Numerical solution of fluid queueing models for communication networks

Discrete stochastic models of queues are commonly employed in communication networks for their analysis and control. Fluid models, largely stochastic, are being used recently due to their simple character. However, asymptotic analysis of queueing models leads to deterministic fluid models and efficient methods for computing their solution are needed. This paper develops procedures for numerical solution of fluid queueing models whose arrival processes with rates that are piecewise constant. Solutions for fluid queue with single input, queue with two classes under priority and a model with two fluid queues in tandem are developed and implemented. The piecewise linear nature of the dynamics are employed to develop these efficient solution procedures by determining the solution at time instances of rate change of the input. This aviods using numerical solution of differential equations and also greatly reduces the computational complexity. Computer programs are developed implementing the numerical solutions. Motivated by their application to communication network sources, ON/OFF fluid inputs are considered for analysis. The developed numerical solution procedures are applied to the ON/OFF sources as special cases of the piecewise constant rate inputs.