Bursty traffic modeling and efficient analysis algorithms via fluid-flow models for ATM IBCN

Abstract

In this paper fluid models for heterogeneous multiplexed traffic are considered. First, some extensions to the general theory applicable to superposed, time-reversible Markovian Rate Processes are given. These refer to the connection between performance metrics, the consideration for singular systems and the continuity of the solution, with respect to the system parameters. The general framework is then carried over to the heterogeneous multiplexing of ON/OFF sources. By combining the general theory with the special structure of the ON/OFF sources several important facets of this structure are highlighted. As a result, more powerful methods that improve computation speed, stability and ease of implementation are produced. More specifically, the numerical part of the method is reduced to a solution of a nonlinear equation per system eigenvalue. The solution is obtainable through a variant of the (locally quadratically convergent) Newton method. For this method, easily computable starting values that guarantee convergence are given. In addition, explicit expressions for the eigenvectors are provided with the potentially unstable quantities factored-out. The paper also provides explicit and stably computable formulae for upper bounds to the coefficients of the spectral components, present in the expressions for the performance measures of interest. Moreover, the paper proves a partial ordering property for the system eigenvalues and presents an algorithm that performs full ordering on-line. This, in many cases, results in a great reduction to the amount of computation, without any significant loss of precision. Lastly, the particular case of heterogeneity where the differences are only identified in the rates within bursts is seen to have features resembling homogeneous systems. The possibility to substitute an “equivalent” homogeneous system of reduced order, for the original heterogeneous one is addressed.