# TRUST-ME: Trust-Based Resource Allocation and Server Selection in Multi-Access Edge Computing
## 2 TRUST-ME System Model  
We consider a multi-access edge computing (MEC) environment with a group of users \(\mathcal{N}=\{1,\ldots,n,\ldots,N\}\) and a set of MEC servers \(\mathcal{S}=\{1,\ldots,s,\ldots,S\}\). Each user has a computing task represented by \(A_{n}=(B_{n},C_{n},\phi_{n},T_{n},e_{n})\), where \(B_{n}\) [bits] is the total data size, and \(C_{n}\) [CPU-cycles] is the required processing cycles, which is defined as \(C_{n}=\phi_{n}B_{n}\), with \(\phi_{n}\) [\(\frac{CPU-cycles}{bits}\)] denoting the computation intensity. Additionally, \(T_{n}\) [sec] and \(e_{n}\) [J] represent the user's latency and energy constraints, respectively. The users fully offload their data \(B_{n}\) to MEC server \(s\). Each MEC server has a computing capacity \(F_{s}\) [\(\frac{CPU-cycles}{sec}\)] and allocates its capacity among the users offloading to it. The allocation vector is denoted by \(\mathbf{f_{s}}=[f_{s,1},\ldots,f_{s,n},\ldots,f_{s,N}]\) [\(\frac{CPU-cycles}{sec}\)], satisfying \(\sum\limits_{\forall n\in\mathcal{N}}f_{s,n}=F_{s}\).  
User \(n\) offloads its data to MEC server \(s\) using the non-orthogonal multiple access (NOMA) technique, with the successive interference cancellation (SIC) implemented at the MEC server (receiver). Assuming the users' channel gains are sorted as \(G_{1}\leq\cdots\leq G_{n}\leq\cdots\leq G_{N_{s}}\), where \(N_{s}\) is the number of users offloading their computing tasks to server \(s\), the throughput for each user \(n\) is given by the following equation [48]:  
\[R_{n,s}=W\log_{2}(1+\frac{P_{n}G_{n}}{I_{0}+\sum\limits_{n^{\prime}=1}^{n-1}G _{n^{\prime}}P_{n^{\prime}}}) \tag{1}\]  
where \(W\) [Hz] denotes the bandwidth, \(P_{n}\) [watts] denotes the transmission power, and \(G_{n}\) denotes the channel gain. It is noted that for simplicity in the notation, we considered that the users \(N_{s}\) associated with MEC server \(s\) have a corresponding channel gain and we denote the channel gain of user \(n\) as \(G_{n}\). The corresponding set of users selecting server \(s\) is denoted as \(\mathcal{N}_{s}\{a,\ldots,n,\ldots,N_{s}\}\). Also, \(I_{0}\) denotes the power spectral density of zero-mean additive white Gaussian noise (AWGN).  
User \(n\)'s time overhead consists of the overhead to transmit and process its data and it is given as follows:  
\[t_{n}=\frac{B_{n}}{R_{n,s}}+\frac{C_{n}}{f_{s,n}} \tag{2}\]  
Based on the experienced latency and the cost to utilize the computing resources of the MEC server, each user experiences a utility by processing its computing task using the MEC server, which is given as follows:  
\[u_{n}=\frac{\frac{\frac{1}{t_{n}}}{\frac{1}{n}}}{\frac{1}{\max \limits_{s\in\mathcal{N}}\{t_{n}\}}}-\beta_{n}.\frac{\mathcal{C}_{s}f_{s,n}}{ \mathcal{C}_{s}\underset{s\in\mathcal{S}}{\max\limits_{s\in\mathcal{S}}\{F_{s}\}}} \tag{3}\]  
where \(t_{n}\) [sec] is the user's experienced latency to transmit and process its computing task, as given by Equation (2); \(\mathcal{C}_{s}\left[\frac{\xi}{CPU-cycles}\right]\) is the MEC server's announced computing price to process the users' data; \(f_{s,n}\left[\frac{CPU-cycles}{sec}\right]\) is the amount of computing resources allocated by MEC server \(s\) to the user \(n\)'s computing task; and \(\beta_{n}\) is a weight factor. It is noted that the user's utility \(u_{n}\) is unitless and the normalization is performed for demonstration purposes in order to capture the pure differences between the users.