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Tail asymptotics of fluid queues in a distributed server system fed by a heavy-tailed ON-OFF flow
Analysis of an M/M/1 queue with vacations and impatience timers which depend on the server's states
1. | Department of Statistics, College of Sciences, Yanshan University, Qinhuangdao 066004 |
2. | Department of Intelligence and Informatics, Konan University, Kobe 658-8501 |
3. | School of Economics and Management, 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] |
C. J. Ancker and A. V. Gafarian, Some queueing problems with balking and reneging, Operations Research, 11 (1963), 88-100.
doi: 10.1287/opre.11.1.88. |
[4] |
F. Baccelli, P. Boyer and G. Hebuterne, Single-server queues with impatient customers, Advances in Applied Probability, 16 (1984), 887-905.
doi: 10.2307/1427345. |
[5] |
F. Baccelli and G. Hebuterne, On queues with impatient customers, in Perforamnce' 81 (F. Kylstra, ed.), North-Holland, Amsterdam, 1981, 159-179. |
[6] |
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. |
[7] |
N. K. Boots and H. Tijms, A multiserver queueing system with impatient customers, Management Science, 45 (1999), 444-448.
doi: 10.1287/mnsc.45.3.444. |
[8] |
O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers, ITC, 14 (1994), 743-756.
doi: 10.1016/B978-0-444-82031-0.50079-2. |
[9] |
S. R. Chakravarthy, A disater queue with Markovian arrivals and impatient customers, Applied Mathematics and Computation, 214 (2009), 48-59.
doi: 10.1016/j.amc.2009.03.081. |
[10] |
D. J. Daley, General customer impatience in the queue GI/G/1, Journal of Applied Probability, 2 (1965), 186-205.
doi: 10.2307/3211884. |
[11] |
S. Dimou, A. Economou and D. Fakinos, The single server vacation queueing model with geometric abandonments, Journal of Statistical Planning and Inference, 141 (2011), 2863-2877.
doi: 10.1016/j.jspi.2011.03.010. |
[12] |
B. Doshi, Single server queues with vacation: A survey, Queueing Systems, 1 (1986), 29-66. |
[13] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue, European Journal of Operational Research, 203 (2010), 143-155.
doi: 10.1016/j.ejor.2009.07.014. |
[14] |
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. |
[15] |
O. Garnett, A. Mandelbaum and M. Reiman, Designing a call center with impatient customers, Manufacturing and Service Operations Management, 4 (2002), 208-227.
doi: 10.1287/msom.4.3.208.7753. |
[16] |
S. Graves, The application of queueing theory to continous perishable inventory systems, Management Science, 28 (1984), 401-406. |
[17] |
Y. W. Shin and T. S. Choo, M/M/s queue with impatient customers and retrials, Applied Mathematical Modelling, 33 (2009), 2596-2606.
doi: 10.1016/j.apm.2008.07.018. |
[18] |
L. Takacs, A single-server queue with limited virtual waiting time, Journal of Applied Probability, 11 (1974), 612-617.
doi: 10.2307/3212710. |
[19] |
H. Takagi, Queueing Analysis, A Foundation of Performance Evaluation, Volume 1: Vacation and Priority Systems, Part 1. North-Holland, Amsterdam, 1991. |
[20] |
N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, Springer, New York, 2006. |
[21] |
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. |
[22] |
D. Yue and W. Yue, Analysis of M/M/c/N queueing system with balking, reneging and synchronous vacations, in Advanced in Queueing Theory and Network Applications (ed. W. Yue etal.), Springer, 2009, 165-180.
doi: 10.1007/978-0-387-09703-9_9. |
[23] |
D. Yue, W. Yue, Z. Saffer and X. Chen, Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, Journal of Industrial and Management Optimization, 10 (2014), 89-112.
doi: 10.3934/jimo.2014.10.89. |
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] |
C. J. Ancker and A. V. Gafarian, Some queueing problems with balking and reneging, Operations Research, 11 (1963), 88-100.
doi: 10.1287/opre.11.1.88. |
[4] |
F. Baccelli, P. Boyer and G. Hebuterne, Single-server queues with impatient customers, Advances in Applied Probability, 16 (1984), 887-905.
doi: 10.2307/1427345. |
[5] |
F. Baccelli and G. Hebuterne, On queues with impatient customers, in Perforamnce' 81 (F. Kylstra, ed.), North-Holland, Amsterdam, 1981, 159-179. |
[6] |
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. |
[7] |
N. K. Boots and H. Tijms, A multiserver queueing system with impatient customers, Management Science, 45 (1999), 444-448.
doi: 10.1287/mnsc.45.3.444. |
[8] |
O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers, ITC, 14 (1994), 743-756.
doi: 10.1016/B978-0-444-82031-0.50079-2. |
[9] |
S. R. Chakravarthy, A disater queue with Markovian arrivals and impatient customers, Applied Mathematics and Computation, 214 (2009), 48-59.
doi: 10.1016/j.amc.2009.03.081. |
[10] |
D. J. Daley, General customer impatience in the queue GI/G/1, Journal of Applied Probability, 2 (1965), 186-205.
doi: 10.2307/3211884. |
[11] |
S. Dimou, A. Economou and D. Fakinos, The single server vacation queueing model with geometric abandonments, Journal of Statistical Planning and Inference, 141 (2011), 2863-2877.
doi: 10.1016/j.jspi.2011.03.010. |
[12] |
B. Doshi, Single server queues with vacation: A survey, Queueing Systems, 1 (1986), 29-66. |
[13] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue, European Journal of Operational Research, 203 (2010), 143-155.
doi: 10.1016/j.ejor.2009.07.014. |
[14] |
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. |
[15] |
O. Garnett, A. Mandelbaum and M. Reiman, Designing a call center with impatient customers, Manufacturing and Service Operations Management, 4 (2002), 208-227.
doi: 10.1287/msom.4.3.208.7753. |
[16] |
S. Graves, The application of queueing theory to continous perishable inventory systems, Management Science, 28 (1984), 401-406. |
[17] |
Y. W. Shin and T. S. Choo, M/M/s queue with impatient customers and retrials, Applied Mathematical Modelling, 33 (2009), 2596-2606.
doi: 10.1016/j.apm.2008.07.018. |
[18] |
L. Takacs, A single-server queue with limited virtual waiting time, Journal of Applied Probability, 11 (1974), 612-617.
doi: 10.2307/3212710. |
[19] |
H. Takagi, Queueing Analysis, A Foundation of Performance Evaluation, Volume 1: Vacation and Priority Systems, Part 1. North-Holland, Amsterdam, 1991. |
[20] |
N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, Springer, New York, 2006. |
[21] |
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. |
[22] |
D. Yue and W. Yue, Analysis of M/M/c/N queueing system with balking, reneging and synchronous vacations, in Advanced in Queueing Theory and Network Applications (ed. W. Yue etal.), Springer, 2009, 165-180.
doi: 10.1007/978-0-387-09703-9_9. |
[23] |
D. Yue, W. Yue, Z. Saffer and X. Chen, Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy, Journal of Industrial and Management Optimization, 10 (2014), 89-112.
doi: 10.3934/jimo.2014.10.89. |
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