A Two-Step Fitting Approach of Batch Markovian Arrival Processes for Teletraffic Data

Abstract

Batch Markovian arrival process (BMAP) is a powerful stochastic process model for fitting teletraffic data since its MAP structure can capture the mode of packet interarrival times and its batch structure can capture packet size distributions. Compared with Poisson-related models and simple MAP models richly studied in the literature, the BMAP model and its fitting approach are much less investigated. Motivated by a practical project collaborated with Huawei company, we propose a new two-step parameter fitting approach of the BMAP model for teletraffic data generated from IP networks. The first step is the phase-type fitting for packet interarrival times, which is implemented by the framework of EM (expectation maximization) algorithms. The second step is the approximation of the lag correlation values of packet interarrival times and packet sizes, which is implemented by the framework of MM (moment matching) algorithms. The performance of our two-step EM-MM fitting approach is demonstrated by numerical experiments on both simulated and real teletraffic data sets, and compared with the MAP and MMPP (Markovian modulated Poisson process) models to illustrate the advantages of the BMAP model. Numerical examples also show that our proposed two-step fitting approach can obtain a good balance between the computation efficiency and accuracy.