关键词: 公交—地铁复合网络, 脆弱性, 换乘关系, 局部效应, 运力和速度差异

Abstract: Combining the metro’s high capacity with bus flexibility,the “metro-led, bus-assisted” model forms the backbone of urban transit. While transfer connectivity enhances travel convenience, frequent transit disruptions often cause localized impacts. Therefore, assessing bus-metro vulnerability based on transfer relationships is vital for improving urban safety, risk prevention, and emergency response.
Existing studies typically evaluate the vulnerability of public transportation systems by considering both structural and functional aspects. Structural vulnerability relies on network topology metrics, while functional vulnerability involves assessing operational characteristics such as passenger demand satisfaction and flow impact. Most studies assess public transportation system vulnerability using accessibility and efficiency metrics. Accessibility reflects basic urban transportation system needs, while efficiency metrics gauge overall operational effectiveness during disruptions. While current research has addressed the impact of capacity disparities between bus and metro stations on system vulnerability, there remains a lack of characterization of fundamental differences in capacity, operating speed, failure rules, and other aspects between bus and metro systems. Additionally, the bus-metro composite network exhibits significant structural heterogeneity and differentiated station functionalities, but existing studies mostly focus on the overall vulnerability of the system, with less attention paid to local considerations. Furthermore, transfer relationships, as the connection bridges of bus-metro composite networks, are of importance. Research on transfer relationships mainly includes transfer efficiency, transfer costs, transfer behavior, and characteristics of transfer stations. However, further in-depth exploration is needed regarding the impact of transfer relationships on the vulnerability of public transportation systems.
This study focuses on assessing the vulnerability of bus-metro composite networks based on transfer relationships, considering local effects and dual disparities. Firstly, by introducing differences in capacity and speed attributes, a detailed representation of the structure of urban bus-metro systems is provided, creating local composite networks with transfer relationships as references. Subsequently, differentiated failure rules for bus and metro networks are defined. Then, considering passengers’ effective travel range and differences in capacity and speed between buses and metros, a multidimensional vulnerability measurement model of network efficiency including accessibility vulnerability, relative capacity-weighted network efficiency vulnerability, and relative distance-weighted network efficiency vulnerability is innovatively established.
The Xi’an bus-metro network, built on transfer relationships, exhibits an uneven structure. Local accessibility vulnerabilities for metro and bus stations are 4.8% and 5.4%, respectively falling between the overall network and sub-network levels. When accounting for capacity and speed disparities, metro transfer failures intensify local efficiency vulnerability, while bus failures show a reduced impact. Notably, local networks with higher metro station proportions are more vulnerable. Analysis suggests that increasing network density and optimizing capacity and transfer relationships can mitigate vulnerability. These findings guide local-level optimization—considering scale, structure, and transfer counts—while future research should use real-world data to identify balanced network designs that maintain accessibility under varying traffic volumes.

Key words: bus-metro composite network, vulnerability, transfer relationships, local effects, capacity and speed disparities