Operational design for shuttle systems with modular vehicles under oversaturated traffic: Continuous modeling method

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, mode - bus rapid transit, mode - other, operations - capacity, operations - traffic, operations - scheduling, planning - methods


Vehicle scheduling, Time-varying capacity design, Energy consumption, Oversaturated traffic, Continuum approximation


Time-varying capacity design holds an opportunity to reduce the energy consumption of urban mass transit systems, e.g., urban rail transits, bus rapid transits, modular autonomous vehicles. In this paper, we investigate the joint design of dispatch headway and vehicle capacity for one to one shuttle systems with oversaturated traffic to achieve the optimal tradeoff between general vehicle dispatching cost (mainly comprised of vehicle energy consumption) and customer waiting cost. We propose a continuum approximation model from a macroscopic point of view to reveal fundamental analytical insights into the optimal design. By introducing the concept of a preferred virtual arrival demand curve at the origin station, we prove that the investigated problem with possibly oversaturated traffic can be equivalently solved with a simpler revised problem where only unsaturated traffic is present. With this property, we decompose the original problem into a set of independent unit-time revised unsaturated problems that can be analytically solved in each neighborhood across the operational horizon. With two sets of numerical experiments, we show that the CA model offers near-optimum solutions with negligible errors very efficiently and we also verify the theoretical properties. Also, the effectiveness of time-varying vehicle capacity design is demonstrated in shuttle systems under both saturated and unsaturated traffic. Overall, the proposed CA model contributes to the CA methodology literature by extending the CA method for traditional transit dispatching problems with unsaturated traffic to the joint design of dispatch headway and vehicle capacity considering oversaturated traffic, adjustable vehicle capacities and other factors (e.g. minimum dispatch headway).


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


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