Sensitivity analysis and fast computation of packet loss probabil- ities in multiplexer models

A statistical multiplexer is a basic model used in the design and the dimensioning of communication networks. The multiplexer model consists of a finite buffer, to store incoming packets, served by a single server with constant service time, and a more or less complicated arrival process. The aim is to determine the packet loss probability as a function of the capacity of the buffer. An exact analytic approach is unfeasible in real time, and hence we show how techniques from rational approximation theory can be applied to the computation of the packet loss. Since the parameters used in such networks may not produce precise probabilities of interest without having to introduce drastic assumptions, we also carry out a perturbation analysis with respect to these parameters. Using techniques from interval arithmetic, we can deliver sharp bounds for the true uncertainity effect. The latter is very important because the packet loss probability function can be very sensitive to relatively small changes in the network parameters.