Gaussian Fluid Queue with Autocorrelated Input

Abstract

This paper develops a generalization of Brownian motion with stationary, autocorrelated increments as a tractable model for problems in business and finance. We show that any real continuous Gaussian Markov process with stationary increments and smooth covariance function is characterized by three parameters quantifying drift, volatility, and autocorrelations. We model a queue as a functional of a process defined by those characteristics and derive its transient distribution conditional on its history.