Reliable frequency determination: Incorporating information on service uncertainty when setting dispatching headways

Frequency setting requires the determination of the dispatching headways of all bus lines in a city network and constitutes the main activity in the tactical planning of public transport operations. Determining the dispatching headways of bus services in a city network is a multi-criteria problem that typically involves balancing between passenger demand coverage and operational costs. In this study, the problem of setting the optimal dispatching headways is formulated with the explicit consideration of operational variability issues for mitigating the adverse effects of passenger demand and travel time variations inherent to bus operations. The proposed model for setting the dispatching headways of bus lines considers the demand, headway and travel time variations along every section of each bus route for different times of the day, as well as operational costs, vehicle capacity and fleet size constraints. We first formulate the problem while accounting for the consequences of variability in service operations. The resulting optimization problem is then solved by employing a Branch and Bound approach together with Sequential Quadratic Programming in order to find the optimal dispatching headway for each bus line. Experimental results demonstrate (a) the improvement potential of the base case dispatching headways when considering the service reliability; (b) the sensitivity of the determined dispatching headways to changes in different criteria, such as passenger demand and/or bus running costs, and (c) the convergence accuracy of the proposed solution method when compared to heuristic approaches.