Short term traffic flow forecasting using artificial neural networks

Abstract

Keywords: Traffic; forecast; artificial neural networks; SARIMA.

1. Introduction

Short-term traffic flow forecasting is one of the most known topics in the intelligent transportation systems. Traffic flow is usually forecasted by using historical and real-time data. With the emergence of Internet of Things (IoT) and therefore the rapid increase of data sources, realistic and effective solutions can be presented for short-term traffic problems. Real-time traffic flow data is collected from a wide range of data sources such as GPS, street cameras, social networks and online maps. Traffic congestion, which is the most known traffic problem and causes material and immaterial damages, has a substantial effect on citizens living in the cities. If the traffic congestion can be forecasted before it happens, it can be easy to take precautions in short term. Therefore, using the real-time traffic flow data and effective forecasting algorithms the damages of the traffic congestions can be reduced. In this case, the forecasting models that provide the most effective and accurate results can provide substantial benefits. In this study, we propose ANN models for the traffic flow forecasting depends on historical data. Seasonal Autoregressive Integrated Moving Average (SARIMA) method is also implemented to compare the performance of ANN implementation. Moreover, statistical analysis of the historical data is presented. The rest of this paper organized as follows. Some of the related literature about traffic flow forecasting will be reviewed in Section 2. ANN and SARIMA

Corresponding Author: e-mail: zierzurum@eskisehir.edu.tr, tel: (222) 335 05 80 405

Z.I. Erzurum Cicek, Z. Kamisli Ozturk / Sigma J Eng & Nat Sci 9 (4), 405-414, 2018

methods will be given briefly in Section 3 and 4 respectively. In Section 5, information about the datasets, statistical analysis of the data and the computational results will be explained. Finally, the results and the future works will be discussed in Section 6.

2. Literature Review

There are many different kinds of forecasting studies in traffic. In the literature traffic flow, volume, demand, speed, peak traffic volume, number of accidents, duration and severity of accidents are tried to be forecasted. Traffic volume, meteorological information, season, speed rate, vehicle type, age and gender of driver, information about road such as surface, slope and type, the type of accident, the cost of fuel and highway toll are some of the parameters which are used for the forecasts mentioned. In this study, the literature about traffic flow forecasting in recent years is examined. To forecast the traffic flow, Abadi et al. [1] used an autoregressive model and least squares method using current and historical data. Annunziato et al. [2] proposed a hybrid modeling approach which combines Artificial Neural Networks and a simple statistical approach in order to provide a one hour forecast of urban traffic flow rates. In a similar manner, Chan et al. [3] developed a neural network based on an exponential smoothing method to enhance previously used neural network for traffic flow forecasting. Hosseini et al. [4] proposed a novel short-term traffic forecasting model using Multi-Layer Perceptron with Mutual Information and Feature Selection approach. Hou [5] focused on traffic flow forecasting in leisure farm areas using ANNs. In order to forecast real-time traffic flow state, Lu et al. [6] presented a simulated annealing genetic algorithm based fuzzy c-means algorithm. Lv et al. [7] presented a novel deep learning-based traffic flow method for traffic flow forecasting. Matas et al. [8] proposed a dynamic model to forecast traffic flow for tolled motorway in Spain. Moretti et al. [9] presented a hybrid model, which combines ANN, and a statistical approach in order to provide a one-hour forecast of urban traffic flow rates. Oh et al. [10] proposed an urban traffic flow forecasting system using a multifactor pattern recognition model, which combines Gaussian mixture model clustering with an ANN. For short-term traffic forecasting, Zhao et al. [11], proposed a long short-term memory (LSTM) network and also presented a novel algorithm which contains ARIMA algorithm [12]. Do et al. presented a survey about short-term traffic state prediction using network-based methods [13]. As seen from the literature, ANN models are proposed for traffic flow forecasting in general. In this study, we used two ANN models and seasonal ARIMA as a classical time series model to test the performances of these implementations on considered datasets. One of the models was developed with the classical backpropagation algorithm and the other model was implemented using Keras. The backpropagation algorithm was chosen because backpropagation is the most common technique used to train ANNs [13]. Also, Keras uses backpropagation when calculating the weights of ANN interconnections. In literature, there are relatively a few studies [14,15,16] about traffic forecasting in which Keras was used to implement neural networks. Since it is important to get fast and accurate forecasts in traffic, we thought that Keras could provide successful forecasts thanks to its features such as fast, easy-to-implement, modular and developable. Therefore, in this study, we aimed to show the strength of this implementation for studied traffic flow datasets.

3. Artificial Neural Networks

Inspired by biological systems, particularly by research into the human brain, Artificial Neural Networks (ANN) are able to learn from and generalize from experience. ANN provide an attractive alternative tool for both forecasting researchers and practitioners [17]. ANN is one of the commonly used method for forecasting and also used for pattern recognition, clustering,

Short Term Traffic Flow Forecasting using Artificial … / Sigma J Eng & Nat Sci 9 (4), 405-414, 2018

classification and optimization etc. Basically, a supervised learning approach is conducted in forecasting by ANN. An ANN model basically consists of an input layer, a hidden layer and an output layer. Each layer is comprised of neurons that process the input signals and produce an output, while connections between the layers have a weight factor. ANN easily adjusts to any set of inputoutput patterns and through a robust training process forms a model function with the minimum possible error [18]. A basic ANN model is given in Figure 1.

