Analysis of daily variation in bus occupancy rates for city-buses in Uppsala and optimal supply

Recently several papers have analyzed optimal supply of public transport in the sense of optimal prices, frequencies, bus sizes, spacing of bus stops for a public transport authority facing a certain static demand for trips. This paper is motivated by the observation that demand for bus services varies between weekdays even for the same departure analyzes the magnitude of this variation and its implications for optimal supply. This analysis was enabled by the relatively recent adaption of technologies for counting passengers boarding and alighting and motivated by the relatively few published studies of such data. This paper therefore uses calculated rates between bus stops in the Swedish city Uppsala, and analyses the average variation in geography, between directions and between the same departure times and directions. The central results are that; there are parts of lines with systematically higher and lower occupancy rate than average without corresponding supply adaptions, there is substantial variance in the occupancy on buses leaving the same bus stop at the same time on week days, and welfare optimization indicates that providing capacity to cover maximum observed demand with seats in buses is not necessarily optimal.