This paper presents a model of competition between operators on urban local bus routes in which passengers always board the first bus to arrive, and it is costly to revise timetables. The model predicts that timetables are unstable, the operator whose bus was boarded by fewest passengers is the most likely to change its arrival time, and to try to leapfrog its rival by arriving just before, and that there is a tendency for bus arrival times to be clustered together. These predictions are consistent with observed features of the on-the-road competition on urban local bus routes. On express coach routes, where passengers are more likely to research departure times before travelling, and to arrive at the coach station in order to catch their preferred coach, instability does not arise in the model, and has not been noted as a feature of competition in practice.
