Interval prediction of short-term traffic speed with limited data input: Application of fuzzy-grey combined prediction model

Highlights

• Generation of upper and lower bound series of traffic speed.

• An improved grey autoregressive model is constructed.

• Interval prediction of short-term traffic speed.

Abstract

Short-term traffic speed prediction, including level and interval prediction, is a key component of proactive traffic control in the intelligent transportation systems (ITS). In particular, predicting intervals may provide traffic managers with more useful information for making reasonable decisions than predicting traffic levels. In this study, a combined model (FIG-GARM) of fuzzy information granulation (FIG) and grey autoregressive model (GARM) is proposed for the prediction interval (PI) of traffic speed. In order to investigate the performance of the FIG-GARM model, using real-world traffic speed data collected from an urban freeway in Edmonton, Canada, and the proposed FIG-GARM model is compared with the interval-grey model first order single variable (GM (1,1)), FIG-GM (1,1), and interval-GARM for PI of traffic speed. The results show that the FIG-GARM model can generate workable PI of the traffic speed, proving the validity of the proposed model. In addition, the PI of traffic speed obtained by FIG-GARM model has higher prediction interval coverage probability (PICP), narrower width interval (WI), and higher index P, which can provide decision support for the robust and accurate prediction of intelligent transportation systems.

Introduction

Nowadays, urban traffic congestion has attracted attention for the operation of transportation systems around the world. In targeting this issue, many solutions have been provided to alleviate traffic congestion, where proactive systems are very effective (Cheng, Gau, Huang, & Hwang, 2012). Specifically, for proactive systems, a highly accurate prediction of short-term traffic parameters (i.e., flow, speed, occupancy, travel time) is a critical component. Compared with other traffic parameters, traffic speed can more directly reflect the traffic operation status. Moreover, the accurate prediction of short-term traffic speed is more helpful for implementing real-time traffic proactive control strategy (Pan, Sumalee, Zhong, & Indra-payoong, 2013). Past literatures on short-term traffic speed prediction are level prediction, which can only directly predict the average value of the traffic speed based on a series of historical data. However, the performance and accuracy of traffic speed level prediction often be influenced by various uncertainty factors such as weather, incidents, and driver behaviors. Thus, we need a forecast result that can reflect the uncertainty in traffic speed. Specifically, the prediction interval (PI) result can just deal with the uncertainty of traffic speed. Moreover, the accurate prediction interval (PI) of traffic speed can provide more useful information for traffic managers to make reasonable decisions. Therefore, it is also considered a significant concern for the development and implementation of the proactive traffic control systems in the future.

In general, most of the literatures on traffic speed prediction focuses on level prediction, and there has been little research on PI over the past decade. However, more and more scholars have studied the PI of traffic parameters recently. The conventional approaches for PI can be classified into two categories. One is that the PI can be obtained by using the analytical expression to calculate the variance or standard error of variables. For example, the generalised autoregressive conditional heteroscedasticity (GARCH) model, as one of the primary methods, is to obtain the PI results according to the variance error of variables, where the variance error of the variables can be obtained based on the probability density of level prediction results (Andersen, Bollerslev, Christoffersen, & Diebold, 2006). The other is that the upper and lower bounds of PI can be directly obtained by using the lower/upper bound estimation (LUBE) method (Quan et al., 2014).

It is necessary to point out that the above PI methods have higher requirements on the data sample size. However, it is difficult to get large amounts of data for some countries and regions, such as India, due to automated sensors and associated database are being implemented or damaged (Badhrudeen, Raj, & Vanajakshi, 2016). Moreover, such PI methods for short-term traffic parameters have not been developed or tested rigorously with limited data input. Thus, a PI method of short-term traffic parameters based on less data demanding would be more attractive. The grey prediction theory proposed by Deng (1989) provides a way to generate PI under limited data condition. The principle of the grey prediction interval algorithms is to first divide the original data series into upper and lower interval data series, then the PI results can be obtained by forecasting the upper and lower data series respectively. For instance, the grey straight horn band (GPBI) model proposed by Liu and Lin (2006) uses the general straight line to produce the upper and lower data series, and the grey interval prediction model proposed by Chen and Liu (2017) constructed a linear regression function to divide the original data series into two groups. These grey PI models select a simple method of data classification, which will cause a loss of information in the whitenization process. In this way, the results of PI for short-term traffic parameters are less reliable.

Currently, fuzzy theory provides a way of conducting the range values of data series. In this regard, fuzzy information granulation (FIG) is widely used for generating upper and lower interval data series, and this method also can maintain the integrity of the original data without losing any data information (Lu, Chen, Pedrycz, Liu, & Yang, 2015). Therefore, the FIG method can be used to generate the dispersion range of short-term traffic speed data series. The objective of this study is to propose a short-term traffic speed forecast interval system based on the FIG method and the grey prediction model with limited input data. However, the traditional grey prediction model cannot predict the traffic speed series very well because of the random fluctuation features of the traffic speed series. Furthermore, the model does not consider the characteristics that the current traffic speed is generally affected by past traffic conditions. Thus, this paper applies a grey autoregressive model (GARM) to predict the traffic speed, which adds an autoregressive mechanism based on the grey model. In order to verify the effectiveness of the proposed FIG-GARM model for prediction interval of traffic speed time series, the real-world traffic speed data from an urban freeway corridor in Edmonton are taken as the experimental data. The interval-grey model first order single variable (GM (1,1)), FIG-GM (1,1) model, and interval-GARM model are used as comparison models to investigate the PI performance for traffic speed series by calculating the performance indicators, including prediction interval coverage probability (PICP), average width interval (WI), and index P.

The rest of this paper is organized as follows. Section 2 introduces the briefly literature; the proposed model system is described in Section 3; Section 4 gives an empirical case to investigate the PI performance of the proposed model; finally, Section 5 proposes conclusions.