Modeling Oscillation Behavior of Network Traffic by Nested Hidden Markov Model with Variable State-Duration

Network traffic modeling is a fundamental problem in communication. A traffic model should be able to capture and reproduce various properties of a real trace. Despite the widespread success of most numerical models in various applications, few actually focus on the oscillation behavior proven to be one of the basic properties in network traffic. In this paper, a new mathematical method is proposed to model and synthesize stationary and nonstationary oscillatory processes of network traffic. The proposed model is based on the structure of the hierarchical hidden Markov model, which includes two nested hidden Markov chains and one observable process. The first-layer hidden Markov chain with variable state-duration controls the time-varying oscillatory process. Conditional on the first-layer Markov chain, the local fluctuation process is modeled by the second-layer hidden Markov chain. Algorithms are derived for inference of model parameters and traffic synthesis. The proposed approach is compared with four classical models for performance evaluation. The selected performance criterion includes time structure, statistical properties, self-similarity, queuing behavior and multiscale properties. The flexibility and accuracy of the proposed model results in a close fit to the real traces.