Hostname: page-component-7479d7b7d-wxhwt Total loading time: 0 Render date: 2024-07-12T22:14:09.705Z Has data issue: false hasContentIssue false

AN IDENTITY OF THE GI/G/1 TRANSIENT DELAY AND ITS APPLICATIONS

Published online by Cambridge University Press:  11 January 2002

Chia-Li Wang
Affiliation:
Department of Applied Mathematics, National Dong Hwa University, Hualien, Taiwan, Republic of China, E-mail: CWang@mail.ndhu.edu.tw

Abstract

We consider a single-server queue that is initially empty and operates under the first-in–first-out service discipline. In this system, delays (waiting times in queue) experienced by subsequent arriving customers form a transient process. We investigate its transient behavior by constructing a sample-path coupling of the transient and a general (delayed) processes. From the coupling, we obtain an identity that relates the sample paths of these two processes. This identity helps us to better understand the queue's approach to the stationary limit and to derive upper and lower bounds on the expected transient delay. In addition, we use a Brownian-motion model to approximate the identity. This produces an approximation of the expected transient delay. The approximation turns out to be identical to the corresponding first moment of a reflected Brownian motion. Thus, it is easy to compute and its accuracy is supported by numerical experiments.

Type
Research Article
Copyright
© 2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)