Discrete-time Analysis of the Output Process of an Atm Multiplexer with Periodic Input

In this paper we present an exact solution for the distribution function of the busy and idle periods of an ATM multiplexer. Since information in ATM environments is subdivided into xed-size cells, the input and also the output line is considered as discreti-zed into time slots of cell-duration length. The considered multiplexer is of nite capacity and the output-line is assumed to be N times faster than each input line. The input traac is the superposition of M independent and isochronous sources and each source is assumed to transmit exactly one ATM-cell in each N slots. The corresponding queueing model is known in the literature as M D=D=1 ; S model. For diierent load situations we present recursive algorithms which are of polynomial order and eecient in terms of computing time and memory requirements. Also the case of an innnite capacity ATM-multiplexer is considered. Numerical examples show that the mean value and especially the coeecient o f v ariation of the busy period depend strongly on the traac intensity. The numerical results give insight i n to the changes of the traac characteristic when one ATM stage is passed. This forms a basis for the traac characterization and modelling in ATM network context.