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Equilibrium balking strategies in renewal input queue with Bernoulli-schedule controlled vacation and vacation interruption
1. | School of Basic Scienes, Indian Institute of Technology, Bhubaneswar-751007, India, India, India |
2. | School of Computer Application, KIIT University, Bhubaneswar-751024, India |
References:
[1] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Operations Research Letters, 33 (2005), 201-209.
doi: 10.1016/j.orl.2004.05.006. |
[2] |
A. D. Banik, U. C. Gupta and S. S. Pathak, On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation, Applied Mathematical Modelling, 31 (2007), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[3] |
M. A. A. Boon, R. D. van der Mei and E. M. M. Winands, Applications of polling systems, Surveys in Operations Research and Management Science, 16 (2011), 67-82.
doi: 10.1016/j.sorms.2011.01.001. |
[4] |
M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, Wiley, New York, 1983. |
[5] |
M. L. Chaudhry, C. M. Harris and W. G. Marchal, Robustness of rootfinding in single-server queueing models, ORSA Journal on Computing, 2 (1990), 273-286. |
[6] |
H. Chen, J. Li and N. Tian, The GI/M/1 queue with phase-type working vacations and vacation interruption, Journal of Applied Mathematics and Computing, 30 (2009), 121-141.
doi: 10.1007/s12190-008-0161-1. |
[7] |
J. L. Dorsman, O. J. Boxma and R. D. van der Mei, On two-queue Markovian polling systems with exhaustive service, Queueing Systems, 78 (2014), 287-311.
doi: 10.1007/s11134-014-9413-y. |
[8] |
B. T. Doshi, Queueing systems with vacations-A survey, Queueing Systems, 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[9] |
A. Economou, A. Gómez-Corral and S. Kanta, Optimal balking strategies in single-server queues with general service and vacation times, Performance Evaluation, 68 (2011), 967-982.
doi: 10.1016/j.peva.2011.07.001. |
[10] |
A. Economou and S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs, Operations Research Letters, 36 (2008), 696-699.
doi: 10.1016/j.orl.2008.06.006. |
[11] |
N. M. Edelson and D. K. Hilderbrand, Congestion tolls for Poisson queuing processes, Econometrica: Journal of the Econometric Society, 43 (1975), 81-92.
doi: 10.2307/1913415. |
[12] |
V. Goswami and P. V. Laxmi, Analysis of renewal input bulk arrival queue with single working vacation and partial batch rejection, Journal of Industrial and Management Optimization, 6 (2010), 911-927.
doi: 10.3934/jimo.2010.6.911. |
[13] |
P. Guo and P. Zipkin, The effects of the availability of waiting-time information on a balking queue, European Journal of Operational Research, 198 (2009), 199-209.
doi: 10.1016/j.ejor.2008.07.035. |
[14] |
R. Hassin and M. Haviv, To Queue or not to Queue: Equilibrium Behavior in Queueing Systems, Springer, 2003.
doi: 10.1007/978-1-4615-0359-0. |
[15] |
J. Ke, C. Wu and Z. G. Zhang, Recent developments in vacation queueing models: A short survey, International Journal of Operations Research, 7 (2010), 3-8. |
[16] |
J. Keilson and L. D. Servi, Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules, Journal of Applied Probability, 23 (1986), 790-802.
doi: 10.2307/3214016. |
[17] |
G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, SIAM, Philadelphia, PA, 1999.
doi: 10.1137/1.9780898719734. |
[18] |
J. Li and N. Tian, The M/M/1 queue with working vacations and vacation interruptions, Journal of Systems Science and Systems Engineering, 16 (2007), 121-127.
doi: 10.1007/s11518-006-5030-6. |
[19] |
J. Li, N. Tian and Z. Ma, Performance analysis of GI/M/1 queue with working vacations and vacation interruption, Applied Mathematical Modelling, 32 (2008), 2715-2730.
doi: 10.1016/j.apm.2007.09.017. |
[20] |
P. Naor, The regulation of queue size by levying tolls, Econometrica, 37 (1969), 15-24.
doi: 10.2307/1909200. |
[21] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[22] |
L. Takács, Introduction to the Theory of Queues, University Texts in the Mathematical Sciences, Oxford University Press, New York, 1962. |
[23] |
H. Takagi, Analysis and application of polling models, in Performance Evaluation: Origins and Directions, Lecture Notes in Computer Science, 1769, Springer, 2000, 423-442.
doi: 10.1007/3-540-46506-5_18. |
[24] |
L. Tao, Z. Liu and Z. Wang, The GI/M/1 queue with start-up period and single working vacation and Bernoulli vacation interruption, Applied Mathematics and Computation, 218 (2011), 4401-4413.
doi: 10.1016/j.amc.2011.10.017. |
[25] |
L. Tao, Z. Wang and Z. Liu, The GI/M/1 queue with Bernoulli-schedule-controlled vacation and vacation interruption, Applied Mathematical Modelling, 37 (2013), 3724-3735.
doi: 10.1016/j.apm.2012.07.045. |
[26] |
N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, International Series in Operations Research & Management Science, 93, Springer, New York, 2006. |
[27] |
J. Wang and F. Zhang, Equilibrium analysis of the observable queues with balking and delayed repairs, Applied Mathematics and Computation, 218 (2011), 2716-2729.
doi: 10.1016/j.amc.2011.08.012. |
[28] |
U. Yechiali, On optimal balking rules and toll charges in the GI/M/1 queuing process, Operations Research, 19 (1971), 349-370.
doi: 10.1287/opre.19.2.349. |
[29] |
D. Yue, W. Yue and G. Xu, Analysis of customers' impatience in an M/M/1 queue with working vacations, Journal of Industrial and Management Optimization, 8 (2012), 895-908.
doi: 10.3934/jimo.2012.8.895. |
[30] |
F. Zhang, J. Wang and B. Liu, Equilibrium balking strategies in Markovian queues with working vacations, Applied Mathematical Modelling, 37 (2013), 8264-8282.
doi: 10.1016/j.apm.2013.03.049. |
[31] |
H. Zhang and D. Shi, The M/M/1 queue with Bernoulli-schedule-controlled vacation and vacation interruption, Int. J. Inform. Manage. Sci, 20 (2009), 579-587. |
[32] |
G. Zhao, X. Du and N. Tian, GI/M/1 queue with set-up period and working vacation and vacation interruption, Int. J. Inform. Manage. Sci, 20 (2009), 351-363. |
show all references
References:
[1] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Operations Research Letters, 33 