Figure 1. A basic ANN model Backpropagation algorithm is the most famous algorithm, which is used for training of the feed-forward ANNs. The backpropagation algorithm looks for the minimum of the error function in weight space using the method of gradient descent. The combination of weights, which minimizes the error function, is considered to be a solution of the learning problem [19].

4. Autoregressive Integrated Moving Average Method

ARIMA is a famous forecast approach, which first introduced by Box and Jenkins [18]. In ARIMA models a non-stationary time series is made stationary by applying finite differencing of the data points [20]. As the parameters of ARIMA, p, d and q are integers greater than or equal to zero and refer to the order of the autoregressive, integrated, and moving average parts of the model respectively. The ARIMA model turns into to seasonal ARIMA (SARIMA) model when there exist seasonal factors. A seasonal autoregressive notation (P) and a seasonal moving average notation (Q) will form the multiplicative process of SARIMA as (p,d,q)(P,D,Q) s where s shows the length of seasonal period [21]. A time series {𝑍𝑡 |𝑡 = 1, 2, … , 𝑘} is generated by SARIMA (p,d,q)(P,D,Q)s is given in Equation (1) [22]: 𝜙𝑝 (𝐵)Φ𝑝 (𝐵 𝑠 )(1 − 𝐵)𝑑 (1 − 𝐵 𝑠 )𝐷 𝑍𝑡 = 𝜃𝑞 (𝐵)Θ𝑄 (𝐵 𝑠 )𝜀𝑡

where p, d, q, P, D, Q are integers, s is the season length; 𝜙𝑝 (𝐵) = 1 − 𝜙1 𝐵 − 𝜙2 𝐵2 − ⋯ − 𝜙𝑝 𝐵𝑝 , Φ𝑃 (𝐵 𝑠 ) = 1 − Φ𝑠 𝐵 𝑠 − Φ2𝑠 𝐵2𝑠 − ⋯ − Φ𝑃𝑠 𝐵𝑃𝑠 , 𝜃𝑞 (𝐵) = 1 − 𝜃1 𝐵 − 𝜃2 𝐵2 − ⋯ − 𝜃𝑝 𝐵𝑝 and Θ𝑄 (𝐵) = 1 − Θ𝑠 𝐵 𝑠 − Θ2𝑠 𝐵2𝑠 − ⋯ − Θ𝑄𝑠 𝐵𝑄𝑠 are polynomials in B of degree p, q, P, and Q. B is the backward shift operator, and 𝜀𝑡 is the estimated residual at time t. d is the number of regular differences, D is the number of seasonal differences; Zt denotes the observed value at time t, t = 1, 2, ..., k.

Z.I. Erzurum Cicek, Z. Kamisli Ozturk / Sigma J Eng & Nat Sci 9 (4), 405-414, 2018

5. Computational Experiments

In this study, Eskisehir, Turkey and London are selected as testbeds. The traffic flow datasets of London Highways [23] include the data collected every 15 minutes from GPSs on the links between specific roads. Similarly, the traffic flow datasets of Eskisehir were collected every 15 minutes from specific intersections using fish-eye cameras. Both of the datasets include the flow counts of different types of vehicles individually (car, bus, minibus, pickup/panelvan/truck, tramway, bicycle, motorcycle etc). The 30 days of London traffic flow data and the 4 days of Eskisehir traffic flow data can be accessed and total flow values for each 15 minutes period are calculated. To determine the variation of the time series, coefficient of variation is also calculated for each dataset. A coefficient of variation (CV) is a statistical measure of the dispersion of data points in a data series around the mean. The coefficient of variation represents the ratio of the standard deviation to the mean, and it is a useful statistic for comparing the degree of variation from one data series to another, even if the means are drastically different from one another [24]. The size and coefficient of variation of each dataset are given in Table 1 below. As seen from Table 1, the variation of London datasets is quite high. Table 1. The size and CV of datasets Dataset

London1 London2 London3 London4 London5 Eskisehir1 Eskisehir2 Eskisehir3

In addition, regression analysis was conducted to examine the trend in London datasets. The trendlines are determined and evaluated statistically for each dataset. Figure 2 and the results of regression analysis clearly show that there is no trend in London1 and London2 and slight trendlines are detected in London3, London4 and London5. Traffic flow is usually periodic, and the cycle is usually one day. Mostly, the peak hour of traffic is usually in the morning and late afternoon. The peak hour of traffic is usually in the early morning and late afternoon. The traffic flow variation trend of different days is usually similar. As a result, the seasonal property is a factor that can be considered [15]. The seasonal effect can be also observed in the datasets shown in Figure 2 prominently. In order to evaluate the performance of proposed ANN method, a SARIMA model is implemented. Since the traffic flow has a seasonal property, a seasonal method is found more suitable for traffic flow forecasting. ANN and SARIMA is implemented using Python version 3.5 with Statsmodels and Keras libraries. ANN is implemented using Keras API with TensorFlow backend. Keras is a high-level neural networks API, written in Python and capable of running on top of TensorFlow, CNTK, or Theano [25]. Statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration [26].

