Calculating cell loss probabilities for ON-OFF sources in large unbuffered systems

In this paper we consider the problem of calculation of cell loss probabilities when M classes of stationary ON-OFF sources access a given multiplexer of large capacity. We show that when the number of sources of each type is large and scaled according to the capacity we can obtain an explicit analytic formula (O(1) in complexity) in terms of the parameters of the sources. This is based on a measure change technique combined with the use of uniform local limit theorems which gives estimates with a precise notion of the order of errors. We compare our results with standard Gaussian approximations which have been reported showing the improvement in the ATM context where cell loss probabilities are typically of the order 10^-9