## 1 Introduction  
With the continuous acceleration of urbanization and the expansion of the urban scale, the number of motor vehicles and the road traffic flow have sharply increased. Especially in some large and medium-sized cities, traffic congestion is very serious, which brings great inconvenience to citizens' travel. Improving the share rate of public transport is an effective way to solve urban traffic problems, establish the dominant position of urban public transportation, and achieve efficient use of limited road traffic resources [1]. In the process of giving priority to the development of public transport, how to ensure the normal and efficient operation of the public transport system depends not only on the conditions of roads, vehicles, and other facilities but also on the progressiveness of operation management means and technical means. To organize the operation of public transport vehicles more scientifically and reasonably, and to help travelers better plan their itinerary and reduce their waiting time, accurate prediction of bus travel time has become an essential key link [2; 3]. The goal of predicting bus travel time is to predict the time it takes for the bus to pass through two points, such as between two stations [3]. The travel time between two adjacent bus stops also includes the time for bus vehicles to queue up at the intersection and wait to pass through the intersection. Therefore, the factors that affect the accuracy of predicting bus travel time are multifaceted, for example, traffic conditions [4; 5], weather factors [4; 6], traffic incidents [7], differences in driver's driving behavior [8], changes in passenger flow [9], etc. These uncertain factors increase the uncertainty of bus travel and arrival time. This will cause bus bunching [10] and negative impacts such as increased bus operating costs and longer waiting times for passengers [11; 12]. In previous studies, various machine learning-based methods have been proposed for predicting bus travel time. However, most previous studies mainly focused on improving the prediction accuracy of the bus travel time point prediction model. The main drawback of the bus travel time point prediction model is that it cannot provide the confidence interval information of the prediction results [13]. For example, when we travel by bus according to the prediction results of the point prediction model, we will encounter the following two situations: (1) if the predicted results are larger than the actual travel time, we will miss the bus. (2) If the predicted result is smaller than the actual driving time, we may need to wait for a long time [8]. Some scholars have proposed that the prediction intervals (PIs) can be used to quantify the uncertainty of bus travel time point prediction. From the perspective of travelers, predicting the possible range of bus travel time is more meaningful than providing only predicted values for a single arrival time point [14]. Usually, the PIs consist of a lower limit and an upper limit, where the true value falls within these limits. In previous studies, PI techniques mainly include Bayesian techniques [15], Delta techniques [14; 15], the bootstrap method [16; 17], and the upper and lower bound estimation method (LUBE) [18]. According to previous research results, when the data set is small, the PIs constructed based on the bootstrap method are usually more accurate [19; 20]. In addition, the travel time of buses varies greatly at a specific time of the day, and there is also a significant difference in traffic volume between different segments of the road, which significantly affects the accuracy of the travel time prediction. At present, most previous studies use the same prediction model to predict the travel time of the whole line. This method can not accurately predict the travel time of different sections in different periods [21].