# Renewable Energy-Based Energy-Efficient Off-Grid Base Stations for Heterogeneous Network
## 2 System Architecture and Mathematical Modeling
### Resource Scheduling Algorithm  
A resource scheduling algorithm attempts to make an appropriate apportionment of the resources with fulfilling application-wise QoS requirements. Some general requirements are optimized with spectral efficiency ensuring cell throughput, fairness, minimum interference for cell-edge users, and optimum load balancing. PF is one of the well-known schedulers, especially for NRT applications. It deals with two competing qualities, and not only maximizes the total throughput of the network but also ensures at least a minimal level of service. However, better latency, user energy efficiency, and application wise priority cannot be assured by PF. LTE establishes separate resource blocks (RBs) for RT and NRT applications. The RT application includes voice, live streaming video, and online gaming. The NRT application includes buffered streaming video, web browsing, e-mail, chat, FTP, and P2P file sharing. The BSs are fully conscious of the bearers. In our proposed model, the available resources are divided into two parts for the use of RT and NRT services depending on the data rate demand of the users. For RT applications, resources can be scheduled using the existing VT-M-LWDF scheduler, M-LWDF scheduler, or any other popular solution that considers the packet delay. In the proposed model, the main focus has been given on NRT applications. A weighted proportional fair (WPF) scheduling algorithm has been proposed for NRT applications; where the DRX mechanism has been applied, weight will be determined based on the applications and queue size. \[\text{WPF metric}=\text{WF}\times\text{PF metric} \tag{20}\]  
\[\text{WF}=A_{k}(t)\times Q_{k}(t)\times T_{y}^{Inac} \tag{21}\]The amount of pending data or queue size \(Q_{k}(t)\) can be used to indicate the data rate requirement. \(A_{k}(t)\) represents the priority of the user applications. \(T_{y}^{Imac}\) is the inactivity timer that represents the way of power-saving for the resource allocation. In the case of the downlink (DL), the queue size \(Q_{k}(t)\) is already known to BS. On the other side, the UE sends the pending data status or buffer status report (BSR) to the BS in the case of uplink (UL). BSR index represents the buffer content in between a minimum and a maximum range. In our proposed model, \(Q_{k}(t)\) is the average of the maximum and minimum buffer size, as follows:  
\[Q_{k}(t)=\frac{BS_{k}^{min}(t)+BS_{k}^{max}(t)}{2} \tag{22}\]  
The DRX mechanism is incorporated in LTE to attain power-saving and prolonged battery life of the UE. Algorithm 1 is proposed only for NRT applications, so that significant improvement in power saving attained the allowing limited latency. In the algorithm, a novel DRX model has been proposed. NRT applications can support more delay than RT applications. According to [60], a permissible delay for NRT applications after the re-transmission delay is 107 ms. UE has to be in the 'ON' state all the time even if there is no traffic. It is because UE has to keep listening or be ready to decode the Physical Downlink Control Channel (PDCCH). The Physical Downlink Control Channel (PDCCH) is primarily used to carry the scheduling information to individual UEs, i.e., resource assignments for uplink and downlink data and control information. However, continuous ON state increases battery consumption drastically. DRX is a solution to address this problem. Algorithm 1 describes the proposed communication procedure between BS and NRT applications. We assumed an M/G/1 queue, where the packet arrival rate (\(\lambda\)) follows the Markovian process (Poisson process), and the service rate (\(\mu\)) follows a general distribution. Traffic intensity can be calculated from \(\rho=\lambda/\mu\). To calculate the percentage of power saving, we have used the following equation, which has been modified from [61].