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Analysis of renewal input bulk arrival queue with single working vacation and partial batch rejection
1. | School of Computer Application, KIIT University, Bhubaneswar - 751 024, India |
2. | Department of Applied Mathematics, Andhra University, Visakhapatnam - 530 003, India |
References:
[1] |
Y. Baba, Analysis of $GI$/$M$/$1$ queue with multiple working vacations, Oper. Res. Lett., 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 - Anaytic analysis and computation, Appl. Math. Model., 31 (2007), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[3] |
P. J. Burke, Delays in single-server queues with batch input, Oper. Res., 23 (1975), 830-833.
doi: 10.1287/opre.23.4.830. |
[4] |
K. C. Chae, D. E. Lim and W. S. Yang, The $GI$/$M$/$1$ queue and the $GI$/$Geo$/$1$ queue both with single working vacation, Performance Evaluaton, 68 (2009), 356-367.
doi: 10.1016/j.peva.2009.01.005. |
[5] |
K. C. Chae, S. M. Lee and H. W. Lee, On stochastic decomposition in the $GI$/$M$/$1$ queue with single exponential vacation, Oper. Res. Lett., 34 (2006), 706-712.
doi: 10.1016/j.orl.2005.11.006. |
[6] |
B. T. Doshi, Queueing systems with vacations - A survey, Queueing Syst., 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[7] |
B. T. Doshi, Single server queues with vacations, Stochastic Analysis of Computer and Communication Systems, H. Takagi (Editor), Elsevier Science Publishers, 1990, 217-265. |
[8] |
F. Karaesmen and S. M. Gupta, The finite capacity $GI$/$M$/$1$ with server vacations, Journal of the Operational Research Society, 47 (1996), 817-828. |
[9] |
G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modelling," SIAM & ASA, Philadelphia, 1999. |
[10] |
J. H. Li, N. S. Tian and Z. Y. Ma, Performance analysis of $GI$/$M$/$1$ queue with working vacations and vacation interruption, Appl. Math. Model., 32 (2008), 2715-2730.
doi: 10.1016/j.apm.2007.09.017. |
[11] |
W. Liu, X. Xu and N. Tian, Some results on the M/M/1 queue with working vacations, Oper. Res. Lett., 35 (2007), 595-600.
doi: 10.1016/j.orl.2006.12.007. |
[12] |
K. Sikdar, U. C. Gupta and R. K. Sharma, The analysis of a finite-buffer general input queue with batch arrival and exponential multiple vacations, Int. J. Oper. Res., 3 (2008), 219-234.
doi: 10.1504/IJOR.2008.016162. |
[13] |
L. D. Servi and S. G. Finn, $M$/$M$/$1$ queue with working vacations ($M$/$M$/$1$/$WV$), Performance Evaluaton, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[14] |
H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation : Volume 2, Finite Systems," North Holland, 1993. |
[15] |
N. Tian and Z. G. Zhang, "Vacation Queueing Models: Theory and Applications," Springer-Verlag, New York, 2006. |
[16] |
P. Vijaya Laxmi and U. C. Gupta, A unified approach to analyze the $GI^X$/$M$/$1$/$N$ and $GI$/$E_k$/$1$/$N$ queues, Proceedings of the International Conference on Stochastic Processes and Their Applications (eds. A. Vijayakumar and M. Sreenivasan), Narosa Publishers (1998), 206-214. |
[17] |
D. Wu and H. Takagi, $M$/$G$/$1$ queue with multiple working vacations, Performance Evaluaton, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
[18] |
M. M. Yu, Y. H. Tang and Y. H. Fu, Steady state analysis and computation of the $GI^{[x]}$/$M^b$/$1$/$L$ queue with multiple working vacations and partial batch rejection, Computers & Industrial Engineering, 56 (2009), 1243-1253.
doi: 10.1016/j.cie.2008.07.013. |
show all references
References:
[1] |
Y. Baba, Analysis of $GI$/$M$/$1$ queue with multiple working vacations, Oper. Res. Lett., 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 - Anaytic analysis and computation, Appl. Math. Model., 31 (2007), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[3] |
P. J. Burke, Delays in single-server queues with batch input, Oper. Res., 23 (1975), 830-833.
doi: 10.1287/opre.23.4.830. |
[4] |
K. C. Chae, D. E. Lim and W. S. Yang, The $GI$/$M$/$1$ queue and the $GI$/$Geo$/$1$ queue both with single working vacation, Performance Evaluaton, 68 (2009), 356-367.
doi: 10.1016/j.peva.2009.01.005. |
[5] |
K. C. Chae, S. M. Lee and H. W. Lee, On stochastic decomposition in the $GI$/$M$/$1$ queue with single exponential vacation, Oper. Res. Lett., 34 (2006), 706-712.
doi: 10.1016/j.orl.2005.11.006. |
[6] |
B. T. Doshi, Queueing systems with vacations - A survey, Queueing Syst., 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[7] |
B. T. Doshi, Single server queues with vacations, Stochastic Analysis of Computer and Communication Systems, H. Takagi (Editor), Elsevier Science Publishers, 1990, 217-265. |
[8] |
F. Karaesmen and S. M. Gupta, The finite capacity $GI$/$M$/$1$ with server vacations, Journal of the Operational Research Society, 47 (1996), 817-828. |
[9] |
G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modelling," SIAM & ASA, Philadelphia, 1999. |
[10] |
J. H. Li, N. S. Tian and Z. Y. Ma, Performance analysis of $GI$/$M$/$1$ queue with working vacations and vacation interruption, Appl. Math. Model., 32 (2008), 2715-2730.
doi: 10.1016/j.apm.2007.09.017. |
[11] |
W. Liu, X. Xu and N. Tian, Some results on the M/M/1 queue with working vacations, Oper. Res. Lett., 35 (2007), 595-600.
doi: 10.1016/j.orl.2006.12.007. |
[12] |
K. Sikdar, U. C. Gupta and R. K. Sharma, The analysis of a finite-buffer general input queue with batch arrival and exponential multiple vacations, Int. J. Oper. Res., 3 (2008), 219-234.
doi: 10.1504/IJOR.2008.016162. |
[13] |
L. D. Servi and S. G. Finn, $M$/$M$/$1$ queue with working vacations ($M$/$M$/$1$/$WV$), Performance Evaluaton, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[14] |
H. Takagi, "Queueing Analysis - A Foundation of Performance Evaluation : Volume 2, Finite Systems," North Holland, 1993. |
[15] |
N. Tian and Z. G. Zhang, "Vacation Queueing Models: Theory and Applications," Springer-Verlag, New York, 2006. |
[16] |
P. Vijaya Laxmi and U. C. Gupta, A unified approach to analyze the $GI^X$/$M$/$1$/$N$ and $GI$/$E_k$/$1$/$N$ queues, Proceedings of the International Conference on Stochastic Processes and Their Applications (eds. A. Vijayakumar and M. Sreenivasan), Narosa Publishers (1998), 206-214. |
[17] |
D. Wu and H. Takagi, $M$/$G$/$1$ queue with multiple working vacations, Performance Evaluaton, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
[18] |
M. M. Yu, Y. H. Tang and Y. H. Fu, Steady state analysis and computation of the $GI^{[x]}$/$M^b$/$1$/$L$ queue with multiple working vacations and partial batch rejection, Computers & Industrial Engineering, 56 (2009), 1243-1253.
doi: 10.1016/j.cie.2008.07.013. |
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