Volume 2, Issue 1, ICCK Transactions on Systems Safety and Reliability
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ICCK Transactions on Systems Safety and Reliability, Volume 2, Issue 1, 2026: 3-10

Free to Read | Research Article | 29 January 2026
Reliability of Coupled Subway and Bus Networks under Uncertainty
1 School of Economics & Management, Beijing Forestry University, Beijing 100083, China
2 School of Economics & Management, Beijing University of Technology, Beijing 100124, China
3 School of Management Science and Engineering, Central University of Finance and Economics, Beijing 100081, China
* Corresponding Author: Di Wu, [email protected]
ARK: ark:/57805/tssr.2025.612115
Received: 27 October 2025, Accepted: 05 November 2025, Published: 29 January 2026  
Abstract
In urban public transport networks, subway and bus systems complement each other and together form a coupled system that serves passenger travel. However, a disturbance in either subsystem can propagate through coupling nodes across the entire network, thereby reducing overall operational efficiency. Most existing studies focus only on the reliability of a single mode, and few have analyzed the overall reliability of the system while considering the coupling relationship between the two. To address this gap, this paper proposes a probabilistic evaluation model to assess the reliability of the subway and bus coupling system. System reliability is defined as the probability that the network can meet all passenger demand given uncertain demand and limited road and rail capacity. The model accounts for passengers’ travel behavior of “prioritizing the subway” and, by sequentially computing the load on each road section, the subway’s share, and the remaining bus load, determines whether the system is reliable under a given demand combination. This provides an effective quantitative tool for the planning and optimization of integrated urban transportation systems.

Graphical Abstract
Reliability of Coupled Subway and Bus Networks under Uncertainty

Keywords
reliability
coupled subway and bus system
demand uncertainty
capacity constraints
subway priority behavior

Data Availability Statement
Data will be made available on request.

Funding
This work was supported without any funding.

Conflicts of Interest
The authors declare no conflicts of interest.

AI Use Statement
The authors declare that no generative AI was used in the preparation of this manuscript.

Ethical Approval and Consent to Participate
Not applicable.

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Cite This Article
APA Style
Gao, K., Yu, R., Zhang, S., & Wu, D. (2026). Reliability of Coupled Subway and Bus Networks under Uncertainty. ICCK Transactions on Systems Safety and Reliability, 2(1), 3–10. https://doi.org/10.62762/TSSR.2025.612115
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TY  - JOUR
AU  - Gao, Kaiye
AU  - Yu, Rongquan
AU  - Zhang, Sicheng
AU  - Wu, Di
PY  - 2026
DA  - 2026/01/29
TI  - Reliability of Coupled Subway and Bus Networks under Uncertainty
JO  - ICCK Transactions on Systems Safety and Reliability
T2  - ICCK Transactions on Systems Safety and Reliability
JF  - ICCK Transactions on Systems Safety and Reliability
VL  - 2
IS  - 1
SP  - 3
EP  - 10
DO  - 10.62762/TSSR.2025.612115
UR  - https://www.icck.org/article/abs/TSSR.2025.612115
KW  - reliability
KW  - coupled subway and bus system
KW  - demand uncertainty
KW  - capacity constraints
KW  - subway priority behavior
AB  - In urban public transport networks, subway and bus systems complement each other and together form a coupled system that serves passenger travel. However, a disturbance in either subsystem can propagate through coupling nodes across the entire network, thereby reducing overall operational efficiency. Most existing studies focus only on the reliability of a single mode, and few have analyzed the overall reliability of the system while considering the coupling relationship between the two. To address this gap, this paper proposes a probabilistic evaluation model to assess the reliability of the subway and bus coupling system. System reliability is defined as the probability that the network can meet all passenger demand given uncertain demand and limited road and rail capacity. The model accounts for passengers’ travel behavior of “prioritizing the subway” and, by sequentially computing the load on each road section, the subway’s share, and the remaining bus load, determines whether the system is reliable under a given demand combination. This provides an effective quantitative tool for the planning and optimization of integrated urban transportation systems.
SN  - 3069-1087
PB  - Institute of Central Computation and Knowledge
LA  - English
ER  - 
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@article{Gao2026Reliabilit,
  author = {Kaiye Gao and Rongquan Yu and Sicheng Zhang and Di Wu},
  title = {Reliability of Coupled Subway and Bus Networks under Uncertainty},
  journal = {ICCK Transactions on Systems Safety and Reliability},
  year = {2026},
  volume = {2},
  number = {1},
  pages = {3-10},
  doi = {10.62762/TSSR.2025.612115},
  url = {https://www.icck.org/article/abs/TSSR.2025.612115},
  abstract = {In urban public transport networks, subway and bus systems complement each other and together form a coupled system that serves passenger travel. However, a disturbance in either subsystem can propagate through coupling nodes across the entire network, thereby reducing overall operational efficiency. Most existing studies focus only on the reliability of a single mode, and few have analyzed the overall reliability of the system while considering the coupling relationship between the two. To address this gap, this paper proposes a probabilistic evaluation model to assess the reliability of the subway and bus coupling system. System reliability is defined as the probability that the network can meet all passenger demand given uncertain demand and limited road and rail capacity. The model accounts for passengers’ travel behavior of “prioritizing the subway” and, by sequentially computing the load on each road section, the subway’s share, and the remaining bus load, determines whether the system is reliable under a given demand combination. This provides an effective quantitative tool for the planning and optimization of integrated urban transportation systems.},
  keywords = {reliability, coupled subway and bus system, demand uncertainty, capacity constraints, subway priority behavior},
  issn = {3069-1087},
  publisher = {Institute of Central Computation and Knowledge}
}

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