## 1 Introduction
[31] traffic streams estimation based on using a Bayesian model was presented where missing historical traffic information was estimated by utilizing a Gaussian blend display to visually verify the traffic data forecast. Various specialists have shown that hybrid methods have better results in terms of accuracy and precision compared with individual techniques [32]. Hybrid methods based on fuzzy logic can be potential alternatives to enhance precision in traffic flow prediction as described in [33] while in [34] a novel method based on neural networks is utilized in traffic time estimation. Artificial neural networks (ANNs) have been widely used for time series prediction problems since their inception in the 1980s. In classical neural networks, training algorithms akin to back- propagation only try to model the dependence of the output from the input. Restricted Boltzmann Machines (RBMs), instead, are networks of stochastic neurons that can be trained in a greedy fashion. Deep belief networks are obtained by stacking RBMs on one another so that the input to one layer is given by the hidden units of the adjacent layer, as if they were data, and adding a last discriminative layer. The RBM, might even yield better results than traditional neural networks with higher accuracy. In a RBN, the hidden units are independent given the visible states. So, they can quickly get an unbiased sample from the posterior distribution when given a data-vector. This is a big advantage over direct belief nets. The multi-layer perceptron (MLP) and radial basis function networks (RBFN) are well-known approaches. Often gradient descent methods are used for training these approaches and back propagation (BP) is used as the learning algorithm [27]. However, there are some limitations of using conventionally shallow ANNs for real world problems such as traffic flow prediction in highways based on VANET-cellular systems. The first issue is related to the design of the ANN topology. It is found that the larger the size of the hidden layer the more prone the model is to overfitting the training data. The second problem is related to deciding the initial value of the ANN weights. BP is a supervised learning method which uses samples of input and output data to modify weights of connections between units (neurons) across the network layers. The appropriate selection of initial weights can increase the speed with which the model is able to converge. Both these problems are amplified when the input parameter space is very large as in the case of traffic flow prediction. Hence there is a need to be able to transform the input parameters into a reduced and manageable feature space with which to construct the prediction model. Equally there is a need to determine the optimal number of hidden neurons for training the model. Finally, the third problem is determining a suitable learning rate during the models training phase. Here there is a need to incorporate an automated way of selecting the most appropriate learning rates as the model is being trained. To solve these problems, we proposed a novel traffic flow prediction model based on DBNs comprised of multiple stacked restricted Boltzmann machine (RBM) auto-encoders. RBMs are networks of stochastic units with undirected interactions between pairs of visible and hidden units which can be used to learn a probability distribution over its set of inputs. By stacking multiple RBMs onto one another DBNs are trained using greedy layer-wise learning which aims to train each layer of a DBN in a sequential and unsupervised way, feeding lower layer results to the upper layers to capture a representational hierarchy of relationships within the training data [10; 11; 12; 13]. Each trained layer represents feature encoders which can be helpful in the discrimination of the target output space. This unsupervised training process can provide an optimal start for supervised training as well as extract and learn a reduced set of features representing the input parameters.