Efficient fitting of long-tailed data sets into hyperexponential distributions

We propose a new technique for fitting long-tailed data sets into hyperexponential distributions. The approach partitions the data set in a divide and conquer fashion and uses the expectation-maximization (EM) algorithm to fit the data of each partition into a hyperexponential distribution. The fitting results of all partitions are combined to generate the fitting for the entire data set. The new method is accurate and efficient and allows one to apply existing analytic tools to analyze the behavior of queueing systems that operate under workloads that exhibit long-tail behavior, such as queues in Internet-related systems.