Joint modeling of network related events with multi-dimensional Markov Modulated Deterministic Processes

Multiple proposals for modeling networking characteristics have been proposed in the past. However, these proposals have focused in a particular networking characteristic and do not cope with modern requirements for integrated characterization and prediction of network related events. This integrated network characterization should include not only data flow statistics but also higher-level application and protocol statistics and users behaviors (including network actions and mobility profiles). Possible examples of utilizations are the joint modeling of: (i) traffic statistics with lower (wireless) network characteristics (e.g. upload and download packet and byte counts with transmitted and received signal power), (ii) flow statistics with application level statistics (e.g. number of active flows with number of active BitTorrent's multi-source downloads) and (iii) traffic characteristics with network radio statistics and with user location (e.g. amount of generated traffic, receiving signal-to-noise ratio and user distance and angle to a radio base station). Towards this objective, this paper proposes a novel multidimensional discrete Markov Modulated Deterministic Processes (dMMDPs) model, and an associate parameter fitting procedure, that leads to accurate joint estimation of the first and second order statistics of multiple network related events. The procedure matches simultaneously both the multidimensional density distribution function and the autocovariance functions of the univariate marginal statistics. One of the main features of this model is that the number of states is not fixed a priori and can be adapted to the particular dataset and to the network events that are being modeled. The individual autocovariance tail of each univariate marginal statistic can be adjusted to capture the long-range dependence characteristics of the network related events. The procedure then fits the dMMDP parameters in order to match the multi-dimensional distribution, within the constraints imposed by multiple autocovariance matchings. The number of states is also determined as part of this step. As a proof of concept, we applied the inference procedure to a BitTorrent traffic trace, modeling simultaneously the packet count both in the upload and download directions. These two traffic statistics exhibit long-range dependence. Very good results were obtained in terms of approximating the first and second order statistics of the traffic characteristics.