# Intelligent Dynamic Data Offloading in a Competitive Mobile Edge Computing Market
## 2 SDN-Powered Mobile Edge Computing
### Mobile Edge Computing Server Characteristics and Profit  
Each MEC server \(s\) supports a total computing demand of the end-users per time slot equal to \(\sum_{u\in U}b_{u,s}^{(t)}\) from all the end-users that selected the specific MEC server to offload their data. In addition, towards providing incentives to the end-users to select a specific MEC server to be served from, the latter provides some discounts \(f_{s}^{(t)}\) expressed as a percentage of the original announced price of its computing services. Furthermore, the MEC server has an actual cost \(c_{s}^{(t)}[\$/\mathit{bits}]\) in order to process the amount of data that it receives. Please also be reminded that the MEC server charges the end-users with a price \(p_{s}^{(t)}[\$/\mathit{bits}]\) for the computing services that it offers. Additionally, a MEC server increases its positive reputation towards the end-users if it is characterized by a good penetration within the end-users' computing demands. Specifically, the penetration of a MEC server \(s\) is defined as the total amount of data that the server \(s\) processed over the total amount of data that are processed within the SDN-powered MEC system for a total time period \(T\), i.e., \(\frac{\sum_{t\in\{1,\ldots,T\}}\sum_{u\in U}b_{u,s}^{(t)}}{\sum_{s\in S}\sum_{ t\in\{1,\ldots,T\}}\sum_{u\in U}b_{u,s}^{(t)}}\). In addition, we assume that each MEC server \(s\) can handle a total amount of data \(B_{s}^{Max}\). Thus, an indicative parameter showing the congestion of the MEC server per time slot in terms of processing the end-users' offloaded data is expressed as the ratio of the total amount of data \(\sum_{u\in U}b_{u,s}^{(t)}\) that the MEC server processes in time slot \(t\) over its total computing capability of data \(B_{s}^{Max}\), i.e., \(CONG_{s}=\frac{\sum_{u\in U}b_{u,s}^{(t)}}{B_{s}^{Max}}\). Following the above analysis and combining all the aforementioned factors and parameters that characterize the MEC server \(s\), its reputation score within the SDN-powered MEC environment is defined as follows. \[R_{s}^{(t)}=w_{1}\frac{\frac{\sum_{u\in U}(1-f_{k}^{(t)})p_{k}^{(t)}}{k}}{(1- f_{s}^{(t)})p_{s}^{(t)}}+w_{2}\frac{1}{(1+CONG_{s})^{3}}+w_{3}\frac{\sum_{t\in\{1, \ldots,T\}}\sum_{u\in U}b_{u,s}^{(t)}}{\sum_{s\in S}\sum_{t\in\{1,\ldots,T\}} \sum_{u\in U}b_{u,s}^{(t)}} \tag{4}\]  
In Equation (4), the first term expresses the relative pricing of a MEC server \(s\) in terms of offering its computing services to the end-users, the second term expresses the level of MEC server's congestion towards serving the end-users, while the third term expresses its penetration in serving end-users' computing demands. The weights \(w_{1},w_{2},w_{3}\) are configurable parameters that express the relative weight of each term within our study, and it should hold true that \(w_{1}+w_{2}+w_{3}=1\). The revenue of each MEC server \(s\) from processing a total amount of end-users' offloaded data \(\sum_{u\in U}b_{u,s}^{(t)}\) depends on the announced price \(p_{s}^{(t)}\) and the corresponding discount \(f_{s}^{(t)}\) that the MEC server provides, and is given as follows. \[REV_{s}^{(t)}(\mathbf{b}^{(t)},\mathbf{p}^{(t)})=(1-f_{s}^{(t)})p_{s}^{(t)} \sum_{u\in U}b_{u,s}^{(t)} \tag{5}\]  
Figure 2: End-user’s actual perceived satisfaction by data offloading. where \(\mathbf{b^{(t)}}\) is the data offloading vector of all the end-users and \(\mathbf{p^{(t)}}\) denotes the announced prices by all the MEC servers in the system. On the other hand, the MEC server's total monetary cost to perform the processing of the offloaded data, is given as follows. \[C_{s}^{(t)}(\mathbf{b^{(t)}})=c_{s}^{(t)}\sum_{u\in U}b_{u,s}^{(t)} \tag{6}\]  
where \(c_{s}^{(t)}\) is the MEC server's \(s\) computing cost per unit of data. Thus, the MEC server's profit is concluded by subtracting its cost from its revenue and is given as follows.