# Data-Driven Construction of User Utility Functions from Radio Connection Traces in LTE
## 2 Characterization of Quality of Experience  
QoE monitoring in mobile networks is a key factor for operators [23]. As the network evolves, new indicators and counters are included in network equipment with the aim of reflecting service performance (e.g., initial buffering time or web download time for video and web services, respectively). However, user experience, as a subjective matter, cannot be measured but only estimated from network and service performance indicators. For this purpose, QoE models use utility functions to map the value of network Key Performance Indicators (KPIs), reflecting QoS, to user experience [20; 24]. How QoS parameters are mapped into a QoE indicator is a widely studied subject. A generic formula connecting QoE with QoS for different packet data services is described in [16]. It is assumed here that user experience remains constant at a maximum level when some upper QoS threshold is exceeded. Similarly, a minimum QoS threshold can be defined below which a user neglects to continue its connection due to their bad experience. These statements can be formulated as  
\[QoE=\max\{\min\{f(QoS_{1},QoS_{2},\ldots,QoS_{N}),QoE_{max}\},QoE_{min}\}\;, \tag{1}\]  
where \(QoS_{i},\;\forall i\in\{1,2\ldots N\}\), are the \(N\) network performance indicators reflecting service performance, \(QoE\) is the indicator quantifying user experience, \(f\) is the user utility function, and \(QoE_{max}\) and \(QoE_{min}\) define the range of \(QoE\) values. Note that existence of \(QoE\) limits implies that there also exist QoS thresholds, \(QoS_{i,th_{max}}\) and \(QoS_{i,th_{min}}\), above or below which \(QoE\) does not change. Thus, (1) can be reformulated as  
\[ \begin{split}& QoE=f(\max\{\min\{QoS_{1},QoS_{1,th_{max}}\},QoS_{1,th_{ min}}\},\\ &\ldots,\max\{\min\{QoS_{N},QoS_{N,th_{max}}\},QoS_{N,th_{min}} \})\;.\end{split}  \tag{2}\]  
At the same time, user experience is influenced by factors that strongly depend on the requested service. For instance, a user performing a voice call is sensitive to packet delay, whereas a user uploading a photo in a social network is more sensitive to throughput [25]. Thus, different user utility functions are defined for each service [20]. To aid comparison, QoE is commonly measured as the Mean Opinion Score (MOS). MOS scale ranges from 1 (worst experience) to 5 (best experience), i.e., \(MOS^{(s)}_{max}\leq 5\) and \(MOS^{(s)}_{min}\geq 1\). However, some models set more restrictive limits. With these considerations, (1) can be reformulated as  
\[ \begin{split}& MOS^{(s)}=\max\{\min\{f^{(s)}(QoS_{1},QoS_{2}, \ldots,QoS_{N_{\text{QoS}}}),MOS^{(s)}_{max}\},MOS^{(s)}_{th_{min}}\}\\ &=f^{(s)}(\max\{\min\{QoS_{1},QoS^{(s)}_{1,max}\},QoS^{(s)}_{1, min}\}),\\ &\ldots,\max\{\min\{QoS_{N},QoS^{(s)}_{N,max}\},QoS^{(s)}_{N, min}\})\;,\end{split}  \tag{3}\]  
where superscript \(s\) refers to the service under consideration (i.e., \(s\in\{web,video,\ldots\}\)). From (3), it follows that users of different services can experience a different QoE with the same network performance (QoS). Consequently, different QoS requirements must be achieved to guarantee the same MOS for all services in a mobile network [20]. QoS thresholds give extremely valuable information to network operators, as it is not worthwhile to increase \(QoS\) beyond/below a certain threshold if there is no impact on user experience. Unfortunately, the value of QoS thresholds per service, \(QoS_{i,min/max}^{(s)}\) is highly dependent on many factors, such as user expectation (which is not the same for all users), handset features (the user expects a better experience for a more expensive terminal) or network evolution (a specific level of user experience previously seen as acceptable may not be so some months later). All these factors make it very difficult for operators to find precise QoS thresholds for their networks. Nonetheless, approximating these thresholds is still useful for operators as it allows them to assess the overall cell performance from a user experience perspective.