New for old: reusing ATM cell scale analysis at the burst scale

A new burst level queueing analysis has recently been published which challenges the accuracy of fluid-flow analysis for application to ATM. It is similar to the conventional approach in that it is carried out at the burst level, but differs in that the excess rate of cells is handled as a discrete process rather than as a continuous fluid. The method gives a mathematically elegant solution when the arrival process is a single on/off source: the state probabilities are a geometric progression, giving a closed form solution for the cell loss probability. This paper summarises how this new discretised fluid-flow analysis is being extended by the reuse of cell scale queueing analysis. With a single on-off source, the discretised fluid-flow analysis can be considered at the burst level as a queue with geometrically distributed batch input and geometrically distributed service time. The cell scale model provides arbitrarily distributed batch input, with batches arriving as a geometric process. This can be re-interpreted at the burst level as arbitrarily distributed excess-rate batches and geometrically distributed service times. Such a model provides an opportunity to specify more closely the excess rate arrival process and apply the analysis to multiplexing scenarios. It also enables multi-state sources to be modelled, where each one of many on states is entered from the single off state. Such sources are suitable for modelling output processes-this has potential then for extending the analysis to the network scale