# Using GPS Trajectories to Adaptively Plan Bus Lanes
## 1 Introduction  
Bus lanes play an important role in mitigating urban traffic congestion, which is a worldwide urban issue [1]. The purpose of building bus lanes is to give the right of way to bus systems and sustainably alleviate urban traffic congestion by attracting potential riders. As early as 1939, the first bus lane system in the world was constructed in Chicago [2]. Since then, due to their superiority in terms of the corresponding transportation capacity, construction cost, and construction period length, such systems have attracted widespread attention and research worldwide and have become widely accepted as a means of alleviating urban traffic congestion [3; 4]. Under the guidance of bus prioritization, increasing numbers of cities have planned bus lanes [5; 6]. For example, in China, more than two hundred cities, including Beijing, Shanghai, Shenzhen, and Nanjing, have constructed bus lanes. Determining how to effectively plan bus lanes has become a new concern, and planning methods that are adaptive to city scales are urgently needed in practice. Considerable effort has been devoted to finding effective methods to plan bus lanes. The existing bus lane planning methods can be approximately divided into two groups: (1) micromodels that focus on the road segment scale or micronetwork links, and (2) macromodels that focus on the actual city scale. In the first group, [PERSON] et al. [7] simulated the impact of the bus lane configuration on the traffic times of buses and cars based on a microscopic traffic simulation model, NETSIM (network simulation), which is a softwarepackage that can microscopically simulate vehicular movements in a street network. The results showed that the derived bus lanes are effective in easing traffic congestion in specific traffic flows. However, this simulation addressed two main arterial roads, and thus requires more experiments in a large city area. [PERSON] et al. [8] implemented a bus lane planning model at the network level. The road capacity and initial travel time were specified according to experience, and the travel time and traffic flow were specified by a road impedance function (a common method used for traffic simulations regarding the traffic flow and travel time). [PERSON] et al. [9] built a multimodal road impedance function for bus lane planning. This approach can be used to obtain the traffic parameters in a multimodal network with complex traveler choice behaviors, including transportation and route choices. Generally, in micromodels, the parameters related to traffic information (e.g., travel time and flows) are obtained by experience or through traffic simulations. Except for a few models used in experiments involving a single urban road, most models have been tested only on an ideal transport network [10]. For example, [PERSON], [PERSON], [PERSON], and [PERSON] [9] tested a model with a simple four-node and five-link network, and [PERSON] et al. [11] used a network with eight nodes and 13 links. Generally, there has been a lack of verification using complex road networks at the city scale. It is extremely computationally expensive to use traffic simulations to obtain detailed traffic parameters covering a large area [8]. Moreover, solving the model involves a complex combinatorial optimization problem that is generally nonlinear and NP-hard (Non-deterministic Polynomial), and the calculation time is unacceptable for large datasets. Thus, those methods cannot yet be adapted to large city scales. In the second group, [PERSON] and [PERSON] [12] built a transport network planning model for an actual road network. The model used a heuristic search to determine the optimal candidate road segments, and the method was tested in Winnipeg, Canada. [PERSON] and [PERSON] [13] designed a multiobjective programming model of bus lanes. The model considered various input parameters, including the traffic flow, travel time, and construction costs.