An aggregation technique to evaluate the performance of a two-stage buffered ATM switch

This paper illustrates an approximate method to evaluate the cell loss probability of an N x F two-stage ATM switch. Traffic is assumed to be "uniform": arrival processes are simple Bernoulli processes, cells are uniformly directed through output ports, at which finite-capacity buffers are placed. The time evolution of the switch is represented by a Markov process and the transition matrix is generated. In order to solve this matrix system, whose size is very large, an approximate method is proposed, based on the aggregation technique first initiated by Simon and Ando [1]. The purpose of this method is to successfully decompose the transition matrix into blocks, or aggregates, which are then replaced by simple elements to form the aggregated matrix. The resulting smaller matrix may be directly solved. The approximation error, made by the aggregation, completely depends on the way the matrix is decomposed. In this case, the transition matrix is decomposed in such a way that states belonging to the same aggregate have an identical number of non-empty first-stage queues. Consequently, elements of the aggregated matrix may be expressed approximately as a function of the aggregated matrix of the first-stage subsystem, which in turn may be evaluated directly and accurately. By the application of this method, a 21 33 -dimension matrix can be reduced to a 693-dimension matrix. The authors validate the approximation by comparing the results of the aggregation method with the exact results for low parameter values. Copyright Kluwer Academic Publishers 1998