Transient analysis of Markov-fluid-driven queues
The paper focuses on some transient characteristics of Markov-fluid-driven queues. It adopts a new approach for computing the Laplace transform of the busy period expressing it in terms of a number of auxiliary transforms (as many as there are states with net buffer increase). A sufficient number of additional constraints to uniquely determine them are given; this analysis carries over to the correlation function. One shows the tail distribution of the busy period can be written in terms of the asymptotic log-moment generating function of the input process invoking sample-path large deviations. Denoting by \(Q(t)\) the buffer content at time \(t\), the covariance function Cov\((Q(0),Q(t))\) is a measure of dependence between the workload at time 0 and at time \(t\). Using the methodology for analyzing the busy period, one characterizes it by its Laplace transform. In some cases, the correlation function can be determined explicitly. An example illustrates the results obtained in the paper.
scientific article; zbMATH DE number 5942595