Railway Rapid Transit Timetables with Variable and Elastic Demand

This paper focuses on the design of railway timetables considering a variable elastic demand profile along a whole design day. Timetabling is the third stage in the classical hierarchical railway planning process. Most of previous works on this topic consider a uniform demand behavior for short planning intervals. In this paper, we propose a MINLP model for designing non-periodic timetables on a railway corridor where demand is dependent on waiting times. In the elastic demand case, long waiting times lead to a loss of passengers, who may select an alternative transportation mode. The mode choice is modeled using two alternative methods. The first one is based on a sigmoid function and can be used in case of absence of information for competitor modes. In the second one, the mode choice probability is obtained using a Logit model that explicitly considers the existence of a main alternative mode. With the purpose of obtaining optimal departure times, in both cases, a minimization of the loss of passengers is used as objective function. Finally, as illustration, the timetabling MINLP model with both mode choice methods is applied to a real case and computational results are shown.