《On stochastic decomposition in the GIM1 queue with single exponential vacation》.pdf

Operations Research Letters Operations Research Letters 34 (2006) 706–712 /locate/orl On stochastic decomposition in the GI/M/1 queue with single exponential vacation Kyung C. Chaea ,∗, Sang Min Leea , Ho Woo Leeb aDepartment of Industrial Engineering, KAIST, Daejeon 305-701, South Korea bDepartment of Systems Management Engineering, Sungkyunkwan University, Suwon 440-746, South Korea Received 18 April 2005; accepted 28 November 2005 Available online 18 January 2006 Abstract We consider a GI/M/1 queueing system in which the server takes exactly one exponential vacation each time the system empties. We derive the PGF of the stationary queue length and the LST of the stationary FIFO sojourn time. We show that both the queue length and the sojourn time can be stochastically decomposed into meaningful quantities. © 2005 Elsevier B.V. All rights reserved. Keywords: Factorization; Generalized vacations; Queue lengths; Waiting time 1. Introduction length and the Laplace–Stieltjes transform (LST) of the stationary first-in first-out (FIFO) sojourn time. We consider a GI/M/1 queueing system in which