A Behavioural Explanation of the Association Between Bus and Passenger Arrivals at a Bus Stop

The times of arrivals of passengers and departures of buses have been observed at ten bus stops in suburban London. The different bus stops were observed at different times of the day, but the observations at each were repeated at the same time on each of eight different days. Due to the predictability of the bus services, passengers' waiting times were observed to be about 30 per cent less than they would have been had the passengers arrived at random times. An explanation of this involves considering passengers to be of three types: a proportion q whose arrival time is causally coincidental with the bus, a proportion p(1 − q) who arrive at the optimal time (the time at which the expected waiting time is smallest), and a proportion (1 − p)(1 − q) who arrive at random. It was found that p is positively correlated with the expected gain from arriving at the optimal time as opposed to arriving at random. Furthermore, p was found to be larger at those bus stops observed in the peak than at those observed in the off-peak. A number of other results relating various parameters of the bus services are also given.