Evaluation of Recent Computational Approaches in Short-Term Traﬀic Forecasting

. Computational technologies under the domain of intelligent systems are expected to help the rapidly increasing traffic congestion problem in recent traffic management. Traffic management requires efficient and accurate forecasting models to assist real time traffic control systems. Researchers have proposed various computational approaches, especially in short-term traffic flow forecasting, in order to establish reliable traffic patterns models and generate timely prediction results. Forecasting models should have high accuracy and low computational time to be applied in intelligent traffic management. Therefore, this paper aims to evaluate recent computational modeling approaches utilized in short-term traffic flow forecasting. These approaches are evaluated by real-world data collected on the British freeway (M6) from 1 st to 30 th November in 2014. The results indicate that neural network model outperforms generalized additive model and autoregressive integrated moving average model on the accuracy of freeway traffic forecasting.


Introduction
Traffic during peak hours in developed and developing countries is usually congested and such problem is apace rising since the past three decades. Computational technologies particularly intelligent systems are expected to help the rapidly increasing traffic congestion problem in recent traffic management. The use of intelligent systems is an important trend in traffic management, and its objective is to provide innovative services to transportation development and enable various users to better use of transport networks. Advances in computing and communications technologies promote using intelligent systems to manage many problems in transportation, especially the traffic congestion [1][2][3]. Congestion can be reduced by redistributing traffic spatially and temporally. To achieve traffic flow redistribution, it is necessary to get future traffic conditions [4,5]. The authors in [6] also emphasized that it is necessary to continuously forecast the traffic conditions for short time ahead to enable dynamic traffic control. These cause establishing efficient and accurate traffic flow forecasting models to become an important issue in traffic management.
Lieu, et al. [7,8] stated that the way to establish a reliable and efficient intelligent traffic system relies on providing continuous information of the traffic conditions over time. Such traffic information need to be updated in a timely fashion and should generate projections on the expected traffic networks [9]. In the new era of intelligent traffic systems, research has focus on establishing forecasting models to manage the traffic networks [10][11][12]. Many computational approaches have been commonly applied to build forecasting models, such as neural network (NN), generalized additive model (GAM), and autoregressive integrated moving average (ARIMA) [6,[13][14][15][16]. In this paper, above approaches are applied to the traffic data collected on the British freeway (M6) from 1 st to 30 th November in 2014 for evaluation. We evaluate three different approaches and report on their performance. The rest of this paper is organized as follows. Section 2 describes the computational modeling approaches used in this study. Section 3 explains the experimental design. Section 4 discusses the experiment results. Finally, the conclusion is given in Section 5.

Neural Network (NN)
NN is a kind of information processing technique, and it can be trained to learn relationships in a dataset. The NN model has been applied in short-term traffic forecasting for many years, and it has been proven to be effective in solving problems that existing complex relationships, such as traffic flow forecasting [13,[17][18][19]. Since the traffic data with lumpiness may reduce the generalization capability on the short-term traffic flow forecasting on unseen data [20], we applied the exponential smoothing method [21,22] to remove lumpiness in the collected traffic data. After removing the lumpiness, a three-layer feed-forward NN with levenberg-Marquardt algorithm was trained to establish a short-term traffic forecasting model. The traffic data is collected from n sensing stations (S 1 , S 2 , S 3 ,…,S n ), which are located on the freeway (M6). S i captures two traffic condition measures, i.e., the average vehicle speed � ( ) and the average headway ℎ � ( ) between time t and time t+T S , where T S is the sampling time. Future traffic conditions can be forecasted by the NN model, according to the current and past traffic conditions. The current traffic condition is denoted by the current average speed � ( ) and current average headway ℎ � ( ). The past traffic condition is indicated by the past average speed � ( − ) and past average headway ℎ � ( − ), which was collected by Si at time ( − ) with i=1,2,3,…,n and k=1,2,3,…,p, whereas the past traffic data within p sampling time period are collected. The future traffic condition can then be generated by the NN model, which is indicated by ℎ � ( + ) passing through the L th sensing station S L at time ( + ), where future traffic condition with m sampling time ahead is forecasted. The NN model is formulated as: where M is the number of nodes in the hidden layer; Ѱ() is the activation function of the hidden set (sigmoid function is used in this study); , , , ℎ , and 0 are the parameters of the NN model.

