MODELING BUFFER ADMISSION MECHANISMS USING STOCHASTIC AUTOMATA NETWORKS

The stochastic automata networks formalism is an attractive technique to model complex systems with interacting components. Each component of the system is modelled by a single automaton; interactions between components are modelled by labels on the arcs which may represent synchronization and state-dependent transitions. Every automaton is associated with some matrices which allow to build the transition matrix of the underlying Markov chain, using tensor algebra. To illustrate this methodology, we introduce two buffer policies which could be used in ATM switching node. Every policy manages two priority levels which have distinct cell loss requirements. The first buffer policy is based on the push-out mechanism : a high priority cell replaces a low priority cell when the buffer is full. The second policy causes the discarding of all the low priority cells when the user transmits a request to send a burst of cells. In both studies, we compute the loss probabilities of each type of cells under various assumptions.