2-state (semi-)Markov Processes beyond Gilbert-Elliott: Traffic and Channel Models based on 2nd Order Statistics

Two-state Markov models are applied in many performance evaluation studies as a simple form of autocorrelated processes, starting with Gilbert-Elliott channels for the analysis of transmission protocols subject to error bursts. We derive an explicit formula for the 2nd order statistics of 2-state semi-Markov processes in order to adapt them to correlated traffic and error processes. State and transition specific distribution functions are included in a general representation covering the special cases being usually studied in the literature. The results reveal the influence of model parameters on short and long term dependency and give rise to a straightforward procedure for parameter adaption. In general, 2-state models provide a 2-dimensional fitting space, whereas special 2-state cases often have only one parameter left to fit the shape of the 2nd order statistics. In our evaluation of IP packet measurements on aggregation links we experienced that adaptations by general 2-state Markov models achieve a much closer fit to the traffic variability in different time scales than self-similar processes.