# Virtualized MME Design for IoT Support in 5G Systems
## 5 Virtualized MME Design for M2M
### Target Arrival Rate Design  
The dimensioning of the schemes is done at each tier of the vMME separately, based on [22]. To dimension the resources needed at each tier of the vMME model in advance, we define a design parameter name the _target arrival rate per tier_. The target arrival rate is the maximum arrival rate of control messages for which the vMME has to satisfy a mean response time budget (\(\overline{D}_{j}\)) for tier \(j\). That is, the vMME is required to have sufficient processing capacity at tier \(j\) to satisfy \(\overline{D}_{j}\) with an arrival rate up to the target.  
On the one hand, for MBB communications, we set the target arrival rate, \(\lambda_{MBB}^{t}\), equal to the mean arrival rate of MBB control messages (see Section 4.1), then \(\lambda_{MBB}^{t}=\overline{\lambda}_{MBB}\). On the other hand, for M2M communications, the target arrival rate \(\lambda_{h}^{t}\), with \(h\in\{mM2M,IM2M\}\), depends on whether we choose the vMME to satisfy \(\overline{D}_{j}\) at each tier \(j\) during the traffic peaks caused by M2M events. We consider the following three approaches to serve the traffic peaks:  
* _Peak_ : denoted by \(\lambda_{h}^{\emph{peak}}\), we set the target arrival rate equal to the mean arrival rate during the largest event, \(\overline{\lambda}_{h}^{\emph{mexevent}}\). With this setting, each tier \(j\) of the vMME has to satisfy \(\overline{D}_{j}\) for all traffic peaks, including the largest one. Therefore, it follows that: \[\lambda_{h}^{t}=\lambda_{h}^{\emph{peak}}=\overline{\lambda}_{h}^{\emph{ maxevent}}\] (6)
* _Intense smoothing of peaks_ : denoted by \(\lambda_{h}^{\emph{intsmooth}}\), we set the target arrival rate equal to a weighted sum of the mean arrival rates in absence of an event and during an event (see Equation (4)). Therefore, \[\lambda_{h}^{t}=\lambda_{h}^{\emph{intsmooth}}=(1-w_{h})\cdot\overline{ \lambda}_{h}^{\emph{active}}+w_{h}\cdot\overline{\lambda}_{h}^{\emph{event}}\] (7) The parameter \(w_{h}\), with \(h\in\{mM2M,IM2M\}\), defines the weighting factor of both M2M arrival rates. We select \(w_{h}\) such that \(\lambda_{h}^{\emph{intsmooth}}\) is slightly higher than \(\overline{\lambda}_{h}\) (see Equation (5)). With this setting, each tier \(j\) of the vMME is not able to satisfy \(\overline{D}_{j}\) during the traffic peaks. Part of the signaling messages arriving during a traffic peak will be served after the end of the event.
* _Moderate smoothing of peaks_ : denoted by \(\lambda_{h}^{smoothpeak}\), we set the target arrival rate equal to a weighted sum of the mean arrival rates in absence of an event and during the largest event (see Equation (4)). Therefore, it follows that: \[\lambda_{h}^{t}=\lambda_{h}^{smoothpeak}=(1-w_{h})\cdot\overline{\lambda}_{h} ^{active}+w_{h}\cdot\overline{\lambda}_{h}^{maxcent}\] (8) With this setting, each tier \(j\) of the vMME is also not able to satisfy \(\overline{D}_{j}\) during the traffic peaks. However, \(\lambda_{h}^{smoothpeak}>\lambda_{h}^{intsmooth}\); therefore, the signaling messages arriving during a traffic peak will be served faster than in the previous case.