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Markovian retrial queues with two way communication
1. | Department of Statistics and O.R., Faculty of Mathematics, Complutense University of Madrid, Madrid 28040, Spain |
2. | Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Tokyo 152-8552, Japan |
References:
[1] |
Z. Aksin, M. Armony and V. Mehrotra, The modern call center: A multi-disciplinary perspective on operations management research, Production and Operations Management, 16 (2007), 665-688.
doi: 10.1111/j.1937-5956.2007.tb00288.x. |
[2] |
J. R. Artalejo and A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated request, Journal of Applied Probability, 34 (1997), 223-233.
doi: 10.2307/3215189. |
[3] |
J. R. Artalejo and A. Gomez-Corral, "Retrial Queueing Systems: A Computational Approach," Springer, Berlin, 2008.
doi: 10.1007/978-3-540-78725-9. |
[4] |
J. R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000-2009, Mathematical and Computer Modelling, 51 (2010), 1071-1081.
doi: 10.1016/j.mcm.2009.12.011. |
[5] |
J. R. Artalejo and J. A. C. Resing, Mean value analysis of single server retrial queues, Asia-Pacific Journal of Operational Research, 27 (2010), 335-345.
doi: 10.1142/S0217595910002739. |
[6] |
K. Avrachenkov, A. Dudin and V. Klimenok, Retrial queueing model MMAP/$M_{2}$/1 with two orbits, Lecture Notes on Computer Science, 6235 (2010), 107-118.
doi: 10.1007/978-3-642-15428-7_12. |
[7] |
S. Bhulai and G. Koole, A queueing model for call blending in call centers, IEEE transactions on Automatic Control, 48 (2003), 1434-1438.
doi: 10.1109/TAC.2003.815038. |
[8] |
B. D. Choi, K. B. Choi and Y. W. Lee, M/G/1 Retrial queueing systems with two types of calls and finite capacity, Queueing Systems, 19 (1995), 215-229.
doi: 10.1007/BF01148947. |
[9] |
B. D. Choi, Y. C. Kim and Y. W. Lee, The M/M/$c$ retrial queue with geometric loss and feedback, Computers & Mathematics with Applications, 36 (1998), 41-52.
doi: 10.1016/S0898-1221(98)00160-6. |
[10] |
A. Deslauriers, P. LfEcuyer, J. Pichitlamken, A. Ingolfsson and A. N. Avramidis, Markov chain models of a telephone call center with call blending, Computers & Operations Research, 34 (2007), 1616-1645.
doi: 10.1016/j.cor.2005.06.019. |
[11] |
G. I. Falin, Model of coupled switching in presence of recurrent calls, Engineering Cybernetics Review, 17 (1979), 53-59. |
[12] |
G. I. Falin and J. G. C. Templeton, "Retrial Queues," Chapman and Hall, London, 1997. |
[13] |
P. Flajolet and R. Sedgewick, "Analytic Combinatorics," Cambridge University Press, Cambridge, 2009. |
[14] |
T. Hanschke, Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts, Journal of Applied Probability, 24 (1987), 486-494. |
[15] |
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. |
[16] |
J. Kim, Retrial queueing system with collision and impatience, Communications of the Korean Mathematical Society, 25 (2010), 647-653.
doi: 10.4134/CKMS.2010.25.4.647. |
[17] |
B. Kim, Stability of a retrial queueing network with different classes of customers and restricted resource pooling, Journal of Industrial and Management Optimization, 7 (2011), 753-765. |
[18] |
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. |
[19] |
A. Krishnamoorthy, T. G. Deepak and V. C. Joshua, An M/G/1 retrial queue with nonpersistent customers and orbital search, Stochastic Analysis and Applications, 23 (2005), 975-997.
doi: 10.1080/07362990500186753. |
[20] |
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. |
[21] |
M. Martin and J. R. Artalejo, Analysis of an M/G/1 queue with two types of impatient units, Advances in Applied Probability, 27 (1995), 840-861.
doi: 10.2307/1428136. |
[22] |
M. F. Neuts and B. M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems, 7 (1990), 169-190.
doi: 10.1007/BF01158473. |
[23] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, M/M/3/3 and M/M/4/4 retrial queues, Journal of Industrial and Management Optimization, 5 (2009), 431-451.
doi: 10.3934/jimo.2009.5.431. |
[24] |
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 (2010), 517-540.
doi: 10.3934/jimo.2010.6.517. |
[25] |
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, (2010), 46-52. |
[26] |
D. A. Samuelson, Predictive dialing for outbound telephone call centers, Interfaces, 29 (1999), 66-81.
doi: 10.1287/inte.29.5.66. |
[27] |
R. Stolletz, "Performance Analysis and Optimization of Inbound Call Centers," Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 2003. |
[28] |
J. Wang, L. Zhao and F. Zhang, Analysis of the finite source retrial queues with server breakdowns and repairs, Journal of Industrial and Management Optimization, 7 (2011), 655-676.
doi: 10.3934/jimo.2011.7.655. |
show all references
References:
[1] |
Z. Aksin, M. Armony and V. Mehrotra, The modern call center: A multi-disciplinary perspective on operations management research, Production and Operations Management, 16 (2007), 665-688.
