Structural decomposition and serial solution of SPN models of the ATM GAUSS switch

Abstract

We address the performance, in particular, the cell loss ratio, of the ATM GAUSS switch under a variety of realistic video and constant bit rate traffic patterns.

We describe the operation of the GAUSS switch and derive a stochastic Petri net model for it. One problem with this model, when subjected to realistic traffic, is that it is too large (in terms of states of the underlying Markov chain) to be analysed. We circumvent this largeness problem by structurally decomposing this model in a number of smaller models that can be solved in a serial fashion, thereby using analysis results of one another. This approach not only speeds up the solution process by several orders of magnitude, it also still yields accurate results.

With respect to the GAUSS switch we show that under realistic traffic, the internal buffers need to be doubled in size, as opposed to analysis results under Poisson traffic, to yield acceptable cell-loss performance. Concluding, this paper serves three aims: (i) it shows the suitability of stochastic Petri nets in the context of ATM system analysis; (ii) it illustrates a structural decomposition method circumventing the state space explosion problem; and (iii) it derives more detailed performance results for the GAUSS switch than has been possible previously.

This work his been done while B.R. Haverkort was assistant professor at the University of Twente, and H.P. Idzenga was writing his M.Sc. thesis [14] there.