Multi-objective optimal control formulations for bus service reliability with traffic signals

•Multi-objective optimal control for bus service reliability with traffic signals.•Integrated model of bus and general traffic with variational method of kinematic wave.•Sensitivity analysis of running times and delays with respect to control actions.•Optimality conditions for different objectives with open loop solution algorithm.•Case study of arterial in Central London with traffic, signal, and bus data.

This paper presents a set of optimal control formulations for maximising bus service reliability through deriving optimal adjustments on signal timings. The traffic dynamics is captured by an underlying kinematic wave model in Hamilton-Jacobi formulation. With traffic data collected through loop detectors and bus positioning devices, the control actions are carried out through adjusting signal timing plans according to short-term estimations of traffic flows and bus arrivals. We derive the optimality conditions of multi-objective control formulations and present an open loop solution algorithm. The proposed control system is applied to a test arterial developed based upon a real-world scenario in Central London, UK. It is found that the model is capable of regulating bus service reliability through utilising traffic signals while managing delays induced to surrounding traffic. The study generates new insights on managing bus service reliability in busy urban networks.