Zone Fare System Design in a Rail Transit Line

Abstract

As a widely existing form of public transit fare structures, zone fare system is traditionally designed in a separate way, which may lead to suboptimal results. This paper aims to concurrently address the zone division and fare calculation issues of the zone fare system design in a rail transit line. It is necessary to consider passengers as well as operators to find an impartial zone fare system. A fair zone fare system is one where the zone fares are as close as possible to the distance-based fares, for the fares of the distance-based fare system are highly correlated with the actual distance of trips. Thus, the fare deviations for the trips between the zone fare system and the distance-based fare system are utilized as the evaluation metric of fairness. To achieve the goal of minimizing fare deviations for all trips, we introduce three indexes: average absolute deviation, average squared deviation, and maximum mileage fare deviation. With the three indexes as the objective functions, we develop a joint optimization algorithm where a novel zone boundary adjustment scheme is proposed as the key technique. Numerical results show that the proposed algorithm can effectively provide a joint optimal scheme and the optimal number of planned zones is 5 for Changsha Metro Line 2. The proposed algorithm can provide guidance for the practical design and adjustment of the zone fare system.