For planning purposes, line supplies are often defined as lines routes and their headways. An optimal departure time allows for a full exploitation of the line’s potential. Headway offset optimization shifts the trips of one or more lines so that the wait time of the passengers is minimized overall or it is close to the optimum wait time per passenger. The procedure headway offset optimization thus optimizes PuT supply, more precisely the timetable position for vehicle journeys.
You can trigger headway offset optimization for individual lines or as a procedure for a set of lines (User Manual: Executing a headway offset optimization). The procedure distinguishes between:
- variable lines: lines with a timetable position that can be moved
- relevant lines: lines whose transfer connections need to be be taken into account
- Lines that are not considered by the procedure.
The vehicle journeys of a variable line are moved together on line and direction level. Coupled or coordinated vehicle journeys are taken into account and retain their relative position even after optimization.
To carry out the procedure, you need an assignment result that includes the transfer passengers between time profiles or vehicle journeys. Transfer passenger data can be obtained from the results of timetable-based assignment or headway-based assignment. The specified analysis period limits the number of transfer passengers and vehicle journeys that are taken into account. Then the transfers/vehicle journeys with a time position that overlaps with the analysis period are considered.
The procedure improves the headway offset between lines by:
- Using local optimization methods
- Random timetable changes
- Using a genetic algorithm (optional)
The objective function is the total of volumes of all transfer passengers multiplied by the VD function value of transfer passenger wait time. The VD function is derived from the current headway offset of the solution. The VD function for the wait time is partly linear with gradient -1/1 and the minimum 0 for the optimum transfer wait time defined by the user.
This approach makes highly demanded connections even more attractive after optimization. The weighting of stops makes it possible to direct transfer flows towards lower volume nodes. And it acts as an additional multiplier in the objective function. If transfers take place between two differently weighted stops, the higher of two weightings is considered.
The result of headway offset optimization is a time offset of the vehicle journeys. You can apply the result directly to the timetable or save it as a transfer file. If there are several equally good solutions, they are stored in parallel.
There is no integrated feedback on the assignment results. Moving the timetable positions deletes the assignment results. A loop in the procedure sequence enables an iterative procedure consisting of optimization and reassignment.
