Title: A general retrial system with additional vacation

Authors: Jau-Chuan Ke, Fu-Min Chang, Ming-Yang Ko

Addresses: Department of Applied Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan. ' Department of Finance, Chaoyang University of Technology, Taichung County 413, Taiwan. ' Department of Accounting Information, National Taichung Institute of Technology, Taichung 404, Taiwan

Abstract: This paper studies a retrial system with batch arrival and general retrial time, where the server may take an additional vacation after the essential vacation. In this system, primary customers arrive according to Poisson processes and receive corresponding service immediately if the server is available upon arrival. When the server is busy or on vacation, arriving customers enter a retrial orbit. If the orbit is empty, the server immediately leaves for the essential vacation. At the end of essential vacation, he may take one additional vacation. It is assumed that the retrial time and service time are all arbitrary distributed. This retrial system has potential applications in the packet-switched networks and the proxy of WWW server. By applying the supplementary variable technique, some important performance measures are derived, which may be useful for network system designers and software system engineers.

Keywords: Andrey Markov; decision processes; optional vacations; retrial queues; stochastic decomposition; supplementary variables; retrial systems; batch arrivals; retrial times; arrival times; additional vacations; essential vacations; Poisson distribution; primary customers; corresponding service; server availability; retrial orbits; service times; arbitrary distribution; packet-switched networks; proxy servers; internet; world wide web; performance measures; system designers; software systems; network designers; systems engineers; services operations; informatics.

DOI: 10.1504/IJSOI.2011.041418

International Journal of Services Operations and Informatics, 2011 Vol.6 No.3, pp.211 - 229

Published online: 22 Jul 2011 *

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