doi: 10.1111/j.1937-5956.2007.tb00288.x. |
[2] |
J. R. Artalejo and A. Gomez-Corral, Steady state solution of a single-server queue with linear repeated request, Journal of Applied Probability, 34 (1997), 223-233.
doi: 10.2307/3215189. |
[3] |
J. R. Artalejo and A. Gomez-Corral, "Retrial Queueing Systems: A Computational Approach," Springer, Berlin, 2008.
doi: 10.1007/978-3-540-78725-9. |
[4] |
J. R. Artalejo, Accessible bibliography on retrial queues: Progress in 2000-2009, Mathematical and Computer Modelling, 51 (2010), 1071-1081.
doi: 10.1016/j.mcm.2009.12.011. |
[5] |
J. R. Artalejo and J. A. C. Resing, Mean value analysis of single server retrial queues, Asia-Pacific Journal of Operational Research, 27 (2010), 335-345.
doi: 10.1142/S0217595910002739. |
[6] |
K. Avrachenkov, A. Dudin and V. Klimenok, Retrial queueing model MMAP/$M_{2}$/1 with two orbits, Lecture Notes on Computer Science, 6235 (2010), 107-118.
doi: 10.1007/978-3-642-15428-7_12. |
[7] |
S. Bhulai and G. Koole, A queueing model for call blending in call centers, IEEE transactions on Automatic Control, 48 (2003), 1434-1438.
doi: 10.1109/TAC.2003.815038. |
[8] |
B. D. Choi, K. B. Choi and Y. W. Lee, M/G/1 Retrial queueing systems with two types of calls and finite capacity, Queueing Systems, 19 (1995), 215-229.
doi: 10.1007/BF01148947. |
[9] |
B. D. Choi, Y. C. Kim and Y. W. Lee, The M/M/$c$ retrial queue with geometric loss and feedback, Computers & Mathematics with Applications, 36 (1998), 41-52.
doi: 10.1016/S0898-1221(98)00160-6. |
[10] |
A. Deslauriers, P. LfEcuyer, J. Pichitlamken, A. Ingolfsson and A. N. Avramidis, Markov chain models of a telephone call center with call blending, Computers & Operations Research, 34 (2007), 1616-1645.
doi: 10.1016/j.cor.2005.06.019. |
[11] |
G. I. Falin, Model of coupled switching in presence of recurrent calls, Engineering Cybernetics Review, 17 (1979), 53-59. |
[12] |
G. I. Falin and J. G. C. Templeton, "Retrial Queues," Chapman and Hall, London, 1997. |
[13] |
P. Flajolet and R. Sedgewick, "Analytic Combinatorics," Cambridge University Press, Cambridge, 2009. |
[14] |
T. Hanschke, Explicit formulas for the characteristics of the M/M/2/2 queue with repeated attempts, Journal of Applied Probability, 24 (1987), 486-494. |
[15] |
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. |
[16] |
J. Kim, Retrial queueing system with collision and impatience, Communications of the Korean Mathematical Society, 25 (2010), 647-653.
doi: 10.4134/CKMS.2010.25.4.647. |
[17] |
B. Kim, Stability of a retrial queueing network with different classes of customers and restricted resource pooling, Journal of Industrial and Management Optimization, 7 (2011), 753-765. |
[18] |
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. |
[19] |
A. Krishnamoorthy, T. G. Deepak and V. C. Joshua, An M/G/1 retrial queue with nonpersistent customers and orbital search, Stochastic Analysis and Applications, 23 (2005), 975-997.
doi: 10.1080/07362990500186753. |
[20] |
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. |
[21] |
M. Martin and J. R. Artalejo, Analysis of an M/G/1 queue with two types of impatient units, Advances in Applied Probability, 27 (1995), 840-861.
doi: 10.2307/1428136. |
[22] |
M. F. Neuts and B. M. Rao, Numerical investigation of a multiserver retrial model, Queueing Systems, 7 (1990), 169-190.
doi: 10.1007/BF01158473. |
[23] |
T. Phung-Duc, H. Masuyama, S. Kasahara and Y. Takahashi, M/M/3/3 and M/M/4/4 retrial queues, Journal of Industrial and Management Optimization, 5 (2009), 431-451.
doi: 10.3934/jimo.2009.5.431. |
[24] |
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 (2010), 517-540.
doi: 10.3934/jimo.2010.6.517. |
[25] |
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, (2010), 46-52. |
[26] |
D. A. Samuelson, Predictive dialing for outbound telephone call centers, Interfaces, 29 (1999), 66-81.
doi: 10.1287/inte.29.5.66. |
[27] |
R. Stolletz, "Performance Analysis and Optimization of Inbound Call Centers," Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin, 2003. |
[28] |
J. Wang, L. Zhao and F. Zhang, Analysis of the finite source retrial queues with server breakdowns and repairs, Journal of Industrial and Management Optimization, 7 (2011), 655-676.
doi: 10.3934/jimo.2011.7.655. |
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