## 3 System Model  
MLWDF is a throughput-optimal scheduling algorithm that considers HOL packet delay, the probability of packet loss and delay threshold along with instantaneous and previous throughput of the user. The scheme is defined by the following Equation (1):  
\[m_{i,j}\textsuperscript{MLWDF}=\frac{-log\delta_{i}}{\tau_{i}}.D_{HOL,i}.\psi_{i,j}, \tag{1}\]  
where  
\[\psi_{i,j}=\frac{r_{i}(t)}{r_{i}(t-1)}. \tag{2}\]  
Here, \(D_{HOL,i}\) denotes HOL packet delay, which is the waiting time between the packet arrival time and the time it is transmitted successfully. \(\delta_{i}\) represents the probability of packet loss and \(\tau_{i}\) is the value of delay threshold. The delay threshold \(\tau_{i}\) for user \(i\) is based on user applications. Table 1 shows the threshold values with priority for different types of data. Here, voice has the highest priority and (Transmission Control Protocol) TCP-based service has the lowest priority. Therefore, the data packet of TCP-based service would be discarded first in a congested queue. The scheduler maximizes the utility function \(r_{i}(t)/r_{i}(t-1)\) for better system performance, which can be defined as weighted transmission rate \(\psi_{i,j}\) in Equation (2). Here, \(r_{i}(t)\) is the instantaneous transmission rate of user \(i\) at transmission time interval (TTI) \(t\) and \(r_{i}(t-1)\) is the previous average transmission rate. Time \(t\) is removed from the rest of the paper to reduce the complexity. For convenience, Table 2 shows the symbols used in this paper. This paper defines the QoS requirement of the user by considering the HOL delay. The delays of the users with different applications must be kept below a predefined value for successful packet transmission. Therefore, the QoS requirement can be defined as follows: \begin{table}
\begin{tabular}{c c c} \hline \hline
**Types of Data** & **Delay Threshold (ms)** & **Priority** \\ \hline Gaming & 50 & 3 \\ Conversational Voice & 100 & 2 \\ Live Video streaming & 100 & 7 \\ TCP-based (HTTP, FTP) & 300 & 8 \\ \hline \hline \end{tabular} TCP: Transmission Control Protocol; HTTP: HyperText Transfer Protocol; FTP: File Transfer Protocol.  
\end{table} 
Table 1: Delay threshold value for different types of data [23]. \begin{table}
\begin{tabular}{c c} \hline \hline
**Symbol** & **Definition** \\ \hline \(i\) & user \\ \(j\) & RB \\ \(t\) & time (TTI index) \\ \(r_{i}\) & instantaneous transmission rate of user \(i\) \\ \(D_{HOL,i}\) & HOL Delay of user \(i\), RB \(j\) \\ \(\delta_{i}\) & probability of packet loss of user \(i\) \\ \(\tau_{i}\) & delay threshold of user \(i\) \\ \(\Omega\) & radius of the inner region \\ \(R_{i}\) & distance from the eNB to user \(i\) \\ \(S_{i}\) & probability from failure rate to success rate of user \(i\) \\ \(\epsilon_{i}\) & the error probability of user \(i\) \\ \(\tau_{ij}\) & received SINR of user \(i\), RB \(j\) \\ \(\zeta_{ij}\) & channel gain from serving eNB of user \(i\), RB \(j\) \\ \(P_{ij}\) & transmit power of serving eNB for user \(i\), RB \(j\) \\ \(I\) & inter-cell interference \\ \(\sigma\) & white noise power spectral density \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Symbols used in the paper. \[Pr\{D_{HOL,i}>\tau_{i}\}\leq\delta_{i}. \tag{3}\]  
Equation (3) states that the probability of HOL delay of exceeding the delay threshold must be equal to or less than the probability of packet loss. This algorithm gives the priority to the user who has high HOL delay to avoid the packet loss. Thus, it can significantly improve the throughput and can serve more users with their required QoS. SINR generally decreases when a user is moving far away from the eNB. Therefore, cell-edge users with lower SINR experience relatively lower throughput and higher packet loss. However, in different cases, the SINR value might be changed due to the weather conditions, geographical area, infrastructure or various types of noises. The MLWDF based proposed model divides the cell area into two different regions: inner and outer.