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On the multi-server machine interference with modified Bernoulli vacation
1. | Department of Applied Statistics, National Taichung University of Science and Technology, Taichung, 404, Taiwan, Taiwan |
References:
[1] |
F. Benson and D. R. Cox, The productivity of machine requiring attention at random intervals, Journal of the Royal Statistical Society B, 13 (1951), 65-82. |
[2] |
E. K. P. Chong and S. H. Zak, An Introduction of Optimization, 2nd edition, John Wiley and Sons, New Jersey, 2001.
doi: 10.1002/9781118033340. |
[3] |
G. Choudhury, A two-stage batch arrival queueing system with a modified Bernoulli schedule vacation under N-policy, Mathematical and Computer Modeling, 42 (2005), 71-85.
doi: 10.1016/j.mcm.2005.04.003. |
[4] |
G. Choudhury and K. Deka, An $M^X/G/1$ unreliable retrial queue with two phases of service and Bernoulli admission mechanism, Applied Mathematics and Comutation, 215 (2009), 936-949.
doi: 10.1016/j.amc.2009.06.015. |
[5] |
G. Choudhury and K. C. Madan, A two phase batch arrival queueing system with a vacation time under Bernoulli schedule, Applied Mathematics and Computation, 149 (2004), 337-349.
doi: 10.1016/S0096-3003(03)00138-3. |
[6] |
G. Choudhury and L. Tadj, The optimal control of an $M^X/G/1$ unreliable server queue with two phases of service and Bernoulli vacation schedule, Mathematical and Computer Modelling, 54 (2011), 673-688.
doi: 10.1016/j.mcm.2011.03.010. |
[7] |
B. T. Doshi, Queueing systems with vacations - a survey, Queueing Systems, 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[8] |
S. M. Gupta, Machine interference problem with warm spares, server vacations and exhaustive service, Performance Evaluation, 29 (1997), 195-211.
doi: 10.1016/S0166-5316(96)00046-6. |
[9] |
J. C. Ke, Vacation policies for machine interference problem with an unreliable server and state-dependent service rate, Journal of the Chineses Institute of Industrial Engineers, 23 (2006), 100-114. |
[10] |
J. C. Ke, S. L. Lee and C. H. Liou, Machine repair problem in production systems with spares and server vacations, RAIRO-Operations Research, 43 (2009), 35-54.
doi: 10.1051/ro/2009004. |
[11] |
J. C. Ke and C. H. Lin, A Markov repairable system involving an imperfect service station with multiple vacations, Asia-Pacific Journal of Operational Research, 22 (2005), 555-582.
doi: 10.1142/S021759590500073X. |
[12] |
J. C. Ke and K. H. Wang, Vacation policies for machine repair problem with two type spares, Applied Mathematical Modelling, 31 (2007), 880-894.
doi: 10.1016/j.apm.2006.02.009. |
[13] |
J. C. Ke, C. H. Wu and W. L. Pearn, Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule, Applied Mathematical Modelling, 35 (2011), 2196-2208.
doi: 10.1016/j.apm.2010.11.019. |
[14] |
J. C. Ke, C. H. Wu and Z. Zhang, Recent developments in vacation queueing models: A short survey, International Journal of Operations Research, 7 (2010), 3-8. |
[15] |
K. C. Madan, W. Abu-Dayyeh and F. Taiyyan, A two server queue with Bernoulli schedules and a single vacation policy, Applied Mathematics and Computation, 145 (2003), 59-71.
doi: 10.1016/S0096-3003(02)00469-1. |
[16] |
R. Oliva, Tradeoffs in responses to work pressure in the service industry, California Management Review, 30 (2001), 26-43.
doi: 10.1109/EMR.2002.1022405. |
[17] |
B. Raphael and I. F. C. Smith, A direct stochastic algorithm for global search, Journal of Applied Mathematics and Computation, 146 (2003), 729-758.
doi: 10.1016/S0096-3003(02)00629-X. |
[18] |
L. Tadj, G. Choudhury and C. Tadj, A quorum queueing system with a random setup time under N-policy and with Bernoulli vacation schedule, Quality Technology and Quantitative Management, 3 (2006), 145-160. |
[19] |
H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, Vacation and Priority Systems. part I, vol. 1, North-Holland, Amsterdam, 1991. |
[20] |
N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, Springer-Verlag, New York, 2006. |
[21] |
K. H. Wang, W. L. Chen and D. Y. Yang, Optimal management of the machine repair problem with working vacation: Newton's method, Journal of Computational and Applied Mathematics, 233 (2009), 449-458.
