**4. Predicting the quality of experience: a quantitative approach**

In our model, QoE quantitatively expresses the prediction of user's satisfaction from QoC-utility function not depending on subjective feelings. The reason is that quantitative metrics are not only more meaningful, but also provide an improved magnitude reference of the measured parameters. From this magnitude reference is possible to benefit the user, and the resource provider environment. In our work, the correctness and runtime are proposed as quantitative metrics for prediction.

In a fog environment, or any distributed system is acceptable that computing resources are provided on demand. The matching between available resources and application requirements is expressed by utility function. The utility function is expressed by the Eq. (17). Utility *U p*ð Þ*<sup>r</sup>* assigned to a particular resource *r*, represents a metric proportion of resources adequacy for application, also given by *p* (*probability of correctness*). Correctness is the main metric applied to measuring the QoC to meet applications demands. The utility is given by Eq. (17).

$$U\_r = \text{corrections}\_r\tag{17}$$

The QoE directly depends on application runtime *rt*, and the response time *t*. Response time is given *t* by sum both execution time and waiting time. So, QoE is expressed in Eq. (18).

$$QoE = \frac{rt}{t} \sum\_{r=0}^{R} U\_r^a \tag{18}$$

The *α* value quantifies the resource importance, *r*, to application, and his value ranging between 0 and 1. The *α* parameter is related with application category, thus, is determinant for utility function. The *α* parameter is expressed by Eq. (19).

$$a = 1 - U(p) \tag{19}$$

In this section, the metric used to predict users QoE was discussed. Next section covers the obtained results from experiments conducted.
