A Poisson Limit for Buffer Overflow Probabilities

A key criterion in the design of high-speed networks is the probability that the buffer content exceeds a given threshold. We consider n independent identical traffic sources modelled as point processes, which are fed into a link with speed proportional to n. Under fairly general assumptions on the input processes we show that the steady state probability of the buffer content exceeding a threshold b > 0 tends to the corresponding probability assuming Poisson input processes. We verify the assumptions for a large class of long-range dependent sources commonly used to model data traffic. Our results show that with superposition, significant multiplexing gains can be achieved for even smaller buffers than suggested by previous results, which consider O(n) buffer size. Moreover, simulations show that for realistic values of the exceedance probability and moderate utilisations, convergence to the Poisson limit takes place at reasonable values of the number of sources superposed. This is particularly relevant for high-speed networks in which the cost of high-speed memory is significant.