Lines spacing and scale economies in the strategic design of transit systems in a parametric city.

In this paper, we incorporate the spacing of transit lines in addition to frequencies, vehicle sizes and routes in both the design and the analysis of scale economies in transit systems. First, we present a way of looking at lines spacing in a simple parallel-lines-model whose properties regarding optimal design and scale economies are derived. Then we introduce this concept of spacing into the parametric description of a city - that permits the representation of different degrees of mono and polycentrism - in order to analyze the choice between basic strategic lines structures as feeder-trunk, hub-and-spoke or direct services, where lines spacing is optimized jointly with frequencies, vehicle sizes and routes of all lines involved. We show that (a) there is a link between optimal spacing and frequency such that waiting and access costs are equal; (b) the inclusion of spacing increases the range of demand volumes where transit networks that include transfers are preferred; (c) the degrees of mono and polycentrism influences optimal spacing; and (d) introducing spacing increases the degree of scale economies.