# Multi-Step Traffic Speed Prediction Based on Ensemble Learning on an Urban Road Network
## 1 Introduction  
Various types of vehicles have pushed human society forward by making the mobility of people and goods possible, providing faster and more comfortable travel experience, facilitating social interactions, and so on. Nevertheless, the rapidly increasing number of vehicles has also brought some severe problems into worldwide cities. Apart from consequences like global warming and fossil fuel depletion, traffic congestion is one of the most negative effects that can be perceived by each traffic participant and it can inevitably result in a series of problems, such as traffic accidents, energy overconsumption, and significant travel delay [1]. In 2017, INRIX released the Urban Mobility Scorecard Annual Report, which showed that traffic congestion was a significant challenge in a large number of major cities around the world. According to this report, urban Americans spent a total of an extra 8.8 billion hours and purchased an extra 3.3 billion gallons of fuel because of congestion in 2017, giving a direct congestion cost of $166 billion [2]. Transportation and traffic researchers believe that the Intelligent Transportation Systems (ITS) is a promising solution to improve transportation management and can provide much better services that can eventually lead to less congestion than traditional methods [3, 4]. Among such services, traffic prediction plays an important role in ITS because forecasting information can be utilized to support traffic guidance, signal optimization, and so on. For example, travelers can re-plan their traveling paths to avoid congestion and incidents, which could save their time and cost by using the forecasting information, such as traffic speed, travel time, and traffic condition [5]. Morever, accurate and timely speed prediction have also been key issues in traffic prediction horizon, even in the ITS horizon. Correspondingly, it has led to an intensive body of works about traffic speed prediction in the recent years.  
However, some major challenges about short-term traffic forecasting have been pointed out as follows [6; 7]:  
1. Traffic prediction based on spatial-temporal characteristics.
2. Further exploration of Artificial Intelligence (AI) in traffic flow prediction.
3. Multi-step prediction for real-life ITS applications to provide relatively long-term future traffic situation for road users and government.  
Based on the aforementioned issues, a novel multi-step speed prediction model is proposed by considering spatial-temporal dependencies and using ensemble learning. The developed method separates original data into mean and residual time series, and then employs direct strategy and the ensemble learning framework of stacking algorithm to multi-step-ahead forecast the residual time series. Main contributions of this paper are listed as follows:  
1. A novel multi-step prediction with detrending and direct strategy is achieved by the ensemble learning model of stacking (DDSELM) to forecast travel speed using spatial-temporal characteristics.
2. The proposed multi-step model is validated by using a very large field dataset of hourly average link traffic speed, which reveals it has good performance.  
The remaining part of this paper is organized as follows: In Section 2, a summary of the state-of-the-art research in exploring traffic speed prediction is presented. Then, Section 3 formulates a new multi-step prediction model with ensemble learning. Subsequently, a field dataset of Zhongshan, China, is employed to validate the effectiveness of our model in Sections 4 and 5, respectively. Finally, the conclusion and future work are presented in Section 6.