###### Abstract  
In addition to the traditional Quality of Service (QoS) metrics of latency, jitter and Packet Loss Ratio (PLR), Quality of Experience (QoE) is now widely accepted as a numerical proxy for the actual user experience. The literature has reported many mathematical mappings between QoE and QoS, where the QoS parameters are measured by the network providers using sampling. Previous research has focussed on sampling errors in QoS measurements. However, the propagation of these sampling errors in QoS through to the QoE values has not been evaluated before. This is important: without knowing how sampling errors propagate through to QoE estimates there is no understanding of the precision of the estimates of QoE, only of the average QoE value. In this paper, we used industrially acquired measurements of PLR and jitter to evaluate the sampling errors. Additionally, we evaluated the correlation between these QoS measurements, as this correlation affects errors propagating to the estimated QoE. Focusing on Video-on-Demand (VoD) applications, we use subjective testing and regression to map QoE metrics onto PLR and jitter. The resulting mathematical functions, and the theory of error propagation, were used to evaluate the error propagated to QoE. This error in estimated QoE was represented as confidence interval width. Using the guidelines of UK government for sampling in a busy hour, our results indicate that confidence intervals around estimated the Mean Opinion Score (MOS) rating of QoE can be between MOS = 1 to MOS = 4 at targeted operating points of the QoS parameters. These results are a new perspective on QoE evaluation and are of potentially great significance to all organisations that need to estimate the QoE of VoD applications precisely. Keywords:quality of experience; quality of service; QoE evaluation video on demand; quality of service; QoS correlation; subjective testing +
Footnote †: journal: Applied  
network service providers [3]. Recently Witbe launched \"Witbe on the go\" that enables the user to determine the QoE at any location in London, for any service provider of VoD applications [4]. The fundamental performance of any packet network at layer 3 can be understood through the QoS parameters packet loss, latency (packet delay) and jitter. These QoS parameters are usually agreed in Service Level Agreements (SLAs) with the network or service providers. For this reason, network and service providers measure the network (either passively or actively) to monitor the levels of these QoS parameters. The most widely used technique is active measurements, which is achieved through packet probing. Active measurements employ statistical sampling and are therefore subject to sampling error [5; 6; 7]. QoE depends on the level of the QoS metrics, and these (QoS metrics) are therefore the independent variables. When any study in the physical, biological or psychological sciences measures how a dependent variable changes with an independent variable, there is always an attempt to capture how errors in the measurement or evaluation of the independent variable will affect the evaluation of the dependent variable [8; 9; 10]. In the case of this paper, the independent variable(s) are the QoS measures of PLR or jitter, or both combined. The dependent variable is QoE, measured on a MOS scale. The fashion in which the sampling errors in QoS propagates to QoE depends on the mathematical function that links them. Considerable previous work, including [PERSON] [11], [PERSON] et al. [12], [PERSON] and [PERSON] [13] and [PERSON] and [PERSON] [14], have already investigated how these QoS parameters affect the QoE for VoD applications. The authors in [11; 12; 15] report that the results of subjective tests can be evaluated as MOS and can be used to map QoE to different QoS parameters like PLR and jitter. All these studies concluded with their own independently derived mathematical relationship between QoE and QoS.