A mathematical model for a two-service skip-stop policy with demand-dependent dwell times

Abstract

This paper presents a discrete-event model for a mass-transit line operated with a two-service skip-stop policy while allowing for train dwell times to vary according to passengers’ demand volumes. The model is formulated by two mathematical constraints on the train’s travel and safe separation times that govern the train dynamics on the line. In addition, the model takes into account trains’ dwell times, which are affected by both the services offered by the operator and passenger demand. The model is written in the max-plus algebra, a mathematical framework that allows us to derive interesting analytical results, including the fundamental diagram of the line, which describes the relationship between the average train time headway (or frequency), the number of trains running on the line and the passenger travel demand. The paper also derives indicators that are capable of quantifying and, thus, assessing the impact of a skip-stop policy on passengers’ travel. Finally, the paper compares two different passenger demand profiles. Results show that long-distance passengers mainly benefit from skip-stop policies, while short-distance travelers may experience an increase in their travel time. For long-distance passengers, the increase in the waiting time is counterbalanced by the decrease in the in-vehicle time, leading to an overall decrease in total passenger travel time.