Public transport trajectory planning with probabilistic guarantees

Document Type

Journal Article

Publication Date


Subject Area

place - urban, mode - bus, operations - frequency, operations - performance, operations - traffic, operations - reliability, infrastructure - traffic signals, planning - methods


Eco-cruise control, Velocity control, Timetable reliability, Shockwave profile model, Chance-constrained optimization, Model predictive control


The paper proposes an eco-cruise control strategy for urban public transport buses. The aim of the velocity control is ensuring timetable adherence, while considering upstream queue lengths at traffic lights in a probabilistic way. The contribution of the paper is twofold. First, the shockwave profile model (SPM) is extended to capture the stochastic nature of traffic queue lengths. The model is adequate to describe frequent traffic state interruptions at signalized intersections. Based on the distribution function of stochastic traffic volume demand, the randomness in queue length, wave fronts, and vehicle numbers are derived. Then, an outlook is provided on its applicability as a full-scale urban traffic network model. Second, a shrinking horizon model predictive controller (MPC) is proposed for ensuring timetable reliability. The intention is to calculate optimal velocity commands based on the current position and desired arrival time of the bus while considering upcoming delays due to red signals and eventual queues. The above proposed stochastic traffic model is incorporated in a rolling horizon optimization via chance-constraining. In the optimization, probabilistic guarantees are formulated to minimize delay due to standstill in queues at signalized intersections. Optimization results are analyzed from two particular aspects, (i) feasibility and (ii) closed-loop performance point of views. The novel stochastic profile model is tested in a high fidelity traffic simulator context. Comparative simulation results show the viability and importance of stochastic bounds in urban trajectory design. The proposed algorithm yields smoother bus trajectories at an urban corridor, suggesting energy savings compared to benchmark control strategies.


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


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