Optimal fleet size, frequencies and vehicle capacities considering peak and off-peak periods in public transport

The fleet for surface transit in urban areas - number of buses and vehicle size - is usually determined by the characteristics of demand during the peak period, adjusting frequencies for other periods where those characteristics are quite different. Here the problem is formulated analytically considering a representative single line where hourly passengers flow and average trip lengths differ between peak and off-peak periods. Analytical and numerical results show that minimizing social costs (operators and users) for the whole day yields a larger fleet of smaller buses than if only the peak period is considered. Contrary to previous results on this issue, optimal frequencies across periods differ by a large amount, as optimal peak and off-peak frequencies are larger and smaller respectively than what would be obtained modeling each period by itself. The optimal bus size lies in-between the capacities obtained when each period is independently optimized. Several other interesting counterintuitive results are shown.