An Application of Stochastic Ordering to the Analysis of the Push-Out Mechanism [chapter]

J. M. Fourneau, N. Pekergin, H. Taleb
1995 Performance Modelling and Evaluation of ATM Networks  
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 lllanner. We consider an i.i.d arrival process of cells and a constant switching time of a cell. Therefore, the system can be moddled 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
more » ... chastic ordering to aggre-giLte the underlying Markov chain to obtain a. bounding 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 B2 states and finally to B states. Several bounds have been computed under various assumptions and they prove that the proposed methodology is numerically efficient.
doi:10.1007/978-0-387-34881-0_12 fatcat:jooazcbkv5egzmlc47d34a3n3a