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 distancebased 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.