Optimal Allocation of Service Frequencies over Transit Network Routes and Time Periods

This study proposes a formulation for the transit network frequency setting problem. The formulation provides an optimal allocation of resources over space and time while recognizing the existence of multiple service patterns along each bus route. Transit agencies must allocate their limited resources optimally to maximize user benefits, operator benefits, or a combination of the two. The coupling of the routes with the service patterns provided along all or portions of the routes is effectively captured, and the user perspective and the operator perspective are merged into one formulation. The service patterns may be scheduled with different subsets of stops for a given route. Users see the resulting combined route headways at the stops. The number of riders varies with the prevailing number of bus trips at a given stop, which is the combination of different pattern dispatch frequencies. Two main formulations are introduced. The first extends work of Furth and Wilson and seeks to maximize the number of riders and the total wait time savings under budget, fleet, policy headway, and bus loading constraints. The second minimizes the net cost under fleet, policy headway, bus loading, minimum ridership, and minimum wait time savings constraints. In both formulations, pattern headways in different time-of-day intervals are the decision variables. This paper provides the mathematical formulation underlying the proposed methodology, describes the solution method and implementation, and demonstrates, by example, important properties of the frequency setting problem in this context, including some that may at first appear counterintuitive.