TRAFFIC TIME SERIES FORECASTING BY FEEDFORWARD NEURAL NETWORK: A CASE STUDY BASED ON TRAFFIC DATA OF MONROE

Short time prediction is one of the most important factors in intelligence transportation system (ITS). In this research, the use of feed forward neural network for traffic time-series prediction is presented. In this paper, the traffic in one direction of the road segment is predicted. The input of the neural network is the time delay data exported from the road traffic data of Monroe city. The time delay data is used for training the network. For generating the time delay data, the traffic data related to the first 300 days of 2008 is used. The performance of the feed forward neural network model is validated using the real observation data of the 301st day.


INTRODUCTION 1.1 Motivation of the study
One of the most important activities related to traffic control is the planning for short-term forecasting, an example of which can be the prediction of daily traffic for the next few days.Prediction of traffic can be used to improve the traffic condition and reduces travel time having the available capacity.Prediction system uses the emerging computer, communication and control technologies for managing and monitoring the transportation.Many factors such as weather condition, exhibitions and holidays can affect the quality of the traffic forecasting.One of the prediction methods is the time-series forecasting.In time-series forecasting, the historical data are collected and analyzed to make a model.Then this model is extrapolated for forecasting the future values (Zhang, 2012).

Research objectives
In recent decades, neural networks have been used increasingly for modeling complex phenomena.Neural networks have a high potential to design model and predict the future data compared to traditional time-series models (Balkin and Ord, 2000).This research aims at modeling the time-series forecasting using feed-forward neural network.

Overview of the related work
Many traditional methods are developed for time-series prediction (Ljung and Box, 1978).However, in recent decades, neural networks have often been used for modeling the prediction (Gershenfeld and Weigend, 1994).He and Lapedes (1994) studied the nonlinear time-series by using neural networks.Time-series prediction can be done using both linear and nonlinear methods.Linear method can be implemented and developed easily.Moreover, they are more understandable and interpretable than nonlinear methods.Nevertheless, this methods has limitation: they cannot capture nonlinear relations and their approximation is not as easy as nonlinear ones (Liang, 2005).Medeiros et al. (2001) used neural networks for modeling the linear time-series.de Groot and Würtz (1991) used feed forward neural network for two benchmark nonlinear time-series.Atiya et al. (1999) present a multistep river flow forecasting.Berardi and Zhang (2003) determined the bias and variance issue in time-series forecasting context.Liang (2005) used Bayesian neural networks for time-series analysis.Balkin and Ord (2000) suggested the neural networks for large scale time-series forecasting.Adya and Collopy (1998) reported the application of time-series forecasting by neural networks.

METHODOLOGY
Describing the methodology of this research consists of two main parts.In the first part, the general theoretical foundation of neural networks is described.In the next part, the usage of neural networks for time series forecasting is described.Figure 1 shows the main steps of this research.

Neural network
Neural networks are computing models to compute the process of information.They are useful for recognizing the pattern or relationship between data (Zhang, 2012).A network is a collection of simple structures which together create a complex system.There are different types of networks, all of which are composed of two components: 1.The set of nodes, each node in the network computing unit which performs processing on the input and output obtained.2. Links between nodes which define the connections and the transition of the data between nodes.These connections can be unidirectional or bidirectional.Interaction between nodes through the network connections are presented by a general behavior.Such behavior does not occur alone in any of the network elements.Extensive application of the general behavior on each node makes a network a powerful tool.The neural networks have three segments: input layer, hidden layer and output layer as showed in the following figure.Error back propagation algorithm is a method of network training which modifies the network weights.This method is used in the feed forward Neural Networks.Feed forward means that the outputs of the neurons in each layer are transferred to the next layer.To implement this approach, the network weights are randomly selected then based on input and output data, errors are calculated.Weights are updated in the sense that the calculated errors are minimized.

