Stochastic ordering and the notion of negligible CDV

Admission control in ATM is facilitated when the rate of cell streams is defined with “negligible CDV” in the sense that multiplexer performance can be predicted conservatively by assuming Poisson arrivals. To say a stream is thus better than Poisson implies the comparison of stochastic processes according to some ordering criterion. This paper investigates possible orderings and considers the conservation of ranking under the operation of multiplexing in deterministic queues. Variability ordering provides useful comparisons for isolated queues and for a saturated tandem with cross traffic. For comparisons in a more general network context we employ large deviations techniques. The analysis form&es and provides supporting evidence in favour of the plausible conjecture that streams retain negligible CDV in a network of ATM multiplexers if all streams have negligible CDV on input.