# Bus Travel Time Prediction Based on the Similarity in Drivers' Driving Styles
## 1 Introduction  
With the increasing number of urban vehicles, traffic congestion and air pollution have become major problems in many cities. One of the important ways to solve urban traffic problems is to prioritize the development of public transportation and reduce the number of private cars used by commuters. The key to the development of public transport is providing good transport services for passengers. It is very important to provide accurate bus travel time information to passengers, which can help travelers plan their trips and reduce waiting time [1, 2]. However, due to the complex urban transportation environment, accurately predicting bus travel time is very difficult. Multiple factors can affect the travel time of buses, such as changes in passenger flow, traffic conditions, the time period of operation, the driver's driving style, weather factors, etc. [3, 4]. These factors lead to great uncertainty in bus travel times [5]. Due to a lack of sufficient data, some of these influencing factors are difficult to quantify, and it is difficult to establish a model that includes all of the factors that affect travel time [6, 7]. For example, existing research does not consider the influence of differences in drivers' individual driving styles on bus travel times. Because each bus is driven by different drivers, the level of driving, driving experience, and driving habits of each driver are different, which has a significant impact on the travel time of buses [3, 7]. For example,when passing the same road section, a driver with an aggressive driving style will likely arrive at the next stop earlier than the scheduled time, a driver with a steady driving style will likely arrive at the next stop on time, and a driver with an overly gentle or cautious driving style will very likely arrive at the next stop later than the scheduled time. Therefore, the difference in travel time caused by differences in driving style increases as the distance traveled increases. As a result, a bus that departs later will gradually catch up with a bus that leaves earlier, resulting in a crowding of buses. This phenomenon is called bus bunching [8], as shown in Figure 1, supposing that the driving style of bus driver a is too gentle, the driving style of bus driver b is more steady, and the driving style of bus driver c is more aggressive. Their departure times are 10 min apart, but differences in driving styles lead them to meet at the 12 th stop. This phenomenon disrupts the regularity of bus operations. Regularity is the main indicator of service reliability since it is the main determinant of passenger waiting times [9]. Bus bunching is not conducive to passengers being able to the bus on time and affects the enthusiasm of passengers towards taking the bus. With the rapid development of GPS positioning technology, big data technology, and machine learning technology, the differences in bus travel time caused by drivers' individual driving behaviors can be found regularly as long as sufficient data are obtained. Figure 1: Bus bunching illustration. This article aims to introduce the factor of the driver's driving style into the bus travel time prediction model through a study of the driving styles of city bus drivers. This is helpful for bus operators to promptly correct the impact of drivers' styles of driving on travel time according to the prediction results, thus reducing the bus bunching phenomenon. To effectively distinguish the driving styles of different drivers, this article first introduces the bus driver driving style judgment model based on hierarchical clustering technology, groups the historical travel time data of different drivers, and then uses the corresponding travel time prediction model to predict bus travel time. The main contributions of this paper can be summarized as follows.