## 3 System Model
### Basic Description  
The FiWi network in our work consists of a wavelength division multiplexing (WDM)-based fiber network (i.e., WDM-based PON) and an 802.11 protocol-based wireless network. At the locations of OLT and ONUs, the cache is deployed for MEC, enabling traffic offloading. Note that the links from ONU to OLT and those from OLT to Internet are both fiber. However, the underlying technologies, such as carrier wavelength, are different. Each user/human/machine has a single transmit antenna. Each MAP/MP/ONU is equipped with \(M\)-receiving antennas. The user/human/machine is served by its nearest MAP/MP/ONU. Through one single or multiple hops in the wireless network, each user/human/machine is connected to one ONU. The set of MAP/MP/ONUs that are connected to user/human/machine \(i\) via \(k\) hops is represented by \(\mathit{Neb}(i,k)\).  
As shown in Figure 2, four kinds of location are involved in the FiWi network scenario. These four kinds of location, in order of the distance from users, are user/human/machine, ONU with MEC, OLT with MEC, and the Internet. The ONU with MEC is seen as one-tier. The OLT with MEC is seen as two-tier. Internet is seen as three-tier. The computing services  
\begin{table}
\begin{tabular}{l l} \hline \hline
**Symbol** & **Description** \\ \hline \(i\) & user/human/machine \(i\) \\ \(k\) & \(k\) hops \\ \(\mathit{Neb}(i,k)\) & Set of MAP/MP/ONUs that are connected to user/human/machine \\ \(\mathbb{I}\) & Set of user/human/machine \\ \(\mathbb{J}\) & Set of ONU \\ \(\mathbb{R}\) & The set of OLT \\ \(\mathbb{C}\) & The Internet \\ \(\mathbf{y}_{j}\) & The received signal vector for MAP \\ \(p_{0}\) & Transmission power \\ \(\mathbf{h}_{ij}\) & wireless channel from \(i\) to \(j\) \\ \(s_{i}\) & Transmission signal \\ \(\mathbf{n}\) & Gaussian noise \\ \(\alpha\) & Coefficient of signal attenuation \\ \(\mathbf{y}_{k}\) & Received signal vector for ONU \\ \(\mathbf{y}_{r}\) & Received signal vector for OLT \\ \(\beta\) & Fiber attenuation coefficient \\ \(L_{rj}\) & The distance from ONU to OLT \\ \(SINR_{i}\) & Received signal to interference plus noise ratio \\ \(\mathbf{h}_{ki}\) & The wireless channel from \(i\) to \(k\) \\ \(\sigma^{2}\) & the noise power of the Gaussian noise \\ \(R_{i}^{X}\) & The data rate of user/human/machine \(i\) via wireless links \\ \(B_{i}^{X}\) & The bandwidth of wireless links \\ \hline \hline \end{tabular}
\end{table}
Table 1: Key Notations.  
traditionally occur on the Internet. The task data have to be transmitted in sequence through user/human/machine, ONU, OLT, and the Internet. After data computing, results or response contents return from the Internet to the user/human/machine. With the application of MEC, data computing can migrate from the Internet to ONU with MEC or OLT with MEC, i.e., the task offloading in Figure 2. The path that involved service reductions from user/human/machine-ONU-OLT-Internet to user/human/machine-ONU or user/human/machine-ONU-OLT. Latency is reduced due to the migration of data computing (i.e., task offloading) from the Internet to ONU with MEC or OLT with MEC. The MEC in ONU (i.e., one-tier) is denoted as MEC-1. The MEC in OLT (i.e., two-tier) is denoted as MEC-2. The original data computing on Internet (i.e., three-tier) is denoted as MEC-3.  
The set of user/human/machine is \(\mathbb{I}\). User/human/machine \(i\in\mathbb{I}\). The set of ONU is \(\mathbb{J}\). ONU \(j\in\mathbb{J}\). The set of OLT is \(\mathbb{R}\). OLT \(r\in\mathbb{R}\). The Internet is \(\mathbb{C}\). Because that there is only one Internet in the world, \(\mathbb{C}\) needs not further refinement.