A continuum approximation approach for designing corridor-based heterogeneous transit service using modular autonomous vehicles

The conventional bus service struggles to efficiently accommodate heterogeneous demand due to the rigid design with fixed vehicle capacity. The advent of modular automated vehicles (MAVs), which can dynamically couple or decouple into variable transit units, offers a novel operation mode with variable transport capacity to respond to demand heterogeneity. To enhance the performance of MAV-based transit corridors, where MAVs can only couple or decouple at certain stations due to space constraints, this study employs the continuum approximation (CA) approach in developing an optimization model aimed at minimizing both patrons’ and agency costs. The problem is split into two: subproblem (1) ordinary operation decisions to determine the locations of ordinary stations and service headway; and subproblem (2) (de)coupling operation decisions to determine the locations of (de)coupling stations, the capacity of (de)coupling stations, and the number of en-route coupling/decoupling MAVs. The closed-form solutions are derived for the subproblem (1) and several linearization techniques are employed to convert the original nonlinear problem (2) into a linear form. To evaluate the proposed model, a hypothetical corridor with heterogeneous demand is examined. We initially compare the CA results with the feasible design after discretization, demonstrating that the approximation errors by the CA approach are acceptable with a maximum deviation of less than 3.40%. In addition, the proposed model can obtain cost savings of 10.60 and 2.01 mins/patron compared to fixed-capacity bus service and two-stage designs (the ordinary operation decisions and (de)coupling operation decisions are optimized separately). The results indicate the effectiveness of adopting MAVs and the necessity of joint design for both ordinary operation and (de)coupling operation decisions. Sensitivity analysis is performed in terms of the demand level, the unit cost of the (de)coupling station, the unit operating cost, and MAV capacity. Finally, we use a real-world case study in Chengdu, China, to demonstrate the application of the proposed model in practice.