## 2 Literature Review  
Vehicles equipped with GPS devices can dynamically provide AVL data containing the real-time location, speed, and time of buses, which have been widely used in the prediction of bus arrival or travel time on the route [9; 10; 11], bus dwell time at the stop [12], the number of boarding passengers [13], the condition of traffic flow [14; 15], etc. Spatial-temporal analysis methods are utilized to figure out where bus bunching happens and explore potential influential factors with the help of AVL data. Statistical methods such as clustering algorithms and sensitivity analysis are usually used to analyze spatial-temporal characteristics, measure the correlations, and group the occurrence of bus bunching into specific patterns [16]. [PERSON] et al. applied the spatial-temporal clustering algorithm to identify hot spots where bus bunching more easily occurs [17]. [PERSON] et al. identified and visualized bus bunching events temporally and spatially to summarize seven attributes for the front bus and six attributes for the following bus, indicating that bus bunching is due to at-stop variation more than between-stop variation [18]. [PERSON] et al. held the opinion that the travel time in particular sections on a roadway follows similar patterns, and spatial clustering algorithms were utilized to identify the group sections with similar characteristics [19]. Furthermore, bus operation is easily influenced by external disturbances, and there are massive and complex potential factors causing bus bunching. For example, [PERSON] et al. first proposed that the impact of bus bunching is not only affected by the initial bus delay but also by passenger arrival rates and bus occupancy rates along the route [1]. [PERSON] et al. argued that unstable traffic conditions and high passenger demands are potential reasons why bus bunching occurs [20]. [PERSON] et al. held the opinion that the influence of the previous bus is the most serious cause and that bus bunching is affected by the front bus more than the following bus [21]. Time series models, regression models, DT, GA, etc. are widely used to model and predict bus travel or arrival time [10; 22; 23; 24] and have been gradually applied to bus bunching problems. [PERSON] et al. utilized decision tree and gene algorithm methods separately to model bus bunching, concluded that decision tree performed better in solving non-linear and complex problems, and determined five factors, namely day of the week, number of left turns, distance to next stop, bus stop closeness, and schedule deviation, to be the most influential factors [25]. [PERSON] et al. built regression models for bus bunching and classified influencing factors into three groups by importance, demonstrating that the sequence of the bus stop, scheduled frequency, and bus dispatch headways are the most significant factors [26]. [PERSON] et al. applied the geographically weighted regression model to bus bunching and took bus stops and network attributes into account, emphasizing the importance of spatial structures [27]. [PERSON] et al. employed duration models for bus bunching events, and results showed that temporal factors and operational characteristics of the initial bus stop had a great impact on the duration of bus bunching [28]. Generally, a planned schedule is adapted for bus routes with low frequency [29; 30]. However, bus routes with high frequency are much more easily affected by abnormal traffic conditions, and the deviation from the planned schedule is more likely to result in bus bunching. Hence, dynamic headway-holding and real-time bus dispatching strategies are proposed based on real-time bus headway and traffic demands. [PERSON] et al. removed the stochastic factors influencing the headway and proposed a target-headway-based holding strategy to stabilize an unstable bus line [31]. [PERSON] et al. proposed prediction-based methods to achieve the best compromise between headway regularity and holding time [32].