Adaptive transit design: Optimizing fixed and demand responsive multi-modal transportation via continuous approximation

Giovanni Calabrò*, Andrea Araldo, Simon Oh, Ravi Seshadri, Giuseppe Inturri, Moshe Ben-Akiva

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


In most cities, transit consists solely of fixed-route transportation, whence the inherent limited Quality of Service for travellers in suburban areas and during off-peak periods. On the other hand, completely replacing fixed-route (FR) with demand-responsive (DR) transit would imply a huge operational cost. It is still unclear how to integrate DR transportation into current transit systems to take full advantage of it. We propose a Continuous Approximation model of a transit system that gets the best from fixed-route and DR transportation. Our model allows deciding whether to deploy a FR or a DR feeder, in each sub-region of an urban conurbation and each time of day, and to redesign the line frequencies and the stop spacing of the main trunk service. Since such a transit design can adapt to the spatial and temporal variation of the demand, we call it Adaptive Transit. Numerical results show that, with respect to conventional transit, Adaptive Transit significantly improves user-related cost, by drastically reducing access time to the main trunk service. Such benefits are particularly remarkable in the suburbs. Moreover, the generalized cost, including agency and user cost, is also reduced. These findings are also confirmed in scenarios with automated vehicles. Our model can assist in planning future-generation transit systems, able to improve urban mobility by appropriately combining fixed and DR transportation.

Original languageEnglish
Article number103643
JournalTransportation Research Part A: Policy and Practice
Publication statusPublished - 2023

Bibliographical note

Funding Information:
This research was supported by the National Research Foundation under its CREATE program and the Singapore-MIT Alliance for Research and Technology, Future Urban Mobility Interdisciplinary Research Group. The work has been partially supported by the project “WEAKI-TRANSIT: WEAK-demand areas Innovative TRANsport Shared services for Italian Towns” (unique project code: E44I17000050001) under the programme of Italian Ministry of University and Research “PRIN 2017”, by the project “ADDRESS” under the University of Catania programme “PIACERI Linea 2”, by the French ANR research project MuTAS (ANR-21-CE22-0025-01) and by the research grant, funded by Institut Francais (Ambassade de France en Italie), received by G. Calabrò.

Publisher Copyright:
© 2023 Elsevier Ltd


  • Continuous approximation
  • Demand-responsive transportation
  • Microsimulation
  • Transit network design


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