Markov-modulated Arrival Processes and Their Application to the Analysis of Active Queue Management Algorithms

The article is devoted to the application of Markov modulated arrival processes (Markov modulated Poisson process — MMPP, Markov modulated Bernoulli process — MMBP and Markov modulated fluid flow — MMFF) models to the analysis of Active Queue Management (AQM) algorithms (Random Early Detection (RED) family, for example). The main ideas and properties of Markov modulated arrival processes (MMAP) are presented as the brief description of RED-type AQM algorithms. A review of the main results obtained with the help of MMAP processes in the analysis of AQM algorithms models is made. The authors formulated problems that also can be solved with the help of MMAP processes when analyzing the systems with RED-like algorithms.