Bilevel Optimization for Bunching Mitigation and Eco-Driving of Electric Bus Lines

The problems of bus bunching mitigation and the energy management of groups of vehicles have traditionally been treated separately in the literature and been formulated in two different frameworks. The present work bridges this gap by formulating the optimal control problem of the bus line eco-driving and regularity control as a smooth, multi-objective nonlinear program. Since this nonlinear program has only a few coupling variables, it is shown how it can be solved in parallel aboard each bus, such that only a marginal amount of computations need to be carried out centrally. This procedure leverages the structure of the bus line by enabling parallel computations and reducing the communication loads between the buses, which makes the problem resolution scalable in terms of the number of buses. Closed-loop control is then achieved by embedding this procedure in a model predictive control. Stochastic simulations based on real passengers and travel times data are realized for several scenarios with different levels of bunching for a line of electric buses. Our method achieves fast recoveries to regular headways as well as energy savings of up to 9.3% when compared with traditional holding or speed control baselines.

I. Introduction

Electric vehicles offer a promising way to mitigate the increasing greenhouse gases emissions of the transport sector. Electric buses in particular combine no tailpipe emissions and lower energy consumption than other types of city buses [1] with the lower marginal emissions that urban public transit has in general [2]. However, bus lines are inherently unstable systems, and they have long been known to develop bus bunching if left uncontrolled [3], [4]. One late bus may cause the accumulation of passengers at stops downstream, which acts as a positive feedback loop on the bus and further increases its delay. Likewise, an early bus encounters fewer passengers at stops than expected, and may ultimately catch up with the preceding bus at which point the buses start bunching. The increased service delays incurred by this so-called bus bunching phenomenon may in turn significantly increase the passenger delays, which may eventually discourage users from choosing to use public transport [5].