Beyond the Mohring effect: Scale economies induced by transit lines structures design

In this paper we study how the spatial arrangement of transit lines (lines structure) influences scale economies in public transport. First we show that the degree of scale economies (DSE) increases discretely whenever passenger volume induces a change in lines structure. The technical elements behind this are explained by using a new three-dimensional concept called directness, encompassing number of transfers, number of stops and passenger route lengths. This is first exemplified in a simple ad-hoc network, and then applied to examine the structural changes that occur in the design of transit lines in a fairly general representation of a city. We show that directness increases whenever lines structure changes as a response to larger demand volumes - increasing DSE at the particular value of flow where this change occurs - because systems with more direct lines for each OD pair diminish in-vehicle times while increasing waiting times mildly, such that users are benefited by lower travel times and operators are benefited by lower idle capacity. After the change, however, DSE decreases within the demand range where the new line structure is maintained, just as in the one line model. The possibility of deciding the line structure introduces directness as a new source of economies of scale which are finally exhausted after full directness is achieved.