Accurate modeling of VoIP traffic QoS parameters in current and future networks with multifractal and Markov models

In this paper, we analyze the jitter and packet loss behavior of Voice over Internet Protocol (VoIP) traffic by means of networks measurements and simulations results. As result of these analyses, we provide a detailed characterization and accurate modeling of these Quality of Service (QoS) parameters. Our studies have revealed that VoIP jitter can be modeled by self-similar processes with short range dependence (SRD) or long range dependence (LRD). The discovery of LRD (a kind of asymptotic fractal scaling) in VoIP jitter was followed by a further work that shows the evidence of multifractal behavior. The implication of these behaviors for VoIP and other interactive multimedia services is that receiver de-jitter buffer may not be large enough to mask the jitter with LRD and multifractal characteristics. On the other hand, we use a description of VoIP packet loss based on microscopic and macroscopic packet loss behaviors, where these behaviors can be modeled by 2-state and 4-state Markov chains, respectively. Based on the above mentioned points, we present a methodology for simulating packet loss. Besides, we found relationships between Hurst parameter (H) with the packet loss rate (PLR); these relationships are based on voice traffic measurements and can be modeled by means of a power-law function, characterized by three fitted parameters. The proposed models can be used to: (i) design a de-jitter buffer, (ii) to implement a synthetic generator of VoIP jitter data traces, where the synthetic jitter data traces can be used as test vectors to carry out the performance evaluation of a de-jitter buffer of VoIP system, and (iii) design effective schemes for packet loss recovery.