M&M: Multi-level Markov Model for Wireless Link Simulations

802.15.4 links experience different level of dynamics at short and long time scales. This makes the design of a suitable model that combines the different dynamics at different timescales a non-trivial problem. In this paper, we propose a novel multilevel approach involving Hidden Markov Models (HMMs) and Mixtures of Multivariate Bernoullis (MMBs) for modeling the long and short time scale behavior of wireless links using experimental data traces collected from multiple 802.15.4 testbeds. We characterize the synthetic traces generated from the model of the wireless link in terms of statistical characteristics as compared to an empirical trace with similar PRR characteristics, such as the mean and variance of the packet reception rates from the data traces, comparison of distributions of run lengths and conditional packet delivery functions of successive packet receptions (1's) and losses (0's). We modified TOSSIM to utilize data traces created using our modeling approach and compare them against the existing radio model in TOSSIM, which uses the Closest-fit Pattern Matching model for modeling variations in noise which affect the link quality. The results show that our proposed modeling approach is able to mimic the behavior of the data traces quite closely, with difference in packet reception rates of the empirical and simulated traces of less than 2.5% on average and 9% in the worst case. Moreover, the simulated links from our proposed approach were able to account for long runs of 1's and 0's as observed in empirical data traces.