On the distribution of the number of packets in the fluid flow approximation of packet arrival streams

Fluid flow approximations are widely used for approximating models of communication systems where packet arrival streams are generated in a regular manner over certain intervals (constant rate). The appropriate model for describing those bursty arrival streams in the fluid flow framework are the well-known Markov modulated rate processes (MMRP). The paper deals with the distribution of the number N(t) of packets in the interval [0,t] of MMRP. For two-state MMRPs and their superpositions the authors derive formulas for the distribution of N(t) and its density. Further they give asymptotic results. The presented numerical results and simulation studies illustrate the goodness of the fluid flow approximation and show that the proposed numerical algorithms work well even in the case of multiplexing a large number of burst silence sources.