On the broadening of cell bursts in an ATM network

The expansion of a burst during its traversal through a number of multiplexing stages in an ATM network is analysed. The phenomenon is first described and demonstrated by simulation experiments. The expansion is caused by a self-induced load increase of the multiplexers by the burst, whereby the latter cells of the burst experience, on the average, longer delays than the first cell. An analytical study on the growth of the interval between the first and the second cell is presented. Assuming Poissonian background traffic, this interval forms a Markov chain, from stage to stage. The transition matrix of the chain is derived by calculating the delay distribution of the second cell conditioned on the delay of the first cell and the interval between the two on the input side of the multiplexer, and then unconditioning this with respect to the delay of the first cell which is distributed as the delay in an M/D/1 queue. A simplified analysis is also given for the growth of the average interval