Towards a general microeconomic model for the operation of public transport

After Vickrey's view, Mohring constructed a microeconomic model to determine the optimal frequency of buses serving a corridor with fixed demand. The main result was that frequency should be proportional to the square root of demand. The role of users' costs was shown to be crucial. This approach has evolved over the past decades, improving our understanding of public transport operations. This paper describes and analyses the evolution of microeconomic models for the analysis of public transport services with parametric demand, leading towards a more comprehensive one. An in-depth review of all the contributions in the academic literature is presented, emphasizing both the treatment of variables and the form of the results mostly in terms of frequency and fleet size. A series of partial new elements is also identified. An extension of Jansson's model for a single period is developed analytically, including the effect of vehicle size on operating costs and the influence of crowding on the value of time. Numerical simulations are used for comparison and analysis. A general model is then proposed where bus operations are optimized accounting for a number of simultaneous relations. Finally, the different models are discussed and compared.