# A Comparative Study on Traffic Modeling Techniques for Predicting and Simulating Traffic Behavior
## 4 Spatiotemporal Traffic Prediction Models
### Summary of Spatiotemporal Traffic Prediction Models  
Having discussed the concepts of the previous models and how they were used in various traffic modeling studies, constructing a comparison to evaluate different aspects of each model will help to decide which one is more suitable for our research. The comparison was restricted to evaluating the predictive accuracy, computational complexity, and evaluation criteria (see Table 1). In terms of prediction accuracy, ST-Kriging prediction accuracy relies on the covariance matrix to produce data samples that are highly correlated. Therefore, defining the correct correlation function in the correlation matrix is important for obtaining an accurate prediction. The Gaussian correlation function and Matern correlation function are two of the most commonly used correlation functions in the correlation matrix in the ST-Kriging method. To identify the best correlation function, estimation tools are required to estimate the correlation function parameters, such as maximum likelihood estimation (MLE) and semivariogram estimation [44]. However, these tools suffer from a number of challenges. In the case of using semivariogram estimation, a plotted semivariogram will be given to determine the appropriate function parameter. Yet, the process of optimizing semivariogram estimation requires deep knowledge of the ST-Kriging approach. On the other hand, maximum likelihood estimation requires a large sample size to identify the correct function parameters. Additionally, the distance between the spatial points in each sample needs to be small [45]. These factors affect the prediction accuracy and need to be taken into consideration when applying the ST-Kriging approach in traffic prediction. Another point to consider is the computational cost of the model, where in ST-Kriging, the computational complexity will be estimated based on the number of data spatial points \(N\). When having a large number of spatial points, the covariance matrix becomes more complex, and thus detecting correlation in space and time becomes more complex as well [46]. In addition, ST-Kriging methods require high training times with a computational complexity of \(O(N^{3})\)[47]. This leads to the conclusion that the overhead cost of the ST-Kriging methods is represented in the high complexity when computing \begin{table}
\begin{tabular}{p{12.3 pt} p{12.3 pt} p{12.3 pt} p{12.3 pt} p{12.3 pt}} \hline \hline  & **Bayesian Inferences** & **ST-Kriging** & **ANNs** \\ \hline
**Computational Complexity** & NP-hard. [41] & \(O(N^{2})\). & \(O(i\times o\times n+n\times o)\) or \(O(n\times o\times(i+1))\) for training a single epoch [42]. \\ \hline
**Performance Evaluation** & Provides a posterior probability distribution with confidence interval. & Ensure linear unbiased predictors. & Epoch with the lowest sum of squared error. \\ \hline
**Weaknesses** & Very computationally intensive due to choosing the proper prior distribution. & \(\bullet\) & Missing value causes error in unmatched dimensions. \(\bullet\) & Requires intensive data training, and this might lead to an overfitting problem. \\ \hline
**Strengths** & \(\bullet\) & Handles large and small data. \(\bullet\) & Handles small data. \(\bullet\) & Handles big data and small data. \(\bullet\) & Accommodates missing values without a separate estimation step [43] \\ \(\bullet\) & \(\bullet\) & Prior knowledge about uncertain input is not required. & \(\bullet\) & Computational efficiency. \(\bullet\) & Computational efficiency due to the parallelity feature. \(\bullet\) & Prior knowledge about uncertain input is not required. \\ \hline
**Overcoming the Limitation** & Use uninformative prior to reducing the computational time, but it can affect the prediction accuracy negatively. & Remove observations that include missing values. & \(\bullet\) & Decrease the number of layers in the network. \(\bullet\) & Use iterative methods to stop the training process such as gradient descent. \\ \hline \hline \end{tabular}
\end{table}