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A heuristic algorithm for the optimization of M/M/$s$ queue with multiple working vacations
1. | Department of Industrial Engineering and Management, National Chiao Tung University, Hsingchu 30050, Taiwan |
2. | Department of Business Administration, Asia University, Wufeng, Taichung 41354, Taiwan |
3. | Department of Applied Statistics, National Taichung Institute of Technology, Taichung 404, Taiwan |
4. | Department of Applied Mathematics, National Chung-Hsing University, Taichung 402, Taiwan |
References:
[1] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Operations Research Letters, 33 (2005), 201-209.
doi: 10.1016/j.orl.2004.05.006. |
[2] |
A. D. Banik, U. C. Gupta and S. S. Pathak, On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation, Applied Mathematical Modelling, 31 (2006), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[3] |
R. L. Burden and J. Douglas, "Numerical Analysis,'' 7th Edition, Brooks/Cole, USA, 2001. |
[4] |
U. Chatterjee and S. P. Mukherjee, GI/M/1 queue with server vacations, Journal of the Operational Research Society, 41 (1990), 83-87. |
[5] |
E. K. P. Chong and S. H. Zak, "An Introduction to Optimization,'' 2nd Edition, Wiley, New York, 2001. |
[6] |
B. T. Doshi, Queueing systems with vacations-a survey, Queueing Systems Theory Appl., 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[7] |
S. W. Fuhrmann and R. B. Cooper, Stochastic decompositions in the M/G/1 queue with generalized vacations, Operations Research, 33 (1985), 1117-1129.
doi: 10.1287/opre.33.5.1117. |
[8] |
F. Karaesmen and S. M. Gupta, The finite capacity GI/M/1 queue with server vacations, Journal of the Operational Research Society, 47 (1996), 817-828. |
[9] |
T. Lee, The M/G/1/N queue with vacation and exhaustive service discipline, Operations Research, 32 (1984), 774-784.
doi: 10.1287/opre.32.4.774. |
[10] |
J.-H. Li, W.-Y. Liu and N.-S. Tian, Discrete time GI/Geo/1 queue with multiple working vacations Queueing Systems, 56 (2007), 53-63.
doi: 10.1007/s11134-007-9030-0. |
[11] |
C.-H. Lin and J.-C. Ke, Multi-server system with single working vacation, Applied Mathematical Modelling, 33 (2009), 2967-2977.
doi: 10.1016/j.apm.2008.10.006. |
[12] |
W.-Y. Liu, X.-L. Xu and N.-S. Tian, Stochastic decomposition in the M/M/1 queue with working vacations, Operations Research Letters, 35 (2007), 595-600.
doi: 10.1016/j.orl.2006.12.007. |
[13] |
M. F. Neuts, "Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach,'' Johns Hopkins Series in the Mathematical Sciences, 2, Johns Hopkins University Press, Baltimore, Md., 1981. |
[14] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[15] |
H. Takagi, "Queueing Analysis: A Foundation of Performance Evaluation," Vol. 1, Vacation and Priority Systems, Part 1, North-Holland Publishing Co., Amsterdam, 1991. |
[16] |
N. Tian, D. Zhang and C. Cao, The GI/M/1 queue with exponential vacations, Queueing Systems Theory Appl., 5 (1989), 331-344.
doi: 10.1007/BF01225323. |
[17] |
J. A. White, J. W. Schmidt and G. K. Benett, "Analysis of Queueing System,'' Operations Research and Industrial Engineering, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. |
[18] |
D. A. Wu and H. Takagi, M/G/1 queue with multiple working vacations, Performance Evaluation, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
show all references
References:
[1] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Operations Research Letters, 33 (2005), 201-209.
doi: 10.1016/j.orl.2004.05.006. |
[2] |
A. D. Banik, U. C. Gupta and S. S. Pathak, On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation, Applied Mathematical Modelling, 31 (2006), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[3] |
R. L. Burden and J. Douglas, "Numerical Analysis,'' 7th Edition, Brooks/Cole, USA, 2001. |
[4] |
U. Chatterjee and S. P. Mukherjee, GI/M/1 queue with server vacations, Journal of the Operational Research Society, 41 (1990), 83-87. |
[5] |
E. K. P. Chong and S. H. Zak, "An Introduction to Optimization,'' 2nd Edition, Wiley, New York, 2001. |
[6] |
B. T. Doshi, Queueing systems with vacations-a survey, Queueing Systems Theory Appl., 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[7] |
S. W. Fuhrmann and R. B. Cooper, Stochastic decompositions in the M/G/1 queue with generalized vacations, Operations Research, 33 (1985), 1117-1129.
doi: 10.1287/opre.33.5.1117. |
[8] |
F. Karaesmen and S. M. Gupta, The finite capacity GI/M/1 queue with server vacations, Journal of the Operational Research Society, 47 (1996), 817-828. |
[9] |
T. Lee, The M/G/1/N queue with vacation and exhaustive service discipline, Operations Research, 32 (1984), 774-784.
doi: 10.1287/opre.32.4.774. |
[10] |
J.-H. Li, W.-Y. Liu and N.-S. Tian, Discrete time GI/Geo/1 queue with multiple working vacations Queueing Systems, 56 (2007), 53-63.
doi: 10.1007/s11134-007-9030-0. |
[11] |
C.-H. Lin and J.-C. Ke, Multi-server system with single working vacation, Applied Mathematical Modelling, 33 (2009), 2967-2977.
doi: 10.1016/j.apm.2008.10.006. |
[12] |
W.-Y. Liu, X.-L. Xu and N.-S. Tian, Stochastic decomposition in the M/M/1 queue with working vacations, Operations Research Letters, 35 (2007), 595-600.
doi: 10.1016/j.orl.2006.12.007. |
[13] |
M. F. Neuts, "Matrix-Geometric Solutions in Stochastic Models. An Algorithmic Approach,'' Johns Hopkins Series in the Mathematical Sciences, 2, Johns Hopkins University Press, Baltimore, Md., 1981. |
[14] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[15] |
H. Takagi, "Queueing Analysis: A Foundation of Performance Evaluation," Vol. 1, Vacation and Priority Systems, Part 1, North-Holland Publishing Co., Amsterdam, 1991. |
[16] |
N. Tian, D. Zhang and C. Cao, The GI/M/1 queue with exponential vacations, Queueing Systems Theory Appl., 5 (1989), 331-344.
doi: 10.1007/BF01225323. |
[17] |
J. A. White, J. W. Schmidt and G. K. Benett, "Analysis of Queueing System,'' Operations Research and Industrial Engineering, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. |
[18] |
D. A. Wu and H. Takagi, M/G/1 queue with multiple working vacations, Performance Evaluation, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
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