On the design of an optimal flexible bus dispatching system with modular bus units: Using the three-dimensional macroscopic fundamental diagram

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, operations - capacity, operations - frequency, operations - traffic, economics - operating costs, ridership - demand, infrastructure - fleet management


Optimal bus dispatching system, Modular bus units, Frequency setting problem, 3D-MFD


This study proposes a novel flexible bus dispatching system in which a fleet of fully automated modular bus units, together with conventional buses, serves the passenger demand. These modular bus units can either operate individually or combined (forming larger modular buses with a higher passenger capacity). This provides enormous flexibility to manage the service frequencies and vehicle allocation, reducing thereby the operating cost and improving passenger mobility.

We develop an optimization model used to determine the optimal composition of modular bus units and the optimal service frequency at which the buses (both conventional and modular) should be dispatched across each bus line. We explicitly account for the dynamics of traffic congestion and complex interactions between the modes at the network level based on the recently proposed three-dimensional macroscopic fundamental diagram (3D-MFD). To the best of our knowledge, this is the first application of the 3D-MFD and modular bus units for the frequency setting problem in the domain of bus operations.

Numerical results show the improvements in the total system cost made by adjusting the number of combined modular bus units and their dispatching frequencies to the evolution of both, the car and the bus passenger demand. A comparison with the commonly used approach that considers only the bus system (neglecting the complex multimodal interactions and congestion propagation) reveals the value of the proposed modeling framework. Finally, a sensitivity analysis of the effect of the operating unit cost of modular bus units, the size of the bus network, and the size of the bus fleet sheds light on the robustness of the proposed optimization framework.


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


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