LARGE DEVIATIONS, THE SHAPE OF THE LOSS CURVE, AND ECONOMIES OF SCALE IN LARGE MULTIPLEXERS Academic Article uri icon

abstract

  • We analyse the queue Q L at a multiplexer with L inputs. We obtain a large deviation result, namely that under very general conditions {Mathematical expression} 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 {Mathematical expression} replacing it with {Mathematical expression}, The difference I(b)-b determines the economies of scale which are to be obtained in large multiplexers. If the limit {Mathematical expression} exists (here t , is the finite time cumulant of the workload process) then {Mathematical expression}. We apply this idea to a number of examples of arrivals processes: heterogeneous superpositions, Gaussian processes, Markovian additive processes and Poisson processes. We obtain expressions for v in these cases, v is zero for independent arrivals, but positive for arrivals with positive correlations. Thus ecconomies of scale are obtainable for highly bursty traffic expected in ATM multiplexing. 1995 J.C. Baltzer AG, Science Publishers.

published proceedings

  • QUEUEING SYSTEMS

altmetric score

  • 3

author list (cited authors)

  • BOTVICH, D. D., & DUFFIELD, N. G.

citation count

  • 189

complete list of authors

  • BOTVICH, DD||DUFFIELD, NG

publication date

  • September 1995