# QoS-Aware Scheduling Algorithm Enabling Video Services in LTE Networks
## 4 Proposed PrOEXPRule Scheduler Design
### Proposed Optimisation Exponential Rule (PrOEXPRule) Scheduling
The estimation of average transmission throughput Rf corresponding to the F flow and real-time throughput for user equipment corresponding to the \(k\) TTI subchannel is expressed as:  
\[\text{Rf}\left(t\right)=0.8\ \text{Rf}\left(t-1\right)+0.2\ \text{Rf}(t), \tag{11}\]  
\[\eta=\text{Rf}\left(t\right)-t, \tag{12}\]  
\[e=\text{exp}\ ((-\eta)/\text{Rf}(t)), \tag{13}\]  
\[J=\frac{1}{\eta}*[1-e*(\frac{\eta}{R(t)}+e)], \tag{14}\]  
For every scheduling interval, the user-specific HOL packet delay distance \((dp_{k}(t))\) is calculated; basic QCI characteristics are used to determine the maximum allowable packet delay and loss. Packet delay data is useful, as it can be used to meet delay and loss requirements (delay limit and HOL delay) along with CQI; user prioritisation is performed on the basis of the nearer-to-deadline approach. \[dp_{k}(t)=T_{k}-D_{k}(t)\ \ \ \ \ k\forall K, \tag{15}\]  
where \(T_{k}\) and \(D_{k}(t)\) denote the delay limit and HOL packet delay for the k user corresponding to time \(t\). Scheduling is performed to serve the user with the least \(dp_{k}(t)\):  
\[W=\text{argmin}dp_{k}(t)\ \ \ \ \ \ \ \ k\forall K, \tag{16}\]  
The best RB value (largest real-time downlink CQI metric provided by the user) \(q_{i,max}(CQI_{k,n})\) is identified from the RB set. User data is transmitted on the RB and the \(dp_{k}(t)\) value is updated. Subsequently, the chosen RB is eliminated from the available RB list. The \(k\) user corresponding to the nth RB has a resource allocation identified by \(a_{k,F}\). The feasible data rate \(r_{k}\) corresponding to the k user's subframe is expressed as:  
\[M_{i,k}=max_{i}\ M_{i,k}, \tag{8}\]0  
Under the following assumptions:  
* An RB will be provided to a user if \(a_{k,F}=1\) and \(a_{k^{\prime},F}=0\ \forall\ k^{\prime}\
eq k\);
* \(D_{k}(t)\) denotes the HOL packet delay corresponding to time \(t\) and user \(k\), and \(D_{k}(t)>dp_{k}(t)\ \forall\ k\);
* \(J_{k}(t)\) denotes the packet jitter corresponding to the transmission at time \(t\) and user \(k\). As the proposed PrOEXPRule technique aims to take into account the QoS factor in the functioning of video services, the metric for transmission is expressed as:  
\[M_{i,k}=max_{i}\ M_{i,k}, \tag{8}\]1  
This expression defines the objective function for the overall achievable data rate for the current TTI. Algorithm PrOEXPRule (Algorithm 1)  
```
1 input
2\(k\) // user equipment count;
3\(N_{th}\) // number of resource block RB\({}_{s}\);
4\(r_{k}\) // data rate required for user k;
5\(P_{k}\) // priority index n for user k (0 or 1);
6\(ar\) ///RB\({}_{s}\) available for serving each user;
7\(N_{k}\) //estimated number of RB\({}_{s}\) required by each user;
8\(D_{k}\) // head of line delay per user k;
9\(T_{k}\) // delay threshold per user k;
10\(\lambda_{j}\) // arrival data rate for each user;
11\(\mu_{j}\) //service time;
12\(r_{k}\) //achievable data rate;
13 ARp//RB\({}_{s}\) allocated to non-priority users;
14 ARnP//average channel gain;
15\(j\) // jitter for each packet unit j;
16 initialisations;
```  
**Algorithm 1**The proposed PrOEXPRule Scheduling.