Generalized Additive Model (GAM)
The GAM has the ability to allow non-parametric fits with relaxed assumptions between predicted and actual values. With this ability, the GAM can provide better fits to data than purely parametric models. The GAM is based on the additive model (AM), which is a nonparametric regression method that assumes the mean of a response variable depends on predictors by a nonlinear function. The AM relates a univariate response variable to a set of other response variables. The GAM extends the generalized AM which assumes linear dependence, by allowing the dependence of the response variable to be nonlinear [23]. The GAM is generalizing the AM to allow the response variable to follow an exponential family distribution [24,25] along with a link function. Given a data set � , 1 , 2 , … , � =1 of data size n, where and are the i th observations of the traffic flow, the AM is formulated as: where ( ) is a smooth function of the i th observation of covariate j, and is the residual. With a link function G, the GAM can be structured as: where 0 is the intercept that is equal to the overall mean of the [23,25]. In this study, a local scoring algorithm which maximizes a likelihood function is used to estimate the used smooth functions in GAM. Also, the generalized cross-sectional validation approach is used to avoid over-fitting in the short-term traffic flow forecasting.

Auto-Regressive Integrated Moving Average (ARIMA)
The ARIMA model, one of the most popular time series approach applied in traffic flow forecasting, is generally referred as ARIMA (p, d, q), where p, d, and q are non-negative integers [26]. p, d, and q refer to the order of the autoregressive, integrated, and moving average parts of the model, respectively. To empirically create a proper model, we followed the Box-Jenkins ARIMA modeling procedure which consists of the following steps: identification, estimation, diagnostic checking, and forecasting [27]. Through continuous modification, the most proper forecasting model can be generated.
In the identification step, the collected traffic data is assessed to determine whether it is stationary. Autocorrelation function (ACF) and Partial Autocorrelation Function (PACF) are used to detect it [28]. If the collected traffic data is not stationary, the differencing approach is applied. The value d is the lowest order of differencing applied to achieve stationary. The second step is to decide whether AR(p) or MA(q) should be used in the model. According to the ACF and PACF plots of the differenced series, it is possible to tentatively identify the value p and/or q. The error residuals can be calculated when the candidate model ARIMA (p, d, q) is estimated.
The candidate model is further tested by Akaike Information Criterion (AIC) and Schwartz's Bayesian Criterion (SBC) in diagnostic checking step [29]. The lower value of AIC and SBC, the more suitable ARIMA (p, d, q) should be. Q-test is also used to determine whether the estimated model is suitable. If the candidate model cannot pass the test, the process should go back to the identification step to develop a better model. The candidate model which passed diagnostic checking is set as the used ARIMA model in short-term traffic flow forecasting. In the ARIMA model, we predict ℎ � ( + ), the average traffic flow at the L th sensing station S L at time ( + ), where future traffic condition with m sampling time ahead is forecasted based on the past traffic flow condition. The past traffic flow condition is defined as L is the lag operation and the ARIMA model is structured as: where p is the order of autoregressive and q is the order of moving average. and are the parameters of the autoregressive and moving average parts, respectively. are error terms for the stationary distribution.

