The analysis of the time-dependent behavior of queues

This book studies the time-dependent behavior of queuing systems which has non-empty initial work load. The technique used to analyze the behavior of the queueing systems studied in this book is based on the Wiener-Hopf factorization. The first major step in the analysis is the derivation of the (system of) transformed Wiener-Hopf equation(s). Wiener-Hopf factorization is then applied to its symbol. Since the queueing systems we consider have a non-zero initial working load, the Wiener-Hopf factorization should be followed by a decomposition on a certain (matrix) function. The Wiener-Hopf factorization and the decomposition yields a (formal) solution of the (system of) equation(s).If the stability condition is fulfilled, then the steady-state distributions of interest can be determined by applying Abel's limit theorem to the solution of the (system of) equation(s).In this book it is shown how the time-dependent distributions converge to the steady-state distribution.

Autorentext

Rieske Hadianti was born in Bandung, Indonesia, on 13 February 1969. Graduated from Faculty of Electrical Engineering, Mathematics and Computer Sciences, University of Twente, the Netherlands. She is a member of Industrial and Financial Mathematics Group at the Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Indonesia.