Local accessibility of hybrid urban public transportation

An increasing number of cities are implementing public bicycle systems to reduce traffic congestion. How to choose the locations of bicycle stations is one of the key questions in urban public transportation systems (UPTSs). This paper proposes a linear urban public transportation model to describe state transition of passengers in the sense of min-plus algebra. Based on the model, we define the local R-accessibility and obtain its necessary and sufficient condition which can be used to determine the locations of public bicycles. By numerical simulations of the UPTS in Ningbo, China, we find that our result has more advantages than the real situation in comparison with several topological characteristics and network robustness.