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TITLE: On the distribution of overflows
SPEAKER: Benjamin Yakir
ABSTRACT:
Long range dependence in stationary processes of increments
corresponds to the situations where
the variance of cumulative sums is dominated by the accumulation of the
covariances between
increments. The Hurst parameter, the exponent of the standard deviation
of the sum as a function of
the number of increments involved, is a characteristic of long range
dependence.
Models of long range dependence, models that involve an Hurst parameter
0.5 < H < 1, are frequently used to
model the incoming workload in computer networks and communication.
Consider a Gaussian arrival process with long range dependence, a
buffer, and a departure process bounded
by the bandwidth. In this talk we will present analytical approximations
of the distribution of the number
of buffer overflows within a given time interval. This approximation is
obtained by equating the number
of buffer overflows with the number of times that a CUSUM process
exceeds a threshold. The distribution
of the later can be analyzed via the combination of a Poisson
approximation and likelihood ratio identities.
