## 2 Related Work and Research Contribution  
The evolution towards high bandwidth and QoS services drives technological evolution towards the design and implementation of fifth generation (5G/6G) broadband wireless networks. Ref. [9] Among these technologies, NFV is one of the most important and consists in decoupling the software running the service functions from the hardware platform. NFV is now considered a key technology for the development of access [10] and core [1] network segments. Since the NFV paradigm has been introduced by ETSI [11; 12], many resource orchestration algorithms have been proposed and investigated [13; 14]. Most of them are based on knowledge of traffic and solving optimization problems and/or heuristics. Offline [15] and Online [16; 17] algorithms have been considered. When traffic variations occur, resource reconfiguration algorithms [18] have been proposed. Most of them are based on a reactive approach according to which resources are reconfigured as soon as traffic changes are detected. These solutions have proven to be ineffective due to the high time required to reconfigure cloud resources which can be in the order of ten minutes [19]. Recently prediction-based proactive approaches have been proposed [19; 20]. Both traditional and Artificial Intelligence techniques are used to estimate traffic and/or needed resources. [PERSON] et al. [21] propose a traffic prediction method for scaling resources in NFV environments based on traffic modeling with an Autoregressive Moving Average (ARMA); the predicted traffic values are obtained by minimizing the Root Mean Squared Error (RMSE). [PERSON] et al. [22] present a joint approach of an Adaptive Demand Forecasting model and an Slice Allocation algorithm in softwarized networks; they apply three of the most popular forecasting techniques: Autoregressive Integrated Moving Average (ARIMA),Holt-Winters and Neural Network Auto-Regressive (NNAR); all of the three forecast methodologies are based on the minimization of the RMSE. Among the solutions based on the prediction of the resources to be allocated, [PERSON] et al. [23] propose regressive algorithms for estimating memory and processing consumption in cloud datacenters. Some solutions [19; 24; 25] have been proposed on the prediction of host load in cloud infrastructures; these solutions are based on time series forecasting with LSTM recurring neural networks; however, all are based on minimizing the RMSE. [PERSON] et al. [26] propose prediction-based VNFI scaling solutions in virtualized Mobile Edge Computing (MEC) environments; the prediction is performed by applying some types of neural networks (convolutional and LSTM) and with the application of federated machine learning; the objective is to scale the resources by either maximizing the Quality of Service or minimizing the operational cost of the service provider; the optimization is performed by minimizing symmetric loss function as the RMSE, MAE (Mean Absolute Error) and Huber function. We have proposed the ATPA algorithm based on Seasonal Auto-Regressive Integrated Moving Average (SARIMA) [5; 6] prediction with asymmetric loss function; because estimation errors are inevitable and because the error sign can have an impact on the network cost depending on the resource allocation and QoS degradation costs, we have proposed a solution in which the defined loss function gives higher (lower) weight to errors that result in a higher (lower) network cost. We have shown how the proposed solution allows for 30% network cost reduction with respect to the case in which a symmetric cost function as RMSE is chosen. Moreover, all the necessary cloud resource prediction techniques proposed in literature are always based on symmetrical cost functions i.e., RMSE and MAE.