# Exclusive Bus Lane Allocation Considering Multimodal Traffic Equity Based on Bi-Level Programming
## 1 Introduction  
To alleviate road traffic congestion, many cities implement a policy of transit priority by constructing exclusive bus lanes (EBLs). For example, in China, more than two hundred cities, including Beijing, Shanghai, Shenzhen and Xi'an, have constructed EBLs [1]. On the one hand, it can make buses enjoy the right of priority access. The travel time of buses can be reduced by about 18%, and the waiting time at the station will be reduced by about 12% [2]. On the other hand, by allocating one or more mixed lanes as EBLs, the driving of other non-bus vehicles will be restricted and driving times will be increased. This can induce some travelers to choose public transportation, which is conducive to alleviating urban traffic congestion to some extent. However, EBLs will increase the delay of other social vehicles while ensuring the priority of buses [3]. How should we allocate EBLs to balance the right of road between buses and other social vehicles? In addition, considering the traveler's trip mode choice and path choice [4], how do we fairly allocate these limited road resources to heterogeneous travelers? Therefore, the allocation of EBLs is a complex optimization problem [5]. In recent years, research on the reasonable allocation of EBLs has become more and more abundant. At present, the research on EBLs can be roughly divided into two categories. One is based on microsimulation models, using simulation software to simulate different parameter settings through measured data. For example, [PERSON] et al. [6] obtained the changes in road indexes before and after allocating EBLs through the mathematical theory modeland VISSIM simulation. [PERSON] et al. [7] evaluated the benefits of EBLs on the MATLAB and VISSIM simulation platforms. [PERSON] et al. [8] used VISSIM microscopic simulation software and additional modules of VisVAP and EnViVer to represent the operation of EBLs. [PERSON] et al. [9] used microscopic simulation models to evaluate traffic operations under different demand levels and bus share ratios. [PERSON] et al. [10] used PTV Vissim software with an additional logic script to control the DBL (dynamic bus lane) activation. [PERSON] et al. [11] determined the parameters of mathematical models of the delay time of private and public transport for various parameters of the bus lane, the length of the bus stop loading area and its distance from the signalized intersection through imitation microscopic modeling. The other type is based on macro analysis models, and the impact of EBLs is analyzed by actual cases. It is attributed to the network design problem (NDP). Generally, the network design problem (NDP) of urban transportation refers to an optimal investment decision problem [12]. The research of the NPD can be divided into planning before EBL allocation and evaluation after EBL allocation. For planning, the bi-level programming model is mainly used. The upper-level model aims to optimize the system-level objectives (e.g., maximizing the traffic network consumer surplus [13], minimizing the total travel time of traffic network users [14], minimizing the equilibrium travel cost [15], etc.). The lower-level model aims to maintain user equilibrium by considering the user's response to the EBL allocation scheme (e.g., stochastic equilibrium assignment under multimodal traffic modes [16], passenger flow assignment model based on minimum generalized travel cost, multimodal traffic network equilibrium model, capacity-constrained traffic assignment model [17], etc.). The bi-level programming model belongs to the NP-hard problem, and its solution process is very complicated. So, it is difficult to find an accurate and effective global optimal algorithm. The current solution methods are mainly divided into two categories: linear bi-level programming algorithms (e.g., pole search algorithm, branch and bound method and penalty function method, etc.) and nonlinear bi-level programming algorithms (e.g., genetic algorithm, simulated annealing algorithm, particle swarm optimization algorithm, etc.).