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Multiserver retrial queues with after-call work
1. | Graduate School of Informatics, Kyoto University, Yoshida-Honmachi, Sakyo-ku, Kyoto 606-8501 |
2. | Department of Computer Science, Gunma University, Kiryu-City, 376-8515 |
References:
[1] |
J. R. Artalejo and M. Pozo, Numerical calculation of the stationary distribution of the main multiserver retrial queue, Annals of Operations Research, 116 (2002), 41-56.
doi: 10.1023/A:1021359709489. |
[2] |
J. R. Artalejo and V. Pla, On the impact of customer balking, impatience and retrials in telecommunication systems, Computers & Mathematics with Applications, 57 (2009), 217-229.
doi: 10.1016/j.camwa.2008.10.084. |
[3] |
L. Bright and G. P. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Stochastic Models, 11 (1995), 497-525.
doi: 10.1080/15326349508807357. |
[4] |
J. E. Diamond and A. S. Alfa, The MAP/PH/1 retrial queue, Stochastic Models, 14 (1998), 1151-1177.
doi: 10.1080/15326349808807518. |
[5] |
G. I. Falin and J. G. C. Templeton, "Retrial Queues," Chapman & Hall, London, 1997. |
[6] |
M. J. Fischer, D. A. Garbin and A. Gharakhanian, Performance modeling of distributed automatic call distribution systems, Telecommunications Systems, 9 (1998), 133-152.
doi: 10.1023/A:1019139721840. |
[7] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: tutorial, review, and research prospects, Manufacturing & Service Operations Management, 5 (2003), 79-141.
doi: 10.1287/msom.5.2.79.16071. |
[8] |
W. M. Jolley and R. J. Harris, Analysis of post-call activity in queueing systems, Proceedings of the 9th International Teletraffic Congress, Torremolinos, (1979), 1-9. |
[9] |
K. Kawanishi, On the counting process for a class of Markovian arrival processes with an application to a queueing system, Queueing Systems, 49 (2005), 93-122.
doi: 10.1007/s11134-005-6478-7. |
[10] |
J. Kim, B. Kim and S.-S. Ko, Tail asymptotics for the queue size distribution in an M/G/1 retrial queue, Journal of Applied Probability, 44 (2007), 1111-1118.
doi: 10.1239/jap/1197908829. |
[11] |
G. Koole and A. Mandelbaum, Queueing models of call centers: an introduction, Annals of Operations Research, 113 (2002), 41-59.
doi: 10.1023/A:1020949626017. |
[12] |
J. D. C. Little, A proof for the queuing formula: $L = \lambda W$, Operations Research, 9 (1961), 383-387.
doi: 10.1287/opre.9.3.383. |
[13] |
M. F. Neuts, "Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach," Johns Hopkins University Press, Baltimore, MD, 1981. |
[14] |
M. F. Neuts and B. M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems, 7 (1990), 169-190.
doi: 10.1007/BF01158473. |
[15] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, State-dependent M/M/$c$/$c+r$ retrial queues with Bernoulli abandonment,, Journal of Industrial and Management Optimization, 6 (): 517.
doi: 10.3934/jimo.2010.6.517. |
[16] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, A simple algorithm for the rate matrices of level-dependent QBD processes,, Proceedings of the 5th International Conference on Queueing Theory and Network Applications, (): 46.
doi: 10.1145/1837856.1837864. |
[17] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, A matrix continued fraction approach to multi-server retrial queues, to appear in Annals of Operations Research, (2011).
doi: 10.1007/s10479-011-0840-4. |
[18] |
R. L. Tweedie, Sufficient conditions for regularity, recurrence and ergodicity and Markov processes, Mathematical Proceedings of the Cambridge Philosophical Society, 78 (1975), 125-136.
doi: 10.1017/S0305004100051562. |
show all references
References:
[1] |
J. R. Artalejo and M. Pozo, Numerical calculation of the stationary distribution of the main multiserver retrial queue, Annals of Operations Research, 116 (2002), 41-56.
doi: 10.1023/A:1021359709489. |
[2] |
J. R. Artalejo and V. Pla, On the impact of customer balking, impatience and retrials in telecommunication systems, Computers & Mathematics with Applications, 57 (2009), 217-229.
doi: 10.1016/j.camwa.2008.10.084. |
[3] |
L. Bright and G. P. Taylor, Calculating the equilibrium distribution in level dependent quasi-birth-and-death processes, Stochastic Models, 11 (1995), 497-525.
doi: 10.1080/15326349508807357. |
[4] |
J. E. Diamond and A. S. Alfa, The MAP/PH/1 retrial queue, Stochastic Models, 14 (1998), 1151-1177.
doi: 10.1080/15326349808807518. |
[5] |
G. I. Falin and J. G. C. Templeton, "Retrial Queues," Chapman & Hall, London, 1997. |
[6] |
M. J. Fischer, D. A. Garbin and A. Gharakhanian, Performance modeling of distributed automatic call distribution systems, Telecommunications Systems, 9 (1998), 133-152.
doi: 10.1023/A:1019139721840. |
[7] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: tutorial, review, and research prospects, Manufacturing & Service Operations Management, 5 (2003), 79-141.
doi: 10.1287/msom.5.2.79.16071. |
[8] |
W. M. Jolley and R. J. Harris, Analysis of post-call activity in queueing systems, Proceedings of the 9th International Teletraffic Congress, Torremolinos, (1979), 1-9. |
[9] |
K. Kawanishi, On the counting process for a class of Markovian arrival processes with an application to a queueing system, Queueing Systems, 49 (2005), 93-122.
doi: 10.1007/s11134-005-6478-7. |
[10] |
J. Kim, B. Kim and S.-S. Ko, Tail asymptotics for the queue size distribution in an M/G/1 retrial queue, Journal of Applied Probability, 44 (2007), 1111-1118.
doi: 10.1239/jap/1197908829. |
[11] |
G. Koole and A. Mandelbaum, Queueing models of call centers: an introduction, Annals of Operations Research, 113 (2002), 41-59.
doi: 10.1023/A:1020949626017. |
[12] |
J. D. C. Little, A proof for the queuing formula: $L = \lambda W$, Operations Research, 9 (1961), 383-387.
doi: 10.1287/opre.9.3.383. |
[13] |
M. F. Neuts, "Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach," Johns Hopkins University Press, Baltimore, MD, 1981. |
[14] |
M. F. Neuts and B. M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems, 7 (1990), 169-190.
doi: 10.1007/BF01158473. |
[15] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, State-dependent M/M/$c$/$c+r$ retrial queues with Bernoulli abandonment,, Journal of Industrial and Management Optimization, 6 (): 517.
doi: 10.3934/jimo.2010.6.517. |
[16] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, A simple algorithm for the rate matrices of level-dependent QBD processes,, Proceedings of the 5th International Conference on Queueing Theory and Network Applications, (): 46.
doi: 10.1145/1837856.1837864. |
[17] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, A matrix continued fraction approach to multi-server retrial queues, to appear in Annals of Operations Research, (2011).
doi: 10.1007/s10479-011-0840-4. |
[18] |
R. L. Tweedie, Sufficient conditions for regularity, recurrence and ergodicity and Markov processes, Mathematical Proceedings of the Cambridge Philosophical Society, 78 (1975), 125-136.
doi: 10.1017/S0305004100051562. |
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