A max-plus algebraic model of bus bunching and control strategies

Disruptions in bus public transport systems, such as congestion, varying demands etc. lead to deviations from timetables in bus headways. An often occurring and problematic phenomenon is bus bunching, where several buses on the same route arrive at a stop at the same time and there are large headways between separate bunches. Thus the bus arrival frequency is effectively diminished and travel time is prolonged, including waiting time and in-vehicle time, which has considerable negative impact on system reliability. In order to improve service performance in terms of travel times and predictable bus arrival frequencies, bus holding strategies need to be employed. We propose a max-plus algebraic approach to modelling bus dynamics and the occurrence of bus bunching. The model is used to propose a bus holding strategy. Numerical results are presented for a simulation of a high-frequency route in a small artificial bus public transport network.