Large deviations, the shape of the loss curve, and economies of scale in large multiplexers

The authors analyse the queue at a multiplexer with L inputs. They obtain a large deviation result, namely that under very general conditions provided the offered load is held constant, where the shape function I is expressed in terms of the cumulant generating functions of the input traffic. This provides an improvement on the usual effective bandwidth approximation , replacing it with . The difference determines the economies of scale which are to be obtained in large multiplexers. If the limit exists (here is the finite time cumulant of the workload process) then lim . The authors apply this idea to a number of examples of arrivals processes: heterogeneous superpositions, Gaussian processes, Markovian additive processes and Poisson processes. They obtain expressions for in these cases. is zero for independent arrivals, but positive for arrivals with positive correlations. Thus economies of scale are obtainable for highly bursty traffic expected in ATM multiplexing.