Multivariate Multi-Order Markov Multi-Modal Prediction With Its Applications in Network Traffic Management

Predicting the future network traffic through big data analysis technologies has been one of the important preoccupations of network design and management. Combining Markov chains with tensors to implement predictions has received considerable attention in the era of big data. However, when dealing with multi-order Markov models, the existing approaches including the combination of states and Z-eigen decomposition still face some shortcomings. Therefore, this paper focuses on proposing a novel multivariate multi-order Markov transition to realize multi-modal accurate predictions. First, we put forward two new tensor operations including tensor join and unified product (UP). Then a general multivariate multi-order (2M) Markov model with its UP-based state transition is proposed. Afterwards, we develop a multi-step transition tensor for 2M Markov models to implement the multi-step state transition. Furthermore, an UP-based power method is proposed to calculate the stationary joint probability distribution tensor (i.e., stationary joint eigentensor, SJE) and realize SJE based multi-modal accurate predictions. Finally, a series of experiments under various Markov models on real-world network traffic datasets are conducted. Experimental results demonstrate that the proposed SJE based approach can improve the prediction accuracy for network traffic by highest up to 38.47 percentage points compared with the Z-eigen based approach.