Connectivity-Based Accessibility for Public Bicycle Sharing Systems

An increasing number of cities are implementing bicycle sharing systems to reduce traffic congestion. Determining the locations of bicycle stations is one of the fundamental challenges in planning of such systems. This paper provides a novel solution on it. The min-plus algebra is introduced to model transport systems for accessibility analysis. A unified model in the sense of the min-plus algebra for an integrated system with both buses and bicycles is presented to dynamically describe the state transitions of passengers in the system. A new accessibility is proposed with regards to a general index $\omega $ such as the geographical distance and the travel time. A necessary and sufficient condition on the accessibility is then provided. The minimization of bicycle stations under the accessibility is formulated to be a 0–1 integer programming problem. The case studies on two cities, Ningbo and Hangzhou, were performed, which show that compared with the current layouts of urban transportation networks, the proposed public bicycle sharing systems have remarkable advantages in topological characteristics and robustness against failures. Note to Practitioners—This paper reports a practical solution for station allocation for public bicycle sharing systems (PBSSs). PBSSs have increased tremendously in recent years and become popular in many countries. They complement the bus and subway systems and contribute to better environment and lifestyle. On the other hand, they cause some serious issues with their planning and operations. The station allocation for PBSSs is one of its fundamental challenges as it greatly affects investment and running costs as well as customer satisfaction. Note that the station allocation for PBSSs should be addressed based on a unified dynamic model taking into consideration the transition of passengers, PBSS, and urban public transportation system together. Thus, a dynamically synthesized, physically realizable, and satisfactory solution for station allocation of PBSSs is significant for the success of practitioners. This paper proposes a framework to analytically obtain the station allocation of bicycle sharing systems based on a new accessibility criterion associated with detailed planning requirements and on a hybrid min-plus model corresponding to an integrated public transportation system. Furthermore, an algorithm for obtaining the minimum number of bicycle stations is presented for ease of actual implementation in applications and demonstrated with numerical simulation on the systems in two cities, Ningbo and Hangzhou. It should be pointed out that our optimization formulation is indicative, and alternative formulations with other objective functions and constraints are possible. But, the proposed accessibility as the most fundamental constraint of transportation systems should be included in any formulation.