## 3 System Model
### Transmission Model  
(1) Communications between C and MEC-BS  
All the MEC stations, including MEC-BS and MEC-NBS, under a C's coverage share the wireless resources of it. In this paper, the impacts of inter-station and intra-station interferences caused by computation offloading have been ignored because of the extremely tiny sizes of them. There are two types of communications between C and MEC-BS (offloading-signal transmission and data-signal transmission, respectively). We define the data-signal transmission rate from MEC-BS to C as \(s_{i}^{\text{BS2C}}\). Then, the time consumed by sending the offloading request of \(r_{j}\) from MEC-BS to C can be defined as follows, if \(r_{j}\) is selected to be offloaded. \[t_{i,j}^{\text{OSB2C}}=\frac{p_{i,j}e_{i}v_{j}}{s_{i}^{\text{BS2C}}}. \tag{4}\]  
The data transmission rate from C to MEC-BS is denoted by \(s_{i}^{\text{C2 BS}}\). Then, we have the time consumed by receiving the offloading response of \(r_{j}\) from C to MEC-BS:  
\[t_{i,j}^{\text{OC2 BS}}=\frac{p_{i,j}e_{i}w_{j}}{s_{i}^{\text{C2 BS}}}. \tag{5}\]  
As for data caching transmission, MEC-BS uses the Cooperative Resource Management Algorithm to determine the most profitable data caching which is required by task \(r_{j}\), the time consumed by sending the data caching request of \(r_{j}\) from MEC-BS to C can be defined as follows:  
\[t_{i,j}^{\text{DBS2C}}=\frac{p_{i,j}e_{i}z_{j}}{s_{i}^{\text{BS2C}}}. \tag{6}\]  
Similarly,we have the time consumed by receiving the data caching response of \(r_{j}\) from C to MEC-BS:  
\[t_{i,j}^{\text{DC2 BS}}=\frac{p_{i,j}e_{i}q_{j}}{s_{i}^{\text{C2 BS}}}. \tag{7}\]  
(2) Communications between C and MEC-NBS  
MEC-NBS can also use the Cooperative Resource Management Algorithm to determine the most profitable data caching which is required by task \(r_{j}\). We define the data-signal transmission rate from \(n_{k}\) to C as \(s_{k}^{\text{NBS2C}}\) the time consumed by sending the data caching request of \(r_{j}\) from \(n_{k}\) to C can be defined as follows:  
\[t_{i,j,k}^{\text{DENS2C}}=\frac{p_{i,j}e_{i}z_{j}}{s_{k}^{\text{NBS2C}}}. \tag{8}\]  
The data transmission rate from C to \(n_{k}\) is denoted by \(s_{k}^{\text{C2 NBS}}\). Then, we have the time consumed by receiving the data caching response of \(r_{j}\) from C to \(n_{k}\):  
\[t_{i,j,k}^{\text{DC2 NBS}}=\frac{p_{i,j}e_{i}q_{j}}{s_{k}^{\text{C2 NBS}}}. \tag{9}\]  
(3) Communications between MEC-BS and MEC-NBS  
For the sake of data security, we assume that data-signal cannot be transmitted between the MEC stations, including MEC-BS and MEC-NBS. Accordingly, there is only one type of communications between MEC-BS and \(n_{k}\), which is the offloading-signal transmission. We define the offloading-signal transmission rate from MEC-BS to \(n_{k}\) through the wired connection between them as \(s_{k}^{\text{B2 NBS}}\). Reversely, \(s_{k}^{\text{NBS2 BS}}\) represents the offloading-signal transmission rate from \(n_{k}\) to MEC-BS through the connection. The time consumed by transmitting the offloading request of \(r_{j}\) from MEC-BS to \(n_{k}\) is expressed as  
\[t_{i,j,k}^{\text{OBS2 NBS}}=\frac{p_{i,j}e_{i}v_{j}}{s_{k}^{\text{BS2 NBS}}}. \tag{10}\]  
Similarly, the time consumed by transmitting the offloading response of \(r_{j}\) from \(n_{k}\) to MEC-BS is expressed as  
\[t_{i,j,k}^{\text{ONS2 BS}}=\frac{p_{i,j}e_{i}w_{j}}{s_{k}^{\text{NBS2 BS}}}. \tag{11}\]  
(4) Communications between MEC-BS and MTsAll the MTs under a MEC-BS's coverage share the wireless resources of it. In this paper, we ignore the computing power of every MTs, so that there is only one type of communications between MTs and MEC-BS which is the offloading-signal data transmission. We define the uplink data transmission rate from \(m_{i}\) to MEC-BS as \(s_{i}^{\text{MT2 BS}}\). Then, the time consumed by sending the offloading request of \(r_{j}\) from \(m_{i}\) to MEC-BS can be defined as follows, if \(r_{j}\) is selected to be offloaded.