STATISTICAL MULTIPLEXING WITH LOSS PRIORITIES IN RATE-BASED CONGESTION CONTROL OF HIGH-SPEED NETWORKS

Statistical multiplexing with loss priorities is a central element in ATM-based Broadband ISDN. Cell priorities arise from the marking schemes employed by the access regulators to identify excess cells, which are dropped during periods of congestion. Also, in real time applications, such as hierarchically coded voice and video, cells are assigned priorities which correspond to their importance to service quality, so that when congestion occurs only the least important are dropped. In this paper we present a stochastic fluid model of statistical multiplexing with loss priorities. In this model each Markov-modulated fluid source generates streams of different priorities. The burstiness of each stream and the correlation between the priority streams are captured in the model. The loss priority is implemented by selectively discarding cells of certain priority classes when the buffer content exceeds a corresponding threshold. To handle high dimensional source models, we develop an algebraic theory for the efficient computation of the spectrum of the statistical multiplexing system, which generalizes previous results for on-off sources. It is shown that to obtain the solution of the statistical multiplexing problem with J priority classes, J different 1-class problems need to be solved, together with a system of linear equations which describe the behavior of the stationary distribution at the thresholds. The numerical results demonstrate the manner in which i) the threshold level controls the-tradeoff between delay of higher priority cells and the loss probability of lower priority cells, and ii) the buffer size controls the loss probability of higher priority cells. Waiting time distributions for each priority class are obtained. These results illuminate the important tradeoffs and provide guidelines for the design of the multiplexer.