From Strategic Modelling of Urban Transit Systems to Golden Rules for their Design and Management

The paper provides a synthetic, "strategic" model of transit systems in urban areas that features out a set of modes, quality of service and terminal access, demand and network usage by users' trips, with some hints of spatial heterogeneity. The model encompasses technical relationships relating fleet size and design parameters such as infrastructure length and station spacing, to frequency, commercial speed and access distance, hence to wait time, running time and access/egress time. Economic features are modelled, too: generalized costs to individual users, demand elasticity, supply costs and system welfare. The model can be used for synthetic statistical description of real-world systems as well as for economic analysis and the assessment of given system states against theoretical references. After introducing the model elements and relationships, we put forward a causal diagram that synthesizes the system under study and constitutes the model architecture. We then turn to mathematical analysis to formalize (i) the determination of a system state on the basis of a supply plan, technical relationships and demand behaviour, (ii) the optimisation of system welfare with respect to the action levers on the supply side. Next, for an uncongested system we establish theoretical conditions for both an optimum system state under fixed demand and a second best optimum under variable demand and tariffs. Three "golden rules" for transit network design and management are established, namely (i) balancing the rolling stock costs and the users' costs of waiting time, (ii) balancing the station costs plus the value to users of the dwelling part of their in-network times, against the users' costs of "longitudinal" access times, (iii) balancing the full supply costs and the users' costs of "transversal" access times. Furthermore, the existence and uniqueness of a System Optimum state are proven and a solution scheme is provided.