A Model to Create Bus Timetables to Attain Maximum Synchronization Considering Waiting Times at Transfer Stops

Due to the steady increased in public transportation demand, there is a need to provide more desirable and user-friendly transit systems. Typically, the public transportation timetables are modeled as an assignment problem, which often has objectives such as reducing the cost of operation, minimizing waiting time between transfer points or improving the quality of performance. This research considers the problem of developing synchronized timetables for bus transit systems with fixed routes when a waiting time limit exist at each transfer stops, for the passengers making connections. The objective of this research is to have maximum number of simultaneous arrivals. Different to previous studies, a simultaneous arrival\u27 has been defined as an arrival of buses of different routes at a transfer point such that the time between these arrivals do not exceed the passenger waiting time range associated with the transfer stop. In other words, at each node, an upper bound and a lower bound are set for the arrivals of two buses and these buses are run within this allowable window. The heuristic developed has been modeled as a mixed integer linear programming problem and applied to some real life problems to evaluate the outcomes. The total number of synchronizations obtained by the model was compared to the maximum possible simultaneous arrivals at each node. Results show that a larger number of simultaneous arrivals are obtained when the waiting time ranges are relaxed. Finally some important applications of the proposed model compared to the existing models are presented