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Performance analysis of MAP/G/1 queue with working vacations and vacation interruption. (English) Zbl 1217.90078
Summary: We consider the MAP/G/1 queue with working vacations and vacation interruption. We obtain the queue length distribution with the method of supplementary variable, combined with the matrix-analytic method and censoring technique. We also obtain the system size distribution at pre-arrival epoch and the Laplace-Stieltjes transform (LST) of waiting time.

90B22Queues and service (optimization)
60K25Queueing theory
Full Text: DOI
[1] Servi, L. D.; Finn, S. G.: M/M/1 queue with working vacation (M/M/1/WV), Perform. evaluation 50, 41-52 (2002)
[2] J.D. Kim, D.W. Choi, K.C. Chae. Analysis of queue-length distribution of the M/G/1 queue with working vacations, in: Hawaii International Conference on Statistics and Related Fields, June 2 -- 8, 2003.
[3] Wu, D.; Takagi, H.: M/G/1 queue with multiple working vacations, Perform. evaluation 63, No. 7, 654-681 (2006)
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[7] Li, J.; Tian, N.; Ma, Z.: Performance analysis of GI/M/1 queue with working vacations and vacation interruption, Appl. math. Model. 32, 2715-2730 (2008) · Zbl 1167.90451 · doi:10.1016/j.apm.2007.09.017
[8] P.P. Bocharov, C. D’Apice, A.V. Pechinkin, S. Salerno, Queueing Theory, Utreche. Boston, 2004.
[9] Breuer, L.; Baum, D.: An introduction to queueing theory and matrix-analytic methods, (2005) · Zbl 1089.60002
[10] Zhao, Y. Q.: Censoring technique in studying block-structured Markov chains, Advance in algorithmic methods for stochastic models, 417-433 (2000)
[11] Li, Q. L.; Zhao, Y. Q.: A constructive method for finding $\beta $-invariant measures for transition matrices of M/G/1 type, Matrix analytic methods theory and applications, 237-264 (2002) · Zbl 1029.60072
[12] Neuts, M. F.: Structured stochastic matrices of M/G/1 type and their application, (1989) · Zbl 0695.60088