Abstract
The authors present a new queueing model with (e, d) setup time. Using the quasi-birth-and-death process and matrix-geometric method, the authors obtain the stationary distribution of queue length and the LST of waiting time of a customer in the system. Furthermore, the conditional stochastic decomposition results of queue length and waiting time are given.
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References
G. Zhang and N. Tian, Analysis of queueing systems with synchronous single vacation for some servers, Queueing System, 2003, 45(2): 161–175.
G. Zhang and N. Tian, Analysis on queueing systems with synchronous vacations of partial servers, Performance Evaluation, 2003, 52(4): 269–282.
N. Tian, X. Xu, Z. Ma, and C. Wei, M/M/c queue with multiple synchronous vacation of partial servers, OR Transactions (in Chinese), 2001, 5(3): 85–94.
X. Xu and G. Zhang, Analysis of Multi-server Queue with a Single Vacation (e, d)-Policy, Performance Evaluation, 2006, 63(8): 625–638
X. Xu, Z. Ma, M. Liu, and N. Tian, Assembly policy of multi-server queueing system, Acta Mathematicae Applicatae Sinica, 2007, 30(2): 218–227.
M. Neuts, Matric-Geometric Solution in Stochastic Models, Johns Hopkins University Press, Baltimore, 1981.
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*This research is supported by the National Natural Science Foundation of China under Grant No. 10671170 and the Doctorial Foundation of Yanshan University under Grant No. B228.
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Xu, X., Tian, N. THE M/M/c QUEUE WITH (e, d) SETUP TIME*. J Syst Sci Complex 21, 446–455 (2008). https://doi.org/10.1007/s11424-008-9126-6
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DOI: https://doi.org/10.1007/s11424-008-9126-6