## 6 Conclusions  
Planning an EBL in big cities can effectively improve the travel time reliability of bus passengers. This paper proposes a reliable and practical method to optimize EBL locations in order to improve travel time reliability on a network, considering the realistic transit demand dynamics. Conclusions are summarized as follows:  
1. The indicator based on buffer time is defined to quantify the transit passenger travel time reliability, which is composed by passenger reliability preference and time volatility. Comparing the traditional methods of traffic models, the methodology proposed in this paper uses statistical modeling and fitting analysis to evaluate travel time and reliability, based on actual AVL data. Data are collected from bus lines that are operating on the EBL of the Third Ring Road in Beijing during peak hours. Calculation results show that unit expectation and standard deviations of travel time are 1.59 min/km and 1.15 min/km, respectively, which can be important parameters to reflect the fluctuation of passenger travel time reliability in the optimization model.
2. A relatively complete framework of a reliability-based EBL location optimization model is established, and is composed of the EBL location and demand assignment optimization. The transit passengers' dynamic choices are considered under different EBL location schemes. A two-stage solution algorithm on the basis of iteration is designed to solve the nonlinear programming model. To solve the complex nonlinear problem, a linearization method is proposed by cutting tangent lines on the concave curves.
3. To validate the model's quality and robustness, the case study is analyzed in Beijing. Results show that the best-performing bus lane locations mainly depend on travel demand, road structure, and traffic conditions. For the network of bus passengers and private car passengers, the best EBL location scheme resulting from the proposed model can evidently improve the travel time reliability by 5.5% in the case study. In addition, comparing with other cities that have applied the EBL like Los Angeles, Beijing has more business districts and office areas, and commuters have higher requirements for the reliability of bus systems. Therefore, the implementation of an EBL can better improve the service level of the public transportation system within the area of highly concentrated demand. It will attract more passengers to choose the bus for commuting.  
There are two main limitations in this paper. First, the impacts from other transportation modes, such as shared bicycles, electric bicycles, and pedestrians, are not considered. Second, the case study in the paper needs to be extended to transit networks with a larger scale. Those limitations need to be improved in future research.  
Conceptualization, W.K.; Methodology, W.K.; Software, W.K.; Validation, W.K.; Formal analysis, W.K.; Investigation, W.K.; Resources, S.Z.; Data curation, W.K.; Writing--review and editing, L.P.; Visualization, W.K.; Supervision, W.K. and F.L.; Project administration, W.K.; Funding acquisition, W.K. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China, grant number 52402413, and the Fundamental Research Funds for the Central Universities, grant number 3122025037.  
Not applicable.  
Data Availability Statement: The data used to support the findings of this study are included within the article. The original GPS and passenger OD data cannot be provided in order to protect the personal privacy of passengers under the regulation of the third-party company.  
The authors declare no conflicts of interest.