Estimation of parameters of input traffic streams from statistically multiplexed output

Given the statistically multiplexed stream observations of two independent and different types of traffic streams, this paper examines the problem of determining the degree of mixing. In data networks a common example of such a pair of different stream would be one conforming to the traditional Poisson model with an exponential inter-arrival distribution and the other obeying long-range dependent traffic characterized by a heavy-tailed distribution. The paper provides an expression for the probability density function of the inter-arrival time of the mixed stream in terms of those of the input streams for the general case. As an example, we consider a mixed output traffic stream for the specific case of multiplexed Poisson and heavy-tailed processes and an approach is provided to estimate input parameters from the first and second order statistics. For arrival rate estimation of the input streams, we propose a look-up table approach based on nearest neighbor search. The simulation results demonstrate that the estimated arrival rates and the moments are indeed close to their respective true values.