Considering passenger choices and overtaking in the bus bunching problem

Bus bunching is a well-known phenomenon on many bus routes where an initial delay to one service can disturb the whole schedule due to resulting differences in dwell times of subsequent buses at stops.This paper deals with the passenger behavior when there is more than one bus serving the stop, focusing on their choices and possible switching actions from the queue of the bus they are waiting to board.A parameter  is introduced to denote the percentage of passengers boarding the front bus of two buses boarding at the same time.Cases when overtaking is allowed or not are distinguished as this will also influence the passenger behavior.A set of discrete state equations is then implemented to obtain the departure times of the buses following the occurrence of an exogenous delay to one of the buses.Evaluation indices are introduced to measure the performance of the bus service along a corridor under different  levels.We find that it is advantageous to keep the percentage of passengers boarding the front bus low.Beside, overtaking is a favourable counter-measure against comparatively high frontbus preference.