tailieunhanh - Computing the bounds on the loss rates

We consider an example network where we compute the bounds on cell loss rates. The stochastic bounds for these loss rates using simple arguments lead to models easier to solve. We proved, using stochastic orders, that the loss rates of these easier models are really the bounds of our original model. For ill-balanced configurations these models give good estimates of loss rates. | Yugoslav Journal of Operations Research 12 (2002), Number 2, 167-184 COMPUTING THE BOUNDS ON THE LOSS RATES . FOURNEAU PRiSM, Universit› de Versailles Saint-Quentin, France {jmf,nih}@ L. MOKDAD LAMSADE, Universit› de Paris Dauphine, France {mokdad}@ N. PEKERGIN CERMSEM, Universit› de Paris I Sorbonne, France Abstract: We consider an example network where we compute the bounds on cell loss rates. The stochastic bounds for these loss rates using simple arguments lead to models easier to solve. We proved, using stochastic orders, that the loss rates of these easier models are really the bounds of our original model. For ill-balanced configurations these models give good estimates of loss rates. Keywords: Discrete time Markov chains, tochastic bounds, ATM switch, loss rates. 1. INTRODUCTION ATM (Asynchronous Transfer Mode) technology is intended to support a wide variety of services and applications and to satisfy a range of Quality-of-Service (QoS). The QoS is measured by a set of parameters intended to characterize the performance of the network. These performances depend generally on the switch performances. We are interested in computing the cell loss rates in a multistage ATM switch. Loss rates are very important because they may be part of the contract on the quality of service between the user and the network provider. Using a numerical method to compute loss rates is very difficult because of the size of the model. So, we propose a stochastic method to compute upper and lower bounds on the loss rates. To do this, we propose two simple systems which are easier to evaluate and which provide upper and lower bounds on the considered performance measure. We prove that the loss rates on the easier systems are really bounds on the original system. We make this proof, using 168 . Fourneau, L. Mokdad, N. Pekergin / Computing the Bounds on the Loss Rates stochastic method based on stochastic ordering and stochastic .