## 3 Problem Formulation  
Figure 3 shows a typical scenario for the mobile networking environment we intend. There is a macro-cell base station and a number of UE groups. Each UE device is equipped with a storage device. UEs in the same group share the same interest in digital content and are willing to share them with group members. Each group has a group header that keeps track of the availability of digital content in the group. UE can consult the header for the availability of a particular content whenever needed. Figure 3: An illustration of the intended environment. There are four possible situations when a UE requests a particular content, as follows:  
1. No one in the group possesses the content. 2. The content is possessed by another member of the same group, and delivery of the content via D2D group communication is within the delay constraint. 3. Another group member possesses the content. However, delivery of the content via D2D group communication exceeds the delay constraint. 4. The content is possessed by another group member. However, neither delivery of the content via D2D group communication nor cellular communication can meet the delay constraint. For situations 1 and 3, the content will be downloaded from the core network via cellular communication. For situations 2 and 4, our approach will play its role and determine the best route for the D2D group communication. We assume that within one macro-cell base station, there are \(s\) groups, \(k\) contents, and \(n\) UEs, where \(s\in\{1,2,3,\cdots,S\}\), \(k\in\{1,2,3,\cdots,K\}\), and \(n\in\{1,2,3,\ \cdots,\ N\}\). To evaluate the preference of a path, we define a utility function considering both throughput and delay. The utility for the path with which UE \(i\) downloads content \(k\) from UE \(j\) is defined as follows:  
\[\mathrm{U}_{total}^{i,k,j}=\alpha\cdot\mathrm{U}_{delay}^{i,k,j}(-1)+\beta \cdot\mathrm{U}_{thr}^{i,k,j} \tag{2}\]  
where \(\mathrm{U}_{delay}^{i,k,j}\) and \(\mathrm{U}_{thr}^{i,k,j}\) are the utility values from the normalization of delay and throughput, respectively; \(\alpha\) and \(\beta\) are weighting coefficients for delay and throughput, respectively; \(0\leq\ \alpha,\ \beta<1\) and \(\alpha+\beta=1\). We prefer a path with less delay, therefore, there is a \(-1\) factor for \(\mathrm{U}_{delay}^{i,k,j}\) in Equation (2). Delay and throughput are different measurement benchmarks. Normalization is required for the utility function to be meaningful. T-score, as follows, is used in our normalization:  
\[T=10\cdot\frac{x-\mu}{\sigma}+50 \tag{3}\]  
The utilities for delay and throughput can then be defined as follows:  
\[\mathrm{U}_{delay}^{i,k,j}=10\cdot\frac{D^{i,k,j}-\mu_{D}}{\sigma_{D}}+50 \tag{4}\]  
\[\mathrm{U}_{thr}^{i,k,j}=10\cdot\frac{T^{i,k,j}-\mu_{T}}{\sigma_{T}}+50 \tag{5}\]  
where \(D^{i,k,j}\) and \(T^{i,k,j}\) are the delay and the throughput of the path with which UE \(i\) downloads content \(k\) from UE \(j\); \(\mu_{D}\) and \(\mu_{T}\) are the mean delay and mean throughput; \(\sigma_{\mathrm{D}}\) and \(\sigma_{T}\) are the standard deviations of delay and throughput. We are interested in the route planning for D2D group communication in the environment, that is, the maximization of the overall utility of the entire environment. This problem can be formulated as a constrained optimization problem:  
\[ \begin{array}{l}\max\sum_{k=1}^{K}\sum_{i=1}^{N}\sum_{j=1}^{N}\mathrm{U}_{ total}^{i,k,j}\cdot x_{i,j}^{k}\\ =max\ \sum_{k=1}^{K}\sum_{i=1}^{N}\sum_{j=1}^{N}(\alpha\cdot\mathrm{U}_{delay}^{ i,k,j}\cdot(-1)+\beta\cdot\mathrm{U}_{thr}^{i,k,j})\cdot x_{i,j}^{k}\end{array}  \tag{6}\]  
s.t.