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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 32, Pages 1715-1723
http://dx.doi.org/10.1155/S0161171204210389

Reservicing some customers in M/G/1 queues under three disciplines

1Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad 9177948953, Iran
2School of Mathematical and Physical Sciences, The University of Newcastle, 2308, NSW, Australia

Received 23 October 2002

Copyright © 2004 Hindawi Publishing Corporation. 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

Consider an M/G/1 production line in which a production item is failed with some probability and is then repaired. We consider three repair disciplines depending on whether the failed item is repaired immediately or first stockpiled and repaired after all customers in the main queue are served or the stockpile reaches a specified threshold. For each discipline, we find the probability generating function (p.g.f.) of the steady-state size of the system at the moment of departure of the customer in the main queue, the mean busy period, and the probability of the idle period.