## 5 Problem Formulation  
The 3 GPP Model [33] defines FTP bursty traffic according to three parameters: file size S, reading time D and the number of devices \(i\), as shown in Figure 6. The device data rate will be:  
\[x_{i}=S_{i}/t_{i} \tag{5}\]  
where \(x_{i}\) is the device achievable data throughput and \(t_{i}\) is the time required to download \(S_{i}\) data (time from the start of reception of the packet until the last bit of the packet is delivered).  
In finite buffer traffic model, which characterise MTC category, the device will stop using the network resources once the payload is successfully transmitted. Therefore, the MTC device data throughput is measured by calculating all successfully transmitted bits are taken into account. This means we actually count how many bits are transmitted in less than simulation time (400 ms), which is generally less than the capacity equation.  
The traffic density of ROI is defined as the total traffic originating from the total sensor networks within the ROI. Therefore, R is the overall traffic density, which represents the sum rate of the data throughput r of all devices in all sensors networks:  
\[R=\sum_{i=1}^{j}x_{i,\ n1}+\sum_{i=1}^{k}x_{i,\ n2}+\sum_{i=1}^{m}x_{i,\ n3}+ \sum_{i=1}^{n}x_{i,\ n4} \tag{6}\]  
Figure 6: MTC traffic model, 3 GPP FTP.  
where: \(n1\), \(n2\), \(n3\) and \(n4\) are four sensor networks with different requirements, \(j\), \(k\), \(m\) and \(n\) represent the number of MTC devices in the four sensor networks, respectively.  
Each network has MTC devices that have certain traffic requirements in order to fulfil their data transaction in a certain time interval. The traffic model of MTC is described as a as low data rate, with small-packet burst traffic [13].  
As per 3 GPP documentation in [38], \"an FTP session is a sequence of file transfers separated by reading times\". There are two main parameters of FTP session: the file size to be transferred and the reading time, which is \"the time interval between end of download of previous file and the user request for the next file\". S has a log-normal distribution with probability distribution function (PDF) as [38]:  
\[f_{x}=\frac{1}{\sqrt{2\pi\alpha}}e^{\frac{-(\ln x-u)^{2}}{2\alpha^{2}}},x>0,\ \sigma=0.35,\mu=14.45 \tag{7}\]  
Therefore, the machines should complete their data transaction of (\(S_{i}\)) with a data rate of \(x_{i}\) during the allowed time of each type. Any machine that fails to reach this bound will be in outage and their data packets will be discarded.  
Once \(RB\) resources are granted to a machine, they shall be removed from the total resources in order to avoid giving the same \(RB\) to more than one machine at a particular tri, thus:  
\[X_{n}(RB)=\ X_{T}(RB)-X_{a}(RB) \tag{8}\]  
where, \(X_{n}\) is the available \(RB\)s after removing the assigned \(RB\)s \(X_{a}\) from the total number of \(RB\)s \(X_{T}\). The same holds correct for the MTC device, any device that complete their data transaction should also be removed from the total number of MTC devices that require scheduling, therefore:  
\[Y_{av}(mtc)=\ Y_{T}(mtc)-Y_{s}(mtc) \tag{9}\]  
where, \(Y_{av}\) represents the MTC sensor that yet to complete data transaction, \(Y_{T}\) represents the total number of devices in the simulation and \(Y_{s}\) represents the scheduled devices that successfully completed their data transaction.