Short Term Traffic Flow Forecasting using Artificial … / Sigma J Eng & Nat Sci 9 (4), 405-414, 2018

Figure 2. The trendlines of London datasets Both of the ANN models have the same architectures. The implemented models have 3 layers: an input, a hidden and an output layers. The number of neurons in the hidden layer is tried as 6,7 and 8 neurons to find a more accurate model using validation dataset. To tune the parameters of SARIMA, a grid search process is applied on (p,d,q) parameters. While the value of parameter p is changed between (0, 1, 2, 4, 6, 8, 10), the parameters d and q are changed in the range of [0,3] for Eskisehir datasets, the parameters p, d and q parameters are changed between 0 and 1 for London datasets because of the long running times. The seasonality parameters (P,D,Q) are fixed as (1,0,0) and the s parameter, length of seasonal period is changed according to dataset. For both of the ANN models, 60% of each dataset is divided into training dataset, while 20% as validation and 20% as test. To validate and test the performance of the forecasting models, mean absolute error (MAE) and mean squared error (MSE) values calculated as using the formula in (2) and (3) respectively where D refers to actual value, F forecasted value and n number of forecasts: 1

Z.I. Erzurum Cicek, Z. Kamisli Ozturk / Sigma J Eng & Nat Sci 9 (4), 405-414, 2018

After training phase, validation and test phase are conducted for both of the ANN models. The MSE and MAE values for 6, 7 and 8 hidden neurons as a result of validation phase is given in Table 2. Table 2. MAE and MSE values of validation phase for the ANN model using Keras n=6 London1 London2 London3 London4 London5 Eskisehir1 Eskisehir2 Eskisehir3

n=7 MSE 124.659 391.451 111.681 19.329 19.288 24.027 3.271 2.721

n=8 MSE 124.685 391.878 111.693 19.455 19.409 24.032 3.279 2.717

MSE 124.702 390.621 111.702 20.460 19.511 24.016 3.277 2.715

At the end of validation phase, the number of hidden neurons is determined specific to datasets. The best test performance values of SARIMA and two ANN models using different parameter sets are given respectively in Table 3. Table 3. MAE and MSE values of obtained forecasts using ARIMA and ANN models

London1 London2 London3 London4 London5 Eskisehir1 Eskisehir2 Eskisehir3

Sarima MAE

MSE 61.043 8229.428 65.261 8913.781 32.665 2101.481 48.472 4660.962 44.757 4783.681 12.466 206.07 8.192 96.958 5.432 44.12

ANN (Keras) MAE MSE 9.877 135.146 15.855 388.271 8.791 120.468 3.937 20.765 3.327 19.007 3.682 14.261 1.927 3.937 1.486 2.404

ANN (Backpropagation) MAE MSE 76.537 10129.27 102.515 18808.136 77.504 12150.098 61.355 6137.646 54.187 6641.898 19.271 523.295 10.346 138.961 5.689 50.823

As seen from Table 2, the ANN model using gives better forecasts than the SARIMA model. Figure 3 and 4 also can be an example for the actual and obtained forecasted values. In parallel with the performance values, it can be seen that ANN using Keras gives more accurate forecasts to actual values than SARIMA from the graphs.

Short Term Traffic Flow Forecasting using Artificial … / Sigma J Eng & Nat Sci 9 (4), 405-414, 2018

Sarima

Figure 3. The comparison of actual and forecasted values for Eskisehir1 dataset London5

0 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 Actual

Sarima

Figure 4. The comparison of actual and forecasted values for London5 dataset Overtraining refers to the time of ANN training that may finally result in worse predictive ability of a network [27]. Therefore, the training process is carefully examined and iteration based graphics for training errors are created. Examples of these graphics are shown in Figure 5. As seen from Figure 5, training errors are decreasing in the training process and this confirms that there is no overtraining problem for ANN models.

Z.I. Erzurum Cicek, Z. Kamisli Ozturk / Sigma J Eng & Nat Sci 9 (4), 405-414, 2018

6. Conclusions

The results of this forecasting study show that the ANN implementation with Pyhton Keras Library can come up with successful and fast results. To determine the efficiency of implemented model, it is needed to make more tests using larger datasets, which includes in streaming real-time data for intelligent transportation systems. As seen from the literature review, the ANN models are enhanced with statistical techniques and evolutionary algorithms. From this point of view, novel hybrid models, which include ANN, can be developed to forecast traffic flow with streaming real-time data for future research. Since Keras is a deep learning library, a deep learning approach for traffic flow forecasting is also planned as future studies. Besides these results, the SARIMA model has been found to be slow with large data, especially when the season length is long. Therefore, a novel SARIMA model can be generated for similar cases. Finally, traffic flow is influenced by lots of parameters in real-life. Meteorological information, type of day, road and vehicle, traffic volume etc. should be taken into account in forecasting studies for traffic flow.

Acknowledgement

This study is supported by Anadolu University Scientific Research Projects Committee (AUBAP- 1709F506).

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