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, 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. This paper present an analytical approximations of the probability of a buffer overflow within a given time interval. The analysis uses and demonstrates a measure-transformation technique.
Key words and phrases: Cusum, likelihood-ratio identity, long-range dependence, maxima of a random field, overshoot correction.