## Appendix A Fundamentals of CNN-LSTM Networks  
To further clarify the Section 4, we provide a brief overview of CNN and LSTM networks, which are integral to the Machine Learning-Based Prediction Unit in the MMS-DSR approach.  
A CNN is a type of Deep Learning model that excels at processing grid-like data structures, such as images or traffic data. CNNs use convolutional layers to automatically learn spatial hierarchies of features from input data. In the MMS-DSR protocol, CNNs are employed to extract spatial features from traffic data (e.g., vehicle positions, speed, and density).  
CNNs operate by applying a set of learnable filters (or kernels) to the input data. Each filter slides over the input matrix, performing a convolution operation, which results in a feature map. These feature maps capture the local spatial patterns of the input data.  
For example, if we have traffic data from \(K\) locations at multiple time instances, the input to the CNN layer can be represented as a matrix \(S\), where each element corresponds to the traffic state at a specific location and time, as shown below:  
\[S=\begin{bmatrix}s_{1,t-N}&s_{1,t-N+1}&\cdots&s_{1,t-1}\\ s_{2,t-N}&s_{2,t-N+1}&\cdots&s_{2,t-1}\\ \vdots&\vdots&\ddots&\vdots\\ s_{K,t-N}&s_{K,t-N+1}&\cdots&s_{K,t-1}\end{bmatrix}\]  
The CNN applies filters to this matrix to generate high-level spatial feature maps, capturing patterns and relationships in the traffic data. The result is passed to the next stage of processing: the LSTM network.  
LSTM networks are a type of RNN designed to handle sequential data and capture temporal dependencies. They are particularly effective at learning long-term relationships in time-series data, which makes them ideal for predicting future traffic states based on past observations.  
LSTM networks consist of specialized units (LSTM cells) that regulate the flow of information through input gates, forget gates, and output gates. These gates allow the network to remember or forget certain pieces of information over time, making LSTMs robust in handling time-dependent data.  
In the context of MMS-DSR, LSTM networks process the spatial features extracted by the CNN to learn temporal patterns in traffic data. The high-level spatial feature map **X**, obtained from the CNN, is fed into the LSTM for sequential processing. The LSTM generates predictions of future network states (e.g., latency, bandwidth, and reliability) based on this input.  
The hybrid CNN-LSTM model used in MMS-DSR combines the strengths of CNNs and LSTMs to extract both spatial and temporal features from traffic data. The CNN first captures spatial patterns in the data, while the LSTM captures the temporal evolution of these patterns over time.  
The spatial feature map output by the CNN is denoted as follows:  
\[X=\begin{bmatrix}x_{1}\\ x_{2}\\ \vdots\\ x_{L}\end{bmatrix}\]  
where \(X\) represents the spatial features, and each \(x_{l}\) corresponds to the feature at time \(t\). This spatial feature map is then fed into the LSTM to capture temporal dependencies. The final output of the CNN-LSTM model is used to compute the predictive reliability score \(P_{prediction}(r,t)\), which plays a crucial role in the MMS-DSR multi-metric scoring function.