Optimal public transit frequency under stochastic demand and fixed vehicle size: Application in the Norwegian car ferry sector

When capacity constraints are present in public transportation services, some travelers may not be able to board the first vessel they desire. Consequently, a type of waiting time cost is introduced, as passengers must wait for (at least) another full headway before the next service arrives. This waiting time has, to a lesser extent, been accounted for in the literature focusing on the optimal frequency of departures in transport. Not including this waiting time cost may lead to an underestimation of the optimal departure frequency. In this paper, we develop a novel optimization framework to incorporate the effect of this waiting time when there is a limited vessel capacity. Two different formulations are applied, which yield consistent results. Our policy recommendation is clear: Both the theoretical and empirical findings suggests that a “third” waiting time component of not being able to board the first vessel is highly relevant for decision-makers when vessel size constraints exists. Not including the extra waiting time costs stemming from capacity constraints leads to starkly different optimal service levels, which clearly indicates the relevance of our findings for practical policy making.