# Profit-Efficient Elastic Allocation of Cloud Resources Using Two-Stage Adaptive Workload Prediction
## 2 Related Work  
### Workload Prediction in the Cloud  
Due to its crucial role in optimizing resource allocation, workload prediction in cloud computing has attracted substantial research attention. Several studies have focused on support vector regression (SVR), deep learning, and time-series analysis algorithms. These approaches have been shown to enhance system performance through providing highly accurate workload predictions. In [11], the authors reviewed various traditional methods for cloud computing workload prediction, including SVR, auto-regressive moving average (ARMA), auto-regressive integrated moving average (ARIMA), linear regression (LR), and artificial neural networks (NNs). Based on an ARIMA model, [PERSON] et al. [12] proposed online computing resource scheduling algorithms. They presented that the QoS is the key element of computing resource allocation in the cloud. Furthermore, [PERSON] et al. [13] categorized workloads into distinct types and subsequently applied different ARIMA models to fit each category. Their results demonstrated that this classification approach significantly improves the workload prediction accuracy. [PERSON] et al. [14] used LR, ARIMA, and SVR approaches to predict the cloud service workload. They also classified the workload into distinct types. Deep learning has been demonstrated to achieve excellent performance in time-series signal fitting and prediction. [PERSON] et al. [15] used an NN to predict the CPU workload, and the NN model outperformed LR in their experiments. [PERSON] et al. [16] proposed a workload prediction model using an NN and a self-adaptive differential evolution algorithm. With the advancement of deep learning technologies, specialized models, such as recurrent neural networks (RNNs) and LSTM networks, have been specifically designed for processing time-series signals. In [17], a deep learning-based prediction algorithm (L-PAW) utilizing an RNN was proposed for workload prediction in the cloud. RNN-based networks are typically capable of extracting valuable information from input data by continuously updating prior information as it processes the sequence. However, as the time interval increases, the gradients tend to vanish, leading to the gradient vanishing problem. This issue results in ineffective parameter updates within the RNN, limiting its ability to efficiently capture long-term memory dependencies. To overcome the limitations of RNNs, advanced architectures such as LSTM networks and gated recurrent units (GRUs) have been proposed. The authors in [18] used an LSTM to predict the workload in cloud computing, which outperformed NNs and other traditional methods. [PERSON] et al. [19] also showed that LSTMs can be effectively adapted for time-series data forecasting, particularly for predicting future server loads in the context of cloud computing. Additionally, recent research has explored novel approaches for cloud computing workload prediction, especially regarding the Transformer architecture. For instance, [PERSON] et al. [20] applied the Transformer architecture for time-series prediction in cloud computing. Their experimental results demonstrated that the Transformer-based approach achieved competitive performance through effectively modeling temporal workload patterns. Furthermore, the authors of [21] evaluated the Transformer architecture against other approaches for cloud workload prediction, and their comparative analysis revealed that the Transformer architecture is particularly suitable for workload forecasting. Building upon the Transformer architecture, several advanced models have been proposed. [PERSON] et al. [22] introduced a hybrid LSTM-Transformer model for multi-task time-series forecasting. Although the Transformer model has a good capability for time-series forecasting, the experiments reported in [21] revealed that its performance is inferior to that of LSTM, particularly when considering single-task scenarios, limited training data conditions, and short-term predictions.