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International Journal of Stochastic Analysis
Volume 2012 (2012), Article ID 145867, 16 pages
An M/M/2 Queueing System with Heterogeneous Servers Including One with Working Vacation
1Department of Mathematics, Cochin University of Science and Technology, Cochin 682022, India
2Department of Mathematics, Government College, Chittur, Palakkad 678104, India
Received 24 February 2012; Accepted 13 May 2012
Academic Editor: Ho Lee
Copyright © 2012 A. Krishnamoorthy and C. Sreenivasan. 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.
- B. T. Doshi, “Queueing systems with vacations—a survey,” Queueing Systems, vol. 1, no. 1, pp. 29–66, 1986.
- H. Takagi, Queueing Analysis Volume 1: Vacations and Priority System, North-Holland, Amsterdam, The Netherlands, 1991.
- N. Tian and Z. G. Zhang, Vacation Queueing Models, International Series in Operations Research & Management Science no. 93, Springer, New York, NY, USA, 2006.
- X. Chao and Y. Q. Zhao, “Analysis of multi-server queues with station and server vacations,” European Journal of Operational Research, vol. 110, no. 2, pp. 392–406, 1998.
- Y. Levy and U. Yechiali, “An queue with servers' vacations,” Information Systems and Operational Research, vol. 14, no. 2, pp. 153–163, 1976.
- B. Vinod, “Exponential queues with servers' vacations,” Journal of the Operational Research Society, vol. 37, no. 10, pp. 1007–1014, 1986.
- E. P. C. Kao and K. S. Narayanan, “Analyses of an M/M/N/ queue with server's vacations,” European Journal of Operational Research, vol. 54, no. 2, pp. 256–266, 1991.
- L. Servi and S. Finn, “M/M/1 queue with working vacations (M/M/1/WV),” Performance, vol. 50, pp. 41–52, 2002.
- J. Kim, D. Choi, and K. Chae, “Analysis of queue-length distribution of the M/G/1with working vacations,” in Proceedings of the International Conference on Statistics and Related, Honolulu, Hawaii, USA, 2003.
- D. A. Wu and H. Takagi, “M/G/1 queue with multiple working vacations,” Performance Evaluation, vol. 63, no. 7, pp. 654–681, 2006.
- Y. Baba, “Analysis of a GI/M/1 queue with multiple working vacations,” Operations Research Letters, vol. 33, no. 2, pp. 201–209, 2005.
- N.-S. Tian, J.-H. Li, and Z. G. Zhang, “Matrix analytic method and working vacation queues—a survey,” International Journal of Information and Management Sciences, vol. 20, no. 4, pp. 603–633, 2009.
- J. Li and N. Tian, “The M/M/1 queue with working vacations and vacation interruptions,” Journal of Systems Science and Systems Engineering, vol. 16, no. 1, pp. 121–127, 2007.
- M. Zhang and Z. Hou, “Performance analysis of queue with working vacations and vacation interruption,” Applied Mathematical Modelling, vol. 35, no. 4, pp. 1551–1560, 2011.
- M. F. Neuts and Y. Takahashi, “Asymptotic behavior of the stationary distributions in the queue with heterogeneous servers,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 57, no. 4, pp. 441–452, 1981.
- B. Krishna Kumar and S. Pavai Madheswari, “An queueing system with heterogeneous servers and multiple vacations,” Mathematical and Computer Modelling, vol. 41, no. 13, pp. 1415–1429, 2005.
- W. Szpankowski, “Stability conditions for multidimensional queueing systems with computer applications,” Operations Research, vol. 36, no. 6, pp. 944–957, 1988.
- L. I. Sennott, P. A. Humblet, and R. L. Tweedie, “Mean drifts and the nonergodicity of Markov chains,” Operations Research, vol. 31, no. 4, pp. 783–789, 1983.
- G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, Pa, USA, 1999.
- M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models, vol. 2 of Johns Hopkins Series in the Mathematical Sciences, Johns Hopkins University Press, Baltimore, Md, USA, 1981, [1994 version is Dover Edition].
- M. F. Neuts and D. M. Lucantoni, “A Markovian queue with servers subject to breakdowns and repairs,” Management Science, vol. 25, no. 9, pp. 849–861, 1979.
- J. G. Kemeny and J. L. Snell, Finite Markov Chains, The University Series in Undergraduate Mathematics, D. Van Nostrand, Princeton, NJ, USA, 1960.
- V. P. Singh, “Two-server Markovian queues with balking: heterogeneous versus homogeneous servers,” Operations Research, vol. 18, no. 1, pp. 145–159, 1970.