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The FIFO single-server queue with disasters and multiple Markovian arrival streams
Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy
1. | Department of Statistics, College of Sciences, Yanshan University, Qinhuangdao 066004 |
2. | Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501 |
3. | Department of Telecommunications, Budapest University of Technology and Economics, Budapest |
4. | College of Science, Yanshan University, Qinhuangdao 066004, China |
References:
[1] |
E. Altman and U. Yechiali, Analysis of customers' impatience in queues with server vacations, Queueing Systems, 52 (2006), 261-279.
doi: 10.1007/s11134-006-6134-x. |
[2] |
E. Altman and U. Yechiali, Infinite-server queues with systems' additional task and impatient customers, Probability in the Engineering and Informational Sciences, 22 (2008), 477-493.
doi: 10.1007/978-1-4020-8741-7_57. |
[3] |
A. D. Banik, The infinite-buffer single server queue with a variant of multiple vacation policy and batch Markovian arrival process, Applied Mathematical Modelling, 33 (2009), 3025-3039.
doi: 10.1016/j.apm.2008.10.021. |
[4] |
S. Benjaafar, J. Gayon and S. Tepe, Optimal control of a production-inventory system with customer impatience, Operations Research Letters, 38 (2010), 267-272.
doi: 10.1016/j.orl.2010.03.008. |
[5] |
T. Bonald and J. Roberts, Performance modeling of elastic traffic in overload, ACM Sigmetrics Performance Evaluation Review, 29 (2001), 342-343. |
[6] |
B. Doshi, Single server queues with vacation: A survey, Queueing Systems, 1 (1986), 29-66. |
[7] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreilable queue, European Journal of Operational Research, 203 (2010), 143-155. |
[8] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: Tutotial, review, and research prospects, Manufacturing and Service Operations Management, 5 (2003), 79-141.
doi: 10.1287/msom.5.2.79.16071. |
[9] |
J. C. Ke, Operating characteristic analysis on the $M^{[X]}$/G/1 system with a variant vacation policy and balking, Applied Mathematical Modelling, 31 (2007), 1321-1337.
doi: 10.1016/j.apm.2006.02.012. |
[10] |
J. C. Ke and F. M. Chang, Modified vacation policy for M/G/1 retrial queue with balking and feedback, Computer & Industrial Engineering, 57 (2009), 433-443.
doi: 10.1016/j.cie.2009.01.002. |
[11] |
J. C. Ke, H. I. Huang and Y. K. Chu, Batch arrival queue with N-policy and at most J vacations, Applied Mathematical Modelling, 34 (2010), 451-466.
doi: 10.1016/j.apm.2009.06.003. |
[12] |
N. Perel and U. Yechiali, Queues with slow servers and impatient customers, European Journal of Operational Research, 201 (2010), 247-258.
doi: 10.1016/j.ejor.2009.02.024. |
[13] |
H. Takagi, "Queueing Analysis, A Foundation of Performance Evaluation, Volume 1: Vacation and Priority Systems," Part 1. North-Holland Publishing Co., Amsterdam, 1991. |
[14] |
N. Tian and Z. G. Zhang, "Vacation Queueing Models: Theory and Applications," New York: Springer, 2006. |
[15] |
T. Y. Wang, J. C. Ke and F. M. Chang, On the discrete-time Geo/G/1 queue with randomized vacations and at most $J$ vacations, Applied Mathematical Modelling, 35 (2011), 2297-2308.
doi: 10.1016/j.apm.2010.11.021. |
[16] |
U. Yechiali, Queues with system disasters and impatient customers when system is down, Queueing Systems, 56 (2007), 195-202.
doi: 10.1007/s11134-007-9031-z. |
[17] |
D. Yue, W. Yue and G. Xu, Analysis of customers' impatience in an M/M/1 queue with and working vacations, Journal of Industrial and Management Optimization, 8 (2012), 895-908.
