# Data-Driven Construction of User Utility Functions from Radio Connection Traces in LTE
## 4 Estimation of QoS Thresholds on a Per-Service Basis
### Step 2: Estimation of Minimum Qos Thresholds  
As explained in Section 2, each service has its own user utility function, \(f^{(s)}\), combining different QoS indicators. In this work, the analysis is restricted to application groups that have a significant share of connections and are affected by QoS; namely, Voice over LTE (VoLTE), full-buffer data services (e.g., app download, software update, large file download via File Transfer Protocol, etc.) and streaming services (e.g., audio/video, live/buffered, etc.). For simplicity, in each service, only the QoS indicator with the largest impact on QoE for each service is considered (i.e., \(N=1\ \forall\ s\) in (3)). This indicator is not necessarily the same for all services. For instance, packet delay negatively affects user experience for real-time services (e.g., VoLTE or conversational video-streaming), whereas user experience in non-real-time services (e.g., app download) is more sensitive to user data throughput. Previous works have shown that user experience in most services is dominated by a single QoS metric. For instance, in [40], an analytical model to estimate the QoE for a video-streaming service based on different network level metrics (e.g., average session throughput, packet loss ratio and round-trip time) is presented. It is shown there that QoE is strongly correlated with a single QoS metric (average session throughput). On the other hand, it is well accepted that voice calls are mostly affected by packet delay [41]. For this reason, user experience is estimated here from the foremost QoS indicator of the requested service in order to reduce the complexity of the proposed model. Hereafter, it is assumed that the QoE of a connection \(k\) of service \(s\), \(MOS^{(s)}(k)\), is conditioned by the value of the indicator \(i\) with the largest impact for that service, \(QoS_{i}^{(s)}(k)\). When this indicator falls below a certain threshold, \(QoS_{i,min}^{(s)}\) users experience their worst QoE, \(MOS_{min}^{(s)}\), which is reflected in different traffic indicators depending on the service. For instance, unsatisfied VoLTE users tend to shorten their connections, and the effect is therefore observed in connection length. In contrast, in non-real-time services, whether background, interactive or streaming, the effect is more evident in the traffic volume for each connection. As a consequence, an analysis of an additional and service-based traffic indicators (e.g., length connection for VoLTE or data volume for streaming services) is needed in order to detect those low-QoE connections. This traffic indicator is denoted as \(T_{j}^{(s)}(k)\). Then, the QoE estimation of a connection \(k\) of service \(s\) is based on QoS indicator \(j\), \(QoS_{j}^{(s)}(k)\), used to infer the user behavior, and QoS indicator \(i\), \(QoS_{i}^{(s)}\), as the indicator with the largest effect on QoE. As user behavior is not deterministic, this \(QoS_{i}^{(s)}\) has some random component so that connections with the same \(QoS_{i}^{(s)}\) do not end up with identical values of \(QoS_{j}^{(s)}\). To deal with this uncertainty, a percentile curve relating connection \(QoS_{i}^{(s)}\) and \(QoS_{j}^{(s)}\) is constructed for each service by discretizing \(QoS_{i}^{(s)}\) values and computing the 50 th percentile (median) of the distribution of \(QoS_{j}^{(s)}\) per bin, \(QoS_{j,50 th\,ille}^{(s)}(QoS_{i}^{(s)})\). Finally, the QoS threshold for each service, \(QoS_{i,th_{min}}^{(s)}\), is estimated. This minimum QoS threshold determines a boundary between two states: a degraded state, where a user perceives a bad service performance and tends to stop the connection, and a normal state, where service performance is good enough to consume the service normally. As this boundary highly depends on service, the following paragraphs anticipate the ideal user behavior for broad service classes. To this end, Figure 1 shows the expected relationship between the selected QoS and traffic indicators--i.e., \(QoS_{i}^{(s)}(k)\), \(QoS_{j}^{(s)}(k)\) and \(T_{j}^{(s)}(k)\)--for each class.