## 4 An Architecture for IoT and Multimedia Data Handling
### Downstream Data Flow Management
#### 4.1.4 Content Access Mechanism
\begin{table}
\begin{tabular}{c c} \hline \hline
**Definitions** & **Notations** \\ \hline Set of the EC types (MEC, MCC, FC, Cloudlets) & \(\varsigma\) \\ Set of Tier 2 devices & \(\text{l}_{2}=\{\text{BSs},\,\text{APs},\,\varsigma,\dots\ \}\) \\ Set of N eNBs & \(\delta_{\text{eNB}}\) \\ The covered area of a mobile device in Tier 2 & \(\Gamma_{m}\) \\ Set of \(N\) APs & \(\text{V}_{\text{AP}}\) \\ Caching resources in Tier 2 & \(\text{CRL}_{2}\) \\ Caching resources in one eNB & \(\text{C}_{\text{eNB}}\) \\ Caching resources in one AP & \(\text{C}_{\text{AP}}\) \\ Caching resources in one \(\varsigma\) & \(\text{C}_{\varsigma}\) \\ Computing resources in one \(\varsigma\) & \(\text{CO}_{\varsigma}\) \\ End-user types based on the position & \(\text{EU}_{\text{tp}}\) \\ End-users based on the content generator or consumer & \(\text{EU}_{\text{gc}}\) \\ Speed of the end-user mobile device & \(\text{V}_{m}\) \\ List of the eNBs, (eNB\({}_{1}\), eNB\({}_{2}\),....... eNB\({}_{N}\)) & \(\text{L}_{\text{eNB}}\) \\ Types of the requested content & \(\xi\) \\ The component of each data type & \(\text{\mu}_{i}=\{\beta,\,\text{P}_{C},\,\text{t}_{H},\text{C}_{R}\}\) \\ Caching resource of \(l_{2}\), \(j\) used to process content \(i\) & \(p_{ij}\) \\ Computing resource of \(\xi\), \(j\) used to process content \(i\) & \(\Psi_{ij}\) \\ Getting a unit content from mobility supported content & \(\tau_{m}\) \\ provider in Tier 2 devices & \(\tau_{cs}\) \\ Getting a unit content time from Tier 4 devices & \(\tau_{cs}\) \\ Getting a unit content time from a cached content device & \(\tau_{cn}\) \\ Processing latency for \(\text{C}_{R}\) & \(\tau_{R}\) \\ Generated data by an IoT device & \(G_{IoT}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Used notations. devices (e.g., eNBs and APs). So, \(j_{i}^{max}\) is the index of the possible BS where type \(i\) content is cached in and \(j_{i}^{max}\) can be defined by Equation (2). \[\sum_{j=1}^{I_{i}^{max}-1}\frac{\Gamma_{m}}{V_{m}\tau_{m}}<\beta_{i}\leq\sum_{j =1}^{I_{i}^{max}}\frac{\Gamma_{m}}{V_{m}\tau_{m}}. \tag{2}\]  
There are several resource constraints (RCs) during caching and computing in the respective devices. Equations (3) and (4) show the RC of allocated caching resources and computing resources among the storage capacity of Tier 2 devices. Equation (5) shows the RC of the size of cached content in mobility-supported content providers in Tier 2 devices, where the cached content size should not exceed the maximum amount that is required for the end-users. Equation (1) and the three RCs are applicable for Tier 2 devices to support the mobility of the end-users. \[RC1:\quad\sum_{i=1}^{\xi}\frac{P_{i,j}}{1+C_{R}\;\psi_{i,j}}\leq CRL_{2},\;j\in CRL _{2}\;\text{and}\;\forall(C_{eNB},\;C_{AP},\;C_{\varsigma})\in CRL_{2}. \tag{3}\]  
\[RC2:\quad\sum_{i=1}^{\xi}\psi_{i,j}\leq CO_{\varsigma},\;\text{and}\;j\in\varsigma. \tag{4}\]  
\[RC3:\quad P_{i,j}\leq\frac{\Gamma_{m}}{V_{m}\tau_{m}},\;i\in\xi,\;\text{and}\;j \in CRL_{2}\;\text{and}\;\forall(C_{eNB},\;C_{AP},\;C_{\varsigma})\in CRL_{2}. \tag{5}\]  
If the Tier 2 devices do not support mobility, then Equation (1) is modified into Equation (6) where \(\tau_{m}=0\), \(\Gamma_{m}=0\), and \(V_{m}=0\). Similarly, Tier 3 and Tier 4 devices also do not support mobility. There are some content providers that also do not support mobility. Therefore, when the end-users are accessing content from any devices where the content is already cached and do not support mobility, then Equation (7) is applied and the value \(\tau_{m}\) is replaced by \(\tau_{cn}\). \[\min_{\{P_{i,j},\psi_{i,j}\}}\sum_{i=1}^{\xi}P_{c}\sum_{j=1}^{I_{i}^{max}} \frac{\left(\psi_{i,j}\tau_{R}+P_{i,j}\tau_{m}\right)}{\xi}. \tag{6}\]  
\[\min_{\{P_{i,j},\psi_{i,j}\}}\sum_{i=1}^{\xi}P_{c}\sum_{j=1}^{I_{i}^{max}} \frac{\left(\frac{\Gamma_{m}}{V_{m}\tau_{m}}-P_{i,j}\right)\tau_{cs}+\psi_{i, j}\tau_{R}+P_{i,j}\tau_{cn}\right]}{\xi}. \tag{7}\]  
If the cached content devices do not support mobility, then \(\tau_{m}=0\), \(\Gamma_{m}=0\), and \(V_{m}=0\).