## 2 System Model
### Proactive-Energy Saving Optimisation Based CO\({}_{2}\) Reduction  
For a wireless network performance evaluation, the state-of-the-art is to analyse RAN components at system level where multiple components in a typical BS contribute to power consumption depending on traffic load profiles. These components include power amplifiers, back-haul links, amplifier efficiency, signal processing and generation, air conditioning and others. The following equation is to be considered. \[BS_{\rm t}= S\left[\left(\frac{A_{\rm Tx},P_{\rm Tx}}{\gamma_{\rm eff}}\right)+ P_{\rm tr}+P_{\rm rd}+P_{\rm rg}+P_{\rm rc}+P_{\rm ro}\right]+P_{\rm 1}+P_{\rm ra}\, \tag{5}\]  
where \(S\) is the number of sectors in a cell, \(A_{\rm Tx}\) is the number of antennas transmitting per sector, \(P_{\rm Tx}\) is the input power of the antenna and \(\eta_{\rm eff}\) is the power amplifier efficiency, with transceiver \(P_{\rm tr}\), digital signal processor \(P_{\rm rd}\), signal generator \(P_{\rm rg}\), AC-DC converter \(P_{\rm rc}\), back-haul link \(P_{\rm r}\), air conditioning \(P_{\rm ra}\) and other BS components \(P_{\rm ro}\). Given the movement of all passengers in the next tuple with future movement estimated location \(L\in M_{k+\bar{k}}\), we aim to devise cell switching mechanism for SCs in the next interval as \(k+\bar{k}\) in order to control overall energy consumption of the framework. The On-Off switching schedule would comply with coverage KPI and QoS requirements of each UE to be at its estimated next move \(L\in M_{k+\bar{k}}\) while ensuring each BS loading constraints. The total instantaneous power being consumed by a cell is the sum of transmit power and circuit as [28]:  
\[P_{\rm tot}=\rho\big{(}BS_{\rm t}\.P_{\rm cir}+\lambda\.P_{\rm t} \big{)}+P_{\rm HetNet}, \tag{6}\] \[P_{\rm HetNet}=P_{\rm mc}+\sum\limits_{k=2}^{K}P_{\rm sc}^{k}\ \ \forall= \left\{ \begin{aligned} P_{\rm mc}&=BS_{\rm t}^{ \rm mc}+\lambda_{\rm mc}P_{\rm tx}^{\rm mc}\\ &\\ P_{\rm sc}^{k}&=BS_{\rm t}^{\rm sc}+\lambda_{\rm sc}P_{\rm tx }^{\rm sc}\,\end{aligned} \right.\]  
where \(P_{\rm tot}\) represents total instantaneous cell power; \(P_{\rm cir}\) is the constant circuit power which gets drawn when a BS in a given cell \(c\) changes its state from being active to sleep mode while reducing significant power; \(P_{\rm t}\) represents cell transmit power; \(\lambda\) is the load variable that depends on the capacity of the cell, the indicator variable \(\rho\) defines the On-Off state of BS in cell \(c\); \(P_{\rm HetNet}\) is total HetNet power consumption that employs one MC and nine SCs in our case; and \(P_{\rm mc}\) and \(P_{\rm sc}^{k}\) are the power consumptions of MC and K-th SCs, respectively, with \(k=\{2,3,4,..,n\}\) the number of SCs surrounded by a MC. Energy savings leveraging the performance metrics defined by Energy Consumption Ratio (ECR) [8, 29] is one way to quantify cell energy behaviour in \(Joules/bit\), given as:  
\[ECR=\int_{c}\ \frac{P}{\sum\limits_{U\in c}\ B^{u}(w)\.f(\gamma_{u})}\, \tag{7}\]  
where \(f(\gamma_{u})\) denotes a function that returns user's \(u\) achievable spectral efficiency at a given SINR, \(B^{u}(w)\) is the user specific bandwidth and \(P\) is the amount of power consumed. The SINR \(\gamma_{u}\) at future movement estimated location \(M_{k+\bar{k}}\) when associated with a cell \(c\) defined as the ratio of a user's reference signal received power \(RSRP_{u}\) from a cell \(c\) to the sum of all cells \(i\) RSRPs such that \(i\subset C\) with the noise \(N\).