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.