Merging and splitting autocorrelated arrival processes and impact on queueing performance

We have proposed a three-parameter renewal approximation to analyze splitting and superposition of autocorrelated processes. We define the index of dispersion for counts of an ordinary process used in a new and more accurate technique to estimate the third parameter. Then, we express this newly defined index of dispersion for the superposition in terms of the ordinary as well as the stationary indices of dispersion of the originally autocorrelated component processes. Hence, even if the superposition data is not observable, as long as sufficient information exists on component processes, the parameters of the proposed renewal approximation can be estimated accurately. The accurate renewal approximation of a general process helps in sustaining accuracy if it is split, by-passing the need to sample from branched processes. We have tested the impact of our approximation on the accuracy of the mean waiting time, which compared favorably with simulation results of the original systems.