doi: 10.1016/j.cam.2009.07.043. |
show all references
References:
[1] |
F. Benson and D. R. Cox, The productivity of machine requiring attention at random intervals, Journal of the Royal Statistical Society B, 13 (1951), 65-82. |
[2] |
E. K. P. Chong and S. H. Zak, An Introduction of Optimization, 2nd edition, John Wiley and Sons, New Jersey, 2001.
doi: 10.1002/9781118033340. |
[3] |
G. Choudhury, A two-stage batch arrival queueing system with a modified Bernoulli schedule vacation under N-policy, Mathematical and Computer Modeling, 42 (2005), 71-85.
doi: 10.1016/j.mcm.2005.04.003. |
[4] |
G. Choudhury and K. Deka, An $M^X/G/1$ unreliable retrial queue with two phases of service and Bernoulli admission mechanism, Applied Mathematics and Comutation, 215 (2009), 936-949.
doi: 10.1016/j.amc.2009.06.015. |
[5] |
G. Choudhury and K. C. Madan, A two phase batch arrival queueing system with a vacation time under Bernoulli schedule, Applied Mathematics and Computation, 149 (2004), 337-349.
doi: 10.1016/S0096-3003(03)00138-3. |
[6] |
G. Choudhury and L. Tadj, The optimal control of an $M^X/G/1$ unreliable server queue with two phases of service and Bernoulli vacation schedule, Mathematical and Computer Modelling, 54 (2011), 673-688.
doi: 10.1016/j.mcm.2011.03.010. |
[7] |
B. T. Doshi, Queueing systems with vacations - a survey, Queueing Systems, 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[8] |
S. M. Gupta, Machine interference problem with warm spares, server vacations and exhaustive service, Performance Evaluation, 29 (1997), 195-211.
doi: 10.1016/S0166-5316(96)00046-6. |
[9] |
J. C. Ke, Vacation policies for machine interference problem with an unreliable server and state-dependent service rate, Journal of the Chineses Institute of Industrial Engineers, 23 (2006), 100-114. |
[10] |
J. C. Ke, S. L. Lee and C. H. Liou, Machine repair problem in production systems with spares and server vacations, RAIRO-Operations Research, 43 (2009), 35-54.
doi: 10.1051/ro/2009004. |
[11] |
J. C. Ke and C. H. Lin, A Markov repairable system involving an imperfect service station with multiple vacations, Asia-Pacific Journal of Operational Research, 22 (2005), 555-582.
doi: 10.1142/S021759590500073X. |
[12] |
J. C. Ke and K. H. Wang, Vacation policies for machine repair problem with two type spares, Applied Mathematical Modelling, 31 (2007), 880-894.
doi: 10.1016/j.apm.2006.02.009. |
[13] |
J. C. Ke, C. H. Wu and W. L. Pearn, Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule, Applied Mathematical Modelling, 35 (2011), 2196-2208.
doi: 10.1016/j.apm.2010.11.019. |
[14] |
J. C. Ke, C. H. Wu and Z. Zhang, Recent developments in vacation queueing models: A short survey, International Journal of Operations Research, 7 (2010), 3-8. |
[15] |
K. C. Madan, W. Abu-Dayyeh and F. Taiyyan, A two server queue with Bernoulli schedules and a single vacation policy, Applied Mathematics and Computation, 145 (2003), 59-71.
doi: 10.1016/S0096-3003(02)00469-1. |
[16] |
R. Oliva, Tradeoffs in responses to work pressure in the service industry, California Management Review, 30 (2001), 26-43.
doi: 10.1109/EMR.2002.1022405. |
[17] |
B. Raphael and I. F. C. Smith, A direct stochastic algorithm for global search, Journal of Applied Mathematics and Computation, 146 (2003), 729-758.
doi: 10.1016/S0096-3003(02)00629-X. |
[18] |
L. Tadj, G. Choudhury and C. Tadj, A quorum queueing system with a random setup time under N-policy and with Bernoulli vacation schedule, Quality Technology and Quantitative Management, 3 (2006), 145-160. |
[19] |
H. Takagi, Queueing Analysis: A Foundation of Performance Evaluation, Vacation and Priority Systems. part I, vol. 1, North-Holland, Amsterdam, 1991. |
[20] |
N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, Springer-Verlag, New York, 2006. |
[21] |
K. H. Wang, W. L. Chen and D. Y. Yang, Optimal management of the machine repair problem with working vacation: Newton's method, Journal of Computational and Applied Mathematics, 233 (2009), 449-458.
doi: 10.1016/j.cam.2009.07.043. |
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