# Toward Efficient Mobile Electric Vehicle Charging under Heterogeneous Battery Switching Technology
## 3 System Model
### Heterogeneous BSS Selection Concerning BS Reservation and Load Balancing across BSS
#### 3.4.2 Selection of BSS Phase for BS Service  
Here, the selection logic of BSS for \(R_{V}\) is performed by GC. Typically, the current EV reservation and average waiting to switch (ATS) at each BSS across the network is computed by Equation (2). This is to identify the ones which have a minimum waiting time. \[T_{1}=N_{V}\cdot T_{ST} \tag{2}\]  
where \(T_{1}\) refers to \(A_{t}\) (average waiting time of vehicle at each BSS) and \(N_{v}\) represents number of vehicle at BSS. In addition, a \(T_{ST}\) is switching time of single vehicle which is \(\approx\)3-5 min. * Upon sending reservation request from \(R_{V}\), each BSS check that the required \(B_{type}\) is readily fully charge available (line 8 and 9 in Algorithm 1) only if requested battery (\(R_{battery}\)) is available across the network. \begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Description** \\ \hline \(U\) & Set of total vehicle \\ \hline BSS & Battery Switching Station \\ \hline \(R_{battery}\) & Requested Battery \\ \hline \(R_{V}\) & Requested Vehicle \\ \hline \(Q_{Bary}^{\text{End}}\) & Queue of Depleted Battery \\ \hline \(M_{8}^{\text{G}}\) & Maximum number of battery stock \\ \hline ATS & Available Time for switch \\ \hline \(NOL-MSSCA\) & Nonlinear Online Maximum Sensitivity selection Based Charging Algorithm \\ \hline \(R_{f}^{\text{G}}\) & Buffer Time \\ \hline EST & Estimate Total Time \\ \hline \(E_{\text{reg}}^{\text{Con}}\) & Estimate Energy Consumption \\ \hline \(t_{i}\) & Initial Time \\ \hline \(t_{f}\) & Final Time \\ \hline \(R_{e}\) & Battery recharging Time \\ \hline \(T_{1}\) & Estimate Switching Time \\ \hline \(T_{2}\) & Estimate Arrival Time at BSS \\ \hline \(T_{3}\) & Extra Time for Uncertainty \\ \hline \(T_{ST}\) & Switching Time \\ \hline \(N_{V}\) & Number of Vehicle \\ \hline \(C_{entry}^{L_{T}}\) & Current Battery Energy Level \\ \hline \(E_{\text{des}}^{\text{Low}}\) & Expected Charging Time of drained battery \\ \hline \(M_{entry}^{\text{G}}\) & Maximum Battery Energy Level \\ \hline \(V\) & Velocity \\ \hline \(a\) & Charging Power \\ \hline \(\gamma\) & Energy Consumption Per meter \\ \hline \(d\) & Distance \\ \hline \(r\) & position Vector \\ \hline \(r_{\text{ESS}}\) & Position Vector of BSS \\ \hline \(r_{V}\) & Position Vector of vehicle \\ \hline \(M_{8}^{\text{G}}\) & Maximum Stock availability of Battery \\ \hline \(W_{v}\) & Overall Waiting Time of each Vehicle in BSS \\ \hline \(P_{j}\) & Number of charging Pole for recharging Battery \\ \hline \(V_{\text{O}}\) & Queue of Requested Vehicle \\ \hline \(L_{a}\) & Line of Depleted Battery recharging Queue \\ \hline \(RSS_{j}\) & Total number of BSS in the Network \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of notation. * If required \(B_{type}\) is available fully charge in \(BSS_{j}\), the selected BSS calculates its waiting time and maximum number of stock availability (\(M_{B}^{S}>0\)) (line 10 and 11 in Algorithm 1). If none of the \(BSS_{j}\) across the network with the required battery type is available, the GC selects the one which has a minimum value of expected waiting time to switch (EWT). That is, the vehicle has to wait at BSS until the required type of battery is not fully charged in case of \(M_{B}^{S}=0\). Key factors that contribute to the computation of switching the battery of vehicles is the estimation of waiting time to switch (\(W_{T}^{S}\)), expected arrival time of the requested vehicle (\(R_{vt}^{arr}\)) at BSS and Estimate Total Time to Switch (EST) to achieve Available Time for Switching (ATS) at BSS. However, such computation can be achieved easily at local BSS based on current status of charge (\(C_{SOC}\)) upon arrival of EV if on-going charging secession, ATS and at the station is obtained. Thus, computation is generally done when EV is on-the-move mode because the actual situation at the selected station can be quite difficult to obtain before arrival at the station. Therefore, the estimation of ATS is defined below.