establish its solution existence, and propose to solve it using a sensitivity analysis based algorithm. We examine sixteen heuristic rules for choosing ICs. Results based on five hundred experiments suggest that selecting the most used and most congested nodes at system optimum as the ICs delivered the largest travel time savings. Based on this finding, a set of efficient ICs are identified and adopted to test the potential of a full-scale scheme. The results from numerical experiments indicate that these checkpoints are highly effective in reducing traffic congestion at a reasonable cost of control and unfairness. In particular, they outperform, by a large margin, other choices such as most congested nodes at user equilibrium.

Original languageEnglish (US)
Article number103278
JournalTransportation Research Part C: Emerging Technologies
StatePublished - Sep 2021


  • Intermediate checkpoint
  • Mathematical program with equilibrium constraints
  • Multi-hop control
  • System optimal
  • User equilibrium

ASJC Scopus subject areas

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


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