Abstract
In this paper, we compute the stochastic bounds on the cell loss rates in an ATM switch. The spatial priority in the buffer is controlled by the Push-Out mechanism, while the time priority is managed in the FIFO manner. We consider an i.i.d arrival process of cells and a constant switching time of a cell. Therefore, the system can be modelled by a discret-time Markov chain, however the size of the chain is approximatively 2B, where B is the buffer size. We propose a methodology based on the stochastic ordering to aggregate the underlying Markov chain to obtain a. hounding Markov chain. In other words, the performance indices defined by the reward functions are bounded stochastically by the reward functions of the bounding Markov chain. We apply the methodology twice to have the bounding Markov chain reduced to B 2 states and finally to B states. Several bounds have been computed under various assumptions and they prove that the proposed methodology is numerically efficient.
This work has been supported by CNET under grant 92 1B 178 on formal design of cooperative highspeed multimedia systems.
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© 1995 Springer Science+Business Media Dordrecht
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Fourneau, J.M., Pekergin, N., Taleb, H. (1995). An Application of Stochastic Ordering to the Analysis of the Push-Out Mechanism. In: Kouvatsos, D.D. (eds) Performance Modelling and Evaluation of ATM Networks. ATM 1994. IFIP — The International Federation for Information Processing. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-34881-0_12
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DOI: https://doi.org/10.1007/978-0-387-34881-0_12
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