A space–time diurnal method for short-term freeway travel time prediction
Introduction
Travel time information is an important measure of roadway traffic conditions. It is necessary to obtain accurate travel time prediction since the travel time information is an essential input to Intelligent Transportation Systems (ITS) applications, particularly to the Advanced Traveler Information Systems (ATIS). Because of the highly dynamic and nonlinear nature of traffic condition over time and space, travel time prediction remains a difficult yet important challenge for transportation engineers (Xia et al., 2011). There is a rich body of literature on the development of short-term travel time prediction approaches. Previously, van Lint et al. (2005) categorized the explored techniques into three major strands: model-based approaches (e.g., DynaMIT (Ben-Akiva et al., 2002), DynaSMART (Hu, 2001)), instantaneous approaches (e.g., Zhang and Rice, 2003), and data-driven approaches. So far, many techniques and models developed for short-term travel time prediction belong to the category of data-driven approaches. Examples include generalized linear regression (Zhang and Rice, 2003, Sun et al., 2003), nonlinear time series (Ishak and Al-Deek, 2002), Kalman filters (Chien and Kuchipudi, 2003, Nanthawichit et al., 2003, Chu et al., 2005, van Lint, 2008, Xia et al., 2011), support vector regression (Lam and Toan, 2008), and various neural network models (Park et al., 1999, Rilett and Park, 2001, van Lint et al., 2002, van Lint et al., 2005, van Lint, 2006, Wei and Lee, 2007, van Hinsbergen et al., 2009, Zeng and Zhang, 2013).
Despite a large number of short-term travel time prediction approaches have been developed in the past decade, a few studies take into account spatial and temporal travel time information simultaneously in the prediction model. Such techniques are particularly useful in predicting the freeway link travel times since the traffic condition on the neighboring links can help identify the traffic condition on the target link. Previously, Park and Rilett (1999) examined the artificial neural networks, which have the ability to include the spatial and temporal travel time information in predicting multiple-periods link travel times. Upstream and downstream traffic data have also been considered by van Lint (2006) as spatial inputs in the neural network modeling framework for route travel time prediction. Up to now, some researchers consider the traffic data from several locations in the traffic flow prediction models. Stathopoulos and Karlaftis (2001) examined temporal and spatial variations of traffic flow in urban areas. Williams (2001) proposed a multivariate ARIMA approach that includes upstream sensor data to model traffic flow. Stathopoulos and Karlaftis (2003) developed a state-space approach that uses upstream detector data to improve the predictions of traffic flow at downstream locations. Kamarianakis and Prastacos, 2003, Kamarianakis and Prastacos, 2005 introduced the space–time autoregressive integrated moving average (STARIMA) models for predicting traffic flow conditions in an urban network. Sun et al. (2006) and Sun and Xu (2011) proposed different Bayesian network approaches for traffic flow forecasting, which includes spatial information from adjacent road links. Vlahogianni et al. (2007) used genetically optimized modular networks to obtain spatio-temporal prediction of urban traffic volume. A vector auto regressive model was proposed by Chandra and Al-Deek (2009) to predict freeway speeds and volumes using the spatial information from neighboring stations. Min and Wynter (2011) developed a spatio-temporal method for real-time speed and volume prediction by including the spatial characteristics of a road network. Most recently, Zeng and Zhang (in press) examined the importance of considering spatial and temporal input interactions on improving prediction accuracies. Li et al. (2013) extended the probabilistic principle component analysis based imputing method to utilize the information of multiple points by considering temporal and spatial dependence. Pan et al. (2013) proposed a stochastic cell transmission model framework to consider the spatial–temporal correlation of traffic flow and to support short-term traffic state prediction. In this study, we introduced a space–time diurnal (ST-D) method, which merges the spatial and temporal travel time information to obtain accurate short-term travel time prediction of freeway corridors under different traffic conditions. The proposed approach can take into account important characteristics of travel times: spatial and temporal correlation, diurnal pattern, and the nonnegativity of the travel time. Unlike the neural networks and fuzzy logic methods (van Lint et al., 2002, Zhang and Ye, 2008) which use a “black box” approach to predict traffic conditions and often lack a good interpretation of the model, our method makes use of geographically dispersed travel time observations as predictors to obtain short-term prediction and can yield theoretically interpretable prediction models. In this study, the ST-D method is examined using the travel time data collected on a segment along the US-290 in the Houston area. In addition, previous literature usually does not predict more than a single time point into the future. However, prediction on multiple time periods into the future allows for a wider range of applications to make use of the predictions (Min and Wynter, 2011). Thus, this study also seeks to predict travel time for up to 1 h ahead.
The remainder of the paper is organized as follows. In Section 2, we introduce the travel time data in the study. We describe the data collection site and analyze the temporal and spatial correlation as well as the diurnal pattern observed in the data. In Section 3, we provide two versions of the ST-D model for up to 1-h ahead probabilistic prediction of travel time. We also discuss the strategies for selecting predictors, estimating prediction models and choosing appropriate training periods. In Section 4, we evaluate the prediction performance of the ST-D method and compare the proposed models with two conventional prediction models. In Section 5, we provide the conclusions and some future works.
Section snippets
Site information and data collection
The travel time data used in this study is collected on a westbound segment of the US-290 freeway stretch between I-610 and FM-1960 in Houston, Texas. This segment has an imbalanced traffic flow pattern, where the majority of the commuting traffic in the afternoon peak goes westbound. The westbound traffic during the morning peak is less heavy compared with the eastbound traffic due to the directional traffic pattern. The length of the freeway stretch of interest is approximately 12 miles and
The space–time diurnal method
In this section, we describe the ST-D method, to predict the 5-min travel time. The ST-D approach makes use of geographically dispersed travel time observations as predictors to obtain short-term prediction of travel times. The computational requirements of the proposed approach are not demanding and the technique can be readily implemented in real time. Previously, the ST-D method was used in prediction of wind speed (Gneiting et al., 2006, Hering and Genton, 2010). Link D is chosen as the
Prediction performance analysis
In this section, the prediction performance of the ST-D-TN and ST-D-LN models is evaluated using the travel time data on link D in August. In addition, we also compared the prediction performance between the proposed models and two conventional prediction models. The first conventional prediction model is a commonly used auto regressive model, AR(2), which assumes that the value of the predicted travel time series at time t + p takes a linear, weighted form of the observed travel times at
Conclusions
In this study, we proposed a space–time diurnal method to obtain accurate short-term travel time prediction of a freeway corridor under different traffic conditions. The probabilistic prediction can overcome the drawbacks of the point prediction by fitting a probability distribution (i.e., a truncated normal distribution and a lognormal distribution) to describe the uncertainty of the future travel times. The proposed ST-D-TN and ST-D-LN models consider important features of travel times:
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