M.Sc Thesis
M.Sc Student Keyserman Emiliya Investigation of Train Timetable Schedule Methods Department of Civil and Environmental Engineering Professor Shlomo Bekhor

Abstract

The rail timetable problem is one of the most important and complicated problems in public transportation. It is essential to create an optimal timetable to allow passengers transfer between lines with the least possible time waiting at the transfer points. During the last decade several tools were developed to optimize the railroad timetable.

The base model used in this final paper is the Periodic Event Scheduling Problem. Researchers from different countries modified the base model and suited it according to the needs of the specific rail network. In this research we chose the model suggested by Peeters (2003). The author formulated the problem in the form of periodic and linear programming. Since travel time minimization is one of the important goals, we chose to research the aim of minimum time of traveling under the constraints of waiting time and train connectivity between stations. These constraints are modeled as arrival and departure events. The network topology is defined by a directed constrained graph, where every node of the network describes an event. The arcs of network describe the travel time, dwell time and connection time.

To demonstrate the capability of this model, the north-south corridor of the Haifa - Tel Aviv section is chosen. This section comprises 3 regional lines (Haifa - Tel Aviv, Binyamina - Tel Aviv, and Hod HaSharon - Tel Aviv) and 1 express line (direct line Haifa - Tel Aviv).

We performed 5 tests on these lines, which included changes in the constraints and in the objective function, in order to understand which constraints influence the solution.

The model was implemented using the LINDO software, a well-known tool used to solve Linear Programming problems.

The main conclusions found in this research are that the overall schedule is not flexible enough, since most constraints are binding. Additional time constraints cause an increase of extra time in the schedule. Assuming no changes in the objective function, the changes in the constraints increased twice the extra time in the schedule. Adding traveling lines in the network increased the extra time as well.

The changes in the lower bound of connection constraints caused the changes in the schedule (travel time was now longer between the departure and destination), but total time of delay remained the same. Finally, an average of 8% travel time is saved from the optimized results in comparison to the existing rail timetable for the section examined in this research.