Threshold start-up control policy for polling systems |
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Authors: | Günalay Yavuz Gupta Diwakar |
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Institution: | (1) Faculty of Business Administration, Bilkent University, Ankara, 06533, Turkey;(2) Michael G. DeGroote School of Business, McMaster University, Hamilton, Ontario, L8S 4M4, Canada |
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Abstract: | A threshold start-up policy is appealing for manufacturing (service) facilities that incur a cost for keeping the machine
(server) on, as well as for each restart of the server from its dormant state. Analysis of single product (customer) systems
operating under such a policy, also known as the N-policy, has been available for some time. This article develops mathematical analysis for multiproduct systems operating
under a cyclic exhaustive or globally gated service regime and a threshold start-up rule. It pays particular attention to
modeling switchover (setup) times. The analysis extends/unifies existing literature on polling models by obtaining as special
cases, the continuously roving server and patient server polling models on the one hand, and the standard M/G/1 queue with N-policy, on the other hand. We provide a computationally efficient algorithm for finding aggregate performance measures, such
as the mean waiting time for each customer type and the mean unfinished work in system. We show that the search for the optimal
threshold level can be restricted to a finite set of possibilities.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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Keywords: | polling models threshold start-up control dormant/patient server descendant sets globally gated service queueing theory |
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