Schedule-based transit assignment with online bus arrival information

Document Type

Journal Article

Publication Date


Subject Area

place - north america, place - urban, mode - bus, ridership - behaviour, ridership - demand, operations - capacity, operations - reliability, operations - scheduling, planning - signage/information


Congestion, Equilibrium, Online information, Schedule-based, Transit assignment, Variational inequality


Most public transportation services deviate from their published schedule. To cope with the delay caused by the unreliable service, passengers use online information about the bus arrival time which affects their route choice behavior. Current schedule-based transit assignment models fail to capture the passengers’ adaptive response to unreliable service, resulting in an inaccurate estimation of passenger wait time and passenger loads on various transit routes. The current study proposes schedule-based transit assignment models that incorporate online bus arrival information when modeling the passenger route choice in a stochastic and time-dependent transit network. The authors propose that passengers employ strategies when traveling between different origin–destination pairs not only due to the limited capacity of vehicles but also to cope with the transit delay. The passenger routing problem is modeled as a Markov Decision Process, and efficient algorithms are developed to solve this problem. Depending on the vehicle capacity, two types of assignment models are presented, namely, uncapacitated and capacitated assignments. When penalties for arriving at the destination outside the desired arrival time window are not applied, the uncapacitated assignment problem is formulated as a linear program. On the other hand, the capacitated assignment is formulated as a variational inequality problem for which an efficient Method of Successive Averages-based heuristic solution algorithm is proposed. Computational experiments are presented for a small and a large schedule-based transit network. The results show that denied boarding in an unreliable network leads to higher expected costs to passengers compared to the reliable and uncongested network. Furthermore, the analysis shows that the strategies evaluated with reliable schedule assumption lead to unreliable paths in the network and produces more transferring flow than should happen in practice. The application of our method to a subnetwork of the Twin Cities transit network with artificial demand reveals that passengers traveling from a residential area to the University of Minnesota campus may prefer taking a path with transfer in the event of highly unreliable transit service on the direct routes.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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