## 4 System Model  
In the SAVP system, there are \(n\) parking stations \(\left(PS\right)_{n}\), where \(n\) is some fixed value, and \(PS\) denotes a parking station, which is located in various locations in a metropolitan city (e.g., we consider the city of Montreal), such that:  
\[\left(PS\right)_{n}=\left\{\left(PS\right)_{1},\left(PS\right)_{2},\ldotsldots, \ \left(PS\right)_{n-1},\left(PS\right)_{n}\right\} \tag{1}\]  
As mentioned, the SAVP system is comprised of three types of parking: MLB, ORP, and OPP, which are the most common types of parking that are mainly offered in metropolitan areas. For simplicity, we assumed the following: \(\left\{\left(PS\right)_{1},\left(PS\right)_{2},\left(PS\right)_{3}\right\}\in \text{MLB}\), \(\left\{\left(PS\right)_{5},\left(PS\right)_{6},\left(PS\right)_{7}\right\}\in \text{ORP}\), \(\left\{\left(PS\right)_{9},\left(PS\right)_{10},\left(PS\right)_{11}\right\}\in \text{OPP}\). Moreover, for each PS type, we supposed that there would be \(e\) number of parking slots \(\left(PL\right)_{e}\), where \(PL\) denotes a parking slot, such that:  
\[\left(PL\right)_{e}=\left\{\left(PL\right)_{1},\left(PL\right)_{2},\ldotsldots,\ \left(PL\right)_{e-1},\left(PL\right)_{e}\right\} \tag{2}\]  
However, depending on the size of each PS, the number of \(PL\) is fixed, such that \(\left(PL\right)_{e-1}\leq\left(PL\right)_{e}\in\left(PS\right)_{n}\), where \(e\) and \(n\) are some fixed values. Each \(PL\) is installed with an RFID reader of the active type and is considered an edge node (\(EN\)) in the SAVP system. For indoor parking, an RFID reader was installed exactly in the middle of a \(PL\), and each \(PL\) was connected to the fog node (\(FN\)) via routers installed to route the information between the \(PL\) and fog node. In the case of outdoor parking, each \(PL\) was also installed with an RFID reader, which could be mounted onto a panel or the pedestrian walkway, and that was assumed to be protected from any atmospheric obstacles. For both types of parking, we assumed that there were no obstacles and/or interference among the installed \(\left(PL\right)_{e}\). In a \(PS\), the \(\left(PL\right)_{e}\) are connected to the \(\left(FN\right)_{t,\ t=t-1}\), where \(t\) is some fixed value. Each \(FN\) is superior at managing the overall parking traffic in a \(PS\) and is connected to a cloud server (\(CS\)), such that a number of cloud servers are represented by \(\left(CS\right)_{i,\ i=i-1}\), where \(i\) is some fixed value. A two-way communication between the \(\left(FN\right)_{t,\ t=t-1}\) and \(\left(CS\right)_{i,\ i=i-1}\) is carried out through GSM-LTE connectivity. Figure 4 illustrates a number of nodes thatwere assumed to have anonymous identifications and that participated in carrying the information in the SAVP system. From Figure 4, we can see that there is an \(FN\) (e.g., \(\left(FN\right)_{1}\)) that contains several edge nodes \(\left(EN\right)_{z,\ z=z-1}\), where z is some fixed value, such that \(\left(EN\right)_{z,\ z=z-1}\in\left(FN\right)_{1}\in\left(PS\right)_{1}\). Therefore, in a \(PS\) (e.g., \(\left(PS\right)_{1}\)), there is only one \(\left(FN\right)_{1}\) connected to a \(CS\). As mentioned, each \(FN\) is fully functional to manage the overall parking operations of a \(PS\); unlike the \(\left(EN\right)_{z,\ z=z-1}\), the \(\left(FN\right)_{t,\ t=t-1}\) are supposed to be installed with enough computation and energy resources to manage the flow of massive traffic in a \(PS\) (for example, from the AV entrance to exit). Likewise, each \(FN\) is also authorized to manage the overall operations and measurements from the \(\left(EN\right)_{z,\ z=z-1}\) in a \(PS\), so that each \(FN\) can manage the operations of the \(CS\) closer to the \(\left(EN\right)_{z,\ z=z-1}\). As per the defined rules, an \(FN\) can only share the information with the designated \(CS\) (for example, \(\left(FN\right)_{1}\leftrightarrow\left(CS\right)_{1}\)). Likewise, \(\left(EN\right)_{z,\ z=z-1}\leftrightarrow\left(FN\right)_{1}\leftrightarrow \left(CS\right)_{1}\).