doi: 10.3934/jimo.2012.8.895. |
[18] |
Z. G. Zhang and N. Tian, Discrete time Geo/G/1 queue with multiple adaptive vacations, Queueing Systems, 38 (2001), 419-429.
doi: 10.1023/A:1010947911863. |
show all references
References:
[1] |
E. Altman and U. Yechiali, Analysis of customers' impatience in queues with server vacations, Queueing Systems, 52 (2006), 261-279.
doi: 10.1007/s11134-006-6134-x. |
[2] |
E. Altman and U. Yechiali, Infinite-server queues with systems' additional task and impatient customers, Probability in the Engineering and Informational Sciences, 22 (2008), 477-493.
doi: 10.1007/978-1-4020-8741-7_57. |
[3] |
A. D. Banik, The infinite-buffer single server queue with a variant of multiple vacation policy and batch Markovian arrival process, Applied Mathematical Modelling, 33 (2009), 3025-3039.
doi: 10.1016/j.apm.2008.10.021. |
[4] |
S. Benjaafar, J. Gayon and S. Tepe, Optimal control of a production-inventory system with customer impatience, Operations Research Letters, 38 (2010), 267-272.
doi: 10.1016/j.orl.2010.03.008. |
[5] |
T. Bonald and J. Roberts, Performance modeling of elastic traffic in overload, ACM Sigmetrics Performance Evaluation Review, 29 (2001), 342-343. |
[6] |
B. Doshi, Single server queues with vacation: A survey, Queueing Systems, 1 (1986), 29-66. |
[7] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreilable queue, European Journal of Operational Research, 203 (2010), 143-155. |
[8] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: Tutotial, review, and research prospects, Manufacturing and Service Operations Management, 5 (2003), 79-141.
doi: 10.1287/msom.5.2.79.16071. |
[9] |
J. C. Ke, Operating characteristic analysis on the $M^{[X]}$/G/1 system with a variant vacation policy and balking, Applied Mathematical Modelling, 31 (2007), 1321-1337.
doi: 10.1016/j.apm.2006.02.012. |
[10] |
J. C. Ke and F. M. Chang, Modified vacation policy for M/G/1 retrial queue with balking and feedback, Computer & Industrial Engineering, 57 (2009), 433-443.
doi: 10.1016/j.cie.2009.01.002. |
[11] |
J. C. Ke, H. I. Huang and Y. K. Chu, Batch arrival queue with N-policy and at most J vacations, Applied Mathematical Modelling, 34 (2010), 451-466.
doi: 10.1016/j.apm.2009.06.003. |
[12] |
N. Perel and U. Yechiali, Queues with slow servers and impatient customers, European Journal of Operational Research, 201 (2010), 247-258.
doi: 10.1016/j.ejor.2009.02.024. |
[13] |
H. Takagi, "Queueing Analysis, A Foundation of Performance Evaluation, Volume 1: Vacation and Priority Systems," Part 1. North-Holland Publishing Co., Amsterdam, 1991. |
[14] |
N. Tian and Z. G. Zhang, "Vacation Queueing Models: Theory and Applications," New York: Springer, 2006. |
[15] |
T. Y. Wang, J. C. Ke and F. M. Chang, On the discrete-time Geo/G/1 queue with randomized vacations and at most $J$ vacations, Applied Mathematical Modelling, 35 (2011), 2297-2308.
doi: 10.1016/j.apm.2010.11.021. |
[16] |
U. Yechiali, Queues with system disasters and impatient customers when system is down, Queueing Systems, 56 (2007), 195-202.
doi: 10.1007/s11134-007-9031-z. |
[17] |
D. Yue, W. Yue and G. Xu, Analysis of customers' impatience in an M/M/1 queue with and working vacations, Journal of Industrial and Management Optimization, 8 (2012), 895-908.
doi: 10.3934/jimo.2012.8.895. |
[18] |
Z. G. Zhang and N. Tian, Discrete time Geo/G/1 queue with multiple adaptive vacations, Queueing Systems, 38 (2001), 419-429.
doi: 10.1023/A:1010947911863. |
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