Continuum approximation approach to bus network design under spatially heterogeneous demand

• A framework is offered for bus network design under spatially-heterogeneous demand.
• Dense local networks serve high-demand neighborhoods.
• Routes with distinct spacings are aligned using a power-of-two scheme.
• Optimal designs are obtained through continuum approximations.
• Reductions in both agency and user costs are achieved.

A methodological framework is formulated so that continuum approximation techniques can be used to design bus networks for cities where travel demand varies gradually over space. The bus-route configurations that result consist of (i) a main, possibly city-wide grid with relatively large physical spacings between its parallel routes and the stops along those routes; together with (ii) one or more local grids with more closely-spaced routes and stops that serve neighborhoods of higher demand densities. The so-called power-of-two concept is borrowed from the field of inventory control, and is enforced so that local grids can be inserted seamlessly within the main one.The resulting heterogeneous route configurations can reduce the costs to the bus users and the operating agency combined, as compared against the costs of homogeneous bus-route grids. Differences of as much as 8% are observed for numerical examples that cover wide-ranging patterns in spatially-varying demand. Much of the savings are due to the diminished access costs that users enjoy when high-demand neighborhoods are served by local grids with closely-spaced routes and stops.