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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 793801, 19 pages
http://dx.doi.org/10.1155/2012/793801
Research Article

Random -Policy Geo/G/1 Queue with Startup and Closedown Times

Department of Accounting Information, National Taichung University of Science and Technology, Taichung 404, Taiwan

Received 23 July 2012; Revised 6 October 2012; Accepted 7 October 2012

Academic Editor: Han H. Choi

Copyright © 2012 Tsung-Yin Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This study investigates a random -policy Geo/G/1 queue with startup and closedown times. is newly determined every time a new cycle begins. When random customers are accumulated, the server is immediately turned on but is temporarily unavailable to the waiting customers. It needs a startup time before starting providing service. After all customers in the system are served exhaustively, the server is shut down by a closedown time. Using the generating function and supplementary variable technique, analytic solutions of system size, lengths of state periods, and sojourn time are derived.