Experimental Design
The traffic flow data was collected from the British traffic warehouse, and it was captured by ANPR cameras, in-vehicle GPS and inductive loops built into the road surface located between junctions, J40 and J41, of the freeway M6 in the United Kingdom from 1 st to 30 th November in 2014. The main aim of traffic flow forecasting is to help for reducing traffic congestion, therefore the peak traffic period on the business days should be the main target. The traffic time periods are set to 15-minute intervals in the day which also refers to 0 to 95 where 0 indicates 00:00 to 00:15 and 95 refers to 23:45 to 24:00. The collected traffic data was analyzed and it was found all business days had similar traffic headway distribution as shown in Fig. 1. The figure illustrates how the data have daily seasonal patterns, which are periodically repeated. The peak traffic flow condition was occurred in mornings between 7:00 and 9:30 (time period 28 to 37) and evenings between 17:00 and 19:30 (time period 68 to 77) on the business days. To train the models (NN, GAM, and ARIMA) of the selected road section, we excluded weekend traffic data since it has different daily patterns. The total number of days used for evaluation is 20 (business days between 3 rd to 28 th November). The significance level is set to 5% and the confidence interval is 95% in all analyses used in this study. The remained traffic data was divided into two subsets. The data of first subset, namely the training set, was used for establishing the NN, GAM, and ARIMA models. The data of second subset, namely the test set, was applied to evaluate the generalization capability of the trained models. The business days of the first three weeks in November 2014 were set in the training set and the business days of the last week in November 2014 were concluded in the test set. For the time period with 15minute intervals, training data set and testing data set contain 1440 (3*5*96) data and 480 (1*5*96) data, respectively. Since the generalization capability on traffic flow forecasting would be improved by removing the lumpiness from the raw traffic data, we applied the exponential smoothing method to remove lumpiness in the collected data before applying the data to develop proposed models.
In order to evaluate the accuracy and efficiency of the NN, GAM, and ARIMA models, the performance of these models was evaluated by Mean Absolute Percentage Error (MAPE) and Root Mean Square Error (RMSE). MAPE and RMSE indicate the mean and the sample standard deviation of the differences between observed values and predicted values, respectively.

Experiment Results and Discussion
Since the main target in this study is the peak traffic period on the business days, we evaluate the forecast an hour ahead (in the peak traffic period 34 to 37 or 74 to 77) using the models developed in the training phase. The traffic flow conditions on the road section M6-J40 to M6-J41 from the previous one and half hours (in the peak traffic period 28 to 33 or 68 to 73) of the same peak traffic period (morning or evening peak) are used, i.e., the previous 6 records of a peak traffic period are used to predict 4 records ahead during the same peak traffic period. The forecasting models (NN, GAM, and ARIMA) are evaluated in different business days using the testing data set. The forecasted results are compared with real observations in order to know the performance of each model which is evaluated by the MAPE and RMSE. The ARIMA model considers the number of lags to forecast a future value, therefore it is used to forecast the time ( + 2 * ) value. The forecasting performance of NN, GAM, and ARIMA models applied to peak traffic periods of the testing data set are presented in Table 1 and Table 2. For the comparison results displayed in Table 1 and Table 2, we notice that the MAPEs and RMSEs of the NN model are smaller than those of the GAM and ARIMA models during the morning peak and evening peak. Fig.2  Both Tables and Fig. 2 show that the NN model performs much better than the other models as its predicted headway values are close to the observed headway values. Moreover, its MAPE and RMSE values are less than GAM and ARIMA models.

Conclusion
Due to the fact that traffic congestion problem is rapidly increasing, it is urgent to establish intelligent traffic control systems that can redistribute the traffic flow spatially and temporally. In order to reach it, an efficient and accurate forecasting model is necessary to assist real time traffic control systems. Research has applied many computational approaches on short-term traffic forecasting to build forecasting models. While the traffic flow data of a road link can be collected much easier than before, selecting appropriate computational approaches to deal with the demand of forecasting accuracy and efficiency is getting significant. In this paper, we proposed to evaluate some computational approaches in short-term traffic flow forecasting. From the experiment results, we found that on forecasting accuracy, NN model outperforms GAM and ARIMA models on forecasting accuracy of the short-term freeway traffic forecasting.