Abstract
The paper is a review of some results on the discrete-time finite-buffer queueing system which models a communication network multiplexer fed by a self-similar cell traffic. The review includes also some new results. First, the definitions of second-order self-similar processes are given. Then, a queue model is introduced. It has a finite buffer, a number of servers with unit service time, and an input traffic which is an aggregation of independent source-active periods having Pareto-distributed lengths and arriving as Poisson batches. A source generates a Bernoulli sequence of cells. The asymptotic bounds to the buffer-overflow and cell-loss probabilities are given in some cases. The bounds show a true asymptotic behaviour of the probabilities. The bounds decay polynomially with buffer-size growth and exponentially with excess of channel capacity over traffic rate.
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Tsybakov, B. (2000). Communication Network with Self-Similar Traffic. In: Althöfer, I., et al. Numbers, Information and Complexity. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6048-4_18
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DOI: https://doi.org/10.1007/978-1-4757-6048-4_18
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