Using neural network for time-series forecasting
For solving different problems, many type of neural network are developed.For time-series forecasting, the feed forward neural network is mostly used.The following figure represents a feed forward neural network.This kind of neural network is composed of several layers called nodes or neurons.In this network model, there is one input layer and one output layer.The input nodes are used for receiving the data of the past.For the time-series prediction, (yt yt-q … yt-p) are used as inputs.The most important part of the network is the hidden layer.Hidden layer is composed of nodes which are connected to both output and input layers.The output nodes are used for prediction of the future value of the time-series.In the feed forward neural network, the information flow is in one directional.
Where yt is the observed time series value at time t and ɛt+1 is the error term at time t+1.This model shows that the future value of time-series (Yt+1) is a function of the past observations (yt yt-1 … yt-p) with a random error (Zhang, 2012).This kind of models assumes that there is a relationship between future value and the past observation and neural networks are used for identifying this relationship.

Case study and data set
The study area is Monroe city in the state of Louisiana.Monroe is the eighth-largest city of the U.S. For recording the traffic of this city, the data of permanent and temporary stations are used.We used the traffic data of 2008.In addition, the data of permanent station with station-ID 430110 is used.This station records the traffic data each hour.Therefore, 8784 data element is recorded.The following figure shows the location and the specification of the station.

Implementation
Neural network is trained using the data of the first 300 days of the year and the traffic of the 301st day is predicted using this network.We assume that the traffic condition for tomorrow is a function of the traffic of today, yesterday, one week ago, two weeks ago, three weeks ago and four weeks ago at the same time.Therefore, the network has 6 inputs and one output.In this case, the model of equation can be like equation 2.
(2) yt is the observed traffic value of today and yt-1day is traffic data of yesterday and so on and Yt+1day is the traffic of tomorrow.With this assumption, inputs and output of the neural network are like figure 6.In this research, 80% of the data is used for training of network and 20% of the data is used for testing the network.The hidden layer of the neural network has three layers.There are 10 neurons in layer one, 15 neurons in layer two, and one neuron in the last layer.Hybrid tangent sigmoid is used for transfer function.Figure 7 shows the architecture of the neural network.
Figure7.Architecture of the neural network

Result
The mean square error of the training data is 0.0229.Figure 8 shows the procedure of convergence of mean square error of training data.We use this neural network for prediction of the 301st day and compare it with the real number of traffic data as shown in table 1.

CONCLUSION AND DISCUSSION
In this study, feed forward neural network is used for timeseries forecasting of the traffic related to the 301st day of 2008.
We design this neural network for predicting one direction of a road segment.The proposed neural network used the traffic data of today, previous day, one week ago, two weeks ago, three weeks ago and four weeks ago at the same time for predicting tomorrow traffic volume at that time.Some large error can be resulted in the cases of car accidents, bad weather etc.We used above parameters for inputs of neural network.However, to improve the prediction, auto correlation of the data can be derived by some methods like Cochrane-Orcutt.For future work, the traffic of all segments can be predicted.

Figure 2 .
Figure 2.An example of a neural network

Figure 3 .
Figure 3. Feed forward neural networks for time series forecasting This feed forward neural network is functionally equivalent to a nonlinear model, such as the following,

Figure 4 .
Figure 4.The location and specification of the traffic station For our research, we used one direction of the road for timeseries forecasting.The format of data is shown in figure 5.

Figure 5 .
Figure 5 .Format of the traffic data

Figure 6 .
Figure 6 .inputand output data of neural network

Figure 8 .
Figure 8. Procedure of convergence Comparison between the real values of the traffic and the results obtained from the network are presented in Figure 9.The red cycles are the training data and the blue squares are the output training data of the neural network.

Figure 9 .
Figure 9. Results of the neural network for the training dataThe mean square error for the test data which is not used for constructing the network is 0.0345.The results for the test data is presented in Figure10.In this figure, the red cycles are the test data and the blue squares are the output test data of the neural network.

Figure 10 .
Figure 10.Results of the neural network for the test data If the output of the network and the corresponding observed are closed, the network training is acceptable.In other words, if we have a plot with training data on X axis and output of neural network for training data on Y axis, the results are near to diagram y=x, as shown in figure 11.This is true for test data as well, as shown in figure 12.

Table 1 .
Prediction for 24 hours of the 361st day Finally, the root square error between prediction values and actual values is 26.4889 which is acceptable for such a prediction.