# Performance Model for Video Service in 5G Networks
## 2 Problem Description  
By balancing the relative importance of resource utilization (i.e., SE) and the quality of experience (QoE) satisfaction ratio, the resource management problem could be formulated as R = \(\alpha\cdot\text{SE}+\beta\cdot\text{QoE}\), where \(\alpha\) and \(\beta\) represent the weights of SE and QoE [1]. QoE is subjective, so we use QoS instead. Consider an area with \(U\) users, denoted as U = \(\{1,\ \ldots,\ U\}\), uniformly distributed within the area, supporting \(S\) services, denoted as \(S\) = \(\{1,\ \ldots,\ S\}\), and sharing the aggregated bandwidth W. Denote \(U_{s}\) as users supporting service \(s\). Due to the lack of physical resources, sites are shared among services, and are uniformly distributed within the area (with the same inter-site distance (ISD) between the sites). In a real network, instead of maximizing QoS, maximizing the number of users who satisfy the QoS requirements is the target. The problem is written as:  
Problem SM-P1:  
\[\textit{Maximize}\ [\alpha\cdot\text{SE}(w,\textit{isd})+\ \beta\cdot\sum_{s \in S}\sum_{u\in U_{s}}\ \mathcal{N}(q\text{os}_{u}(w,\textit{isd}))] \tag{1}\]  
Over: \(w,\textit{isd}\), where:  
\[w=(w_{1},\ \ldots\ w_{s})\mathcal{N}(q\text{os}_{u}(w,\textit{isd}))=\left\{ \begin{array}{cc}1&q\text{os}_{u}(w,\textit{isd})>T_{s}\\ 0&\textit{Else}\end{array} \right. \tag{2}\]  
Subject to:  
\[\sum_{s\in S}w_{s}=W \tag{3}\]where \(T_{s}\) is the pre-defined threshold for service S. \(qos_{u}(w,isd)>T_{s}\) tells us that the QoS requirement \(T_{s}\) of service \(s\) is satisfied by user u under network attributes, such as the bandwidth distribution of \(w\) and the site separation of \(isd\). To address the complexity, a sub-optimal solution is proposed to put higher priority on the QoS requirement, optimize radio resource utilization using IC approach, and allocate dedicated bandwidth for each service. The proposed solution includes two steps. First, create a performance model for each service. The problem can be transferred into solving the following performance model over different \(w_{s}\) and \(isd\):  
\[PM_{s}(w_{s},isd)=\sum_{u\in U_{s}}\mathcal{N}(qos_{u}(w_{s},isd)) \tag{4}\]  
Second, perform an exhaustive search in the ISD space and W space for all services. The point satisfied the total bandwidth constraint and fulfills the QoS requirements for all services yet with the maximized ISD, is the optimized solution. The core of the solution is solving the performance model for each service. Data analytics and machine learning approaches using regression algorithm that allow automated identification of non-explicit relationships and dependencies are exploited. With the performance model, the following problems are investigated: (1) optimization of the performance model using IC approaches, (2) network design using the performance models, and (3) network optimization. In this research, the proposed UIC approaches are on both time (TIC) and frequency (FIC) domains. First, we modify the approach we proposed in [29], extend it into the time domain, and apply the approach to the video service. Assume the mobile network consists of \(C\) cells, denoted as C = {1,..., C}, \(U\) users, denoted as U = {1,..., U}, and \(B\) sub-bands, denoted as B = {1,..., B}. Consider a SBS network with \(M\) beams per sector, denoted as M = {1,..., M}, and \(T\) transmission time intervals (TTIs) per scheduling period, denoted as T = {1,..., T}. Define \(l_{b}^{u,c,m}(t)\) as user resource allocation indicator which indicates that if \(l_{b}^{u,c,m}(t)=1\), the cell \(c\) will transmit to the user \(u\) using the beam \(m\) on the sub-band \(b\) at time \(t\). Otherwise, \(l_{b}^{u,c,m}(t)=0\); define \(U_{c}\) as the group of users served by the cell \(c\). Define \(l^{c}(t)=\left\{l_{b}^{u,c,m}(t):u\in U_{c},\text{ m}\in\text{M},\text{ b}\in\text{B}\right\}\), \(I(t)=\left\{l^{c}(t):\text{ c}\in\text{C}\right\}\).