# Exclusive Bus Lane Allocation Considering Multimodal Traffic Equity Based on Bi-Level Programming
## 6 Conclusions  
In this paper, the EBL network design problem considering equity is proposed and a bi-level programming model is constructed. The upper-level model is the EBL programming model, and the lower-level model is the SUE model based on logit loading. An improved GA-MSA heuristic algorithm is proposed to solve the model. Finally, taking [PERSON] and [PERSON] networks as examples, the following conclusions are drawn:  
(1) Effectiveness: The heuristic algorithm converges to the 600 iterations. The optimal solution of the upper-level model is 15,004 RMB, and the total system cost is 49,917 RMB. The Gini coefficient is 0.31, and the equity is at a reasonable level. The number of EBLs allocated is six, which are links \(a_{4}\), \(a_{6}\), \(a_{7}\), \(a_{10}\), \(a_{12}\) and \(a_{14}\).  
(2) Superiority: By comparing and analyzing the four different EBL allocation schemes, the allocation scheme considering equity we proposed has a higher bus sharing rate. Although the total system cost is not the lowest, the Gini coefficient is the smallest and the optimal solution of the upper-level model is the smallest. Therefore, from the perspective of social equity, the optimized EBL allocation scheme is more in line with the actual situation.  
(3) Demand level sensitivity: With the increasing demand for travel, the bus sharing rate shows a trend for increasing first and then decreasing, and the Gini coefficient shows a trend for decreasing first and then increasing. At that time, the bus sharing rate is the largest (65%), whereas the Gini coefficient is the smallest (0.3); at this time, the allocation of the EBLs is the most ideal.  
(4) Traveler type sensitivity: Due to the different attractions of cars and buses to different time value travelers, cars are more attractive for high time value travelers, whereas buses are opposite to this. When the proportion of high time value travelers increases, the optimal allocation scheme adds links \(a_{5}\) and \(a_{15}\). When the proportion of low time value travelers increases, link \(a_{10}\) is reduced so that only one bus line \(l_{2}\) passes.  
Although this paper considers two travel modes of cars and buses and the Gini coefficient is added to the upper-level objective function, there are still the following deficiencies, which can be further studied in the future:  
(1) In this paper, the impact of multi-mode traffic, such as autonomous driving and electric buses, is not fully considered. Although the right to use EBLs in this article is limited to buses, carpooling travelers, taxis, etc., can also use EBLs in some cities. How these kinds of vehicles will affect the distribution of EBLs is also worthy of study.  
(2) This paper designs a GA-MSA heuristic algorithm and verifies its effectiveness and feasibility in small-scale road networks. However, in practice, it is more about large-scale road networks. It is crucial to introduce modern technologies, such as multi-criteria decision analysis (MCDA) [36], agent-based modelling [37], large neighborhood search (LNS) and so on, to find approximate optimal solutions for large-scale networks.  
**Author Contributions:** Conceptualization, X.L.; methodology, J.W. and C.W.Y.; software, X.L. and S.Z.; writing--original draft preparation, X.L. and S.Z.; writing--review and editing, J.W. and C.W.Y.; project administration, J.W. All authors have read and agreed to the published version of the manuscript.  
This research was funded by National Natural Science Foundation of China (52172338) and Shaanxi Province 2023 Natural Science Basic Research Plan Project (2023-JC-YB-332).  
**Data Availability Statement:** Not applicable.  
The authors declare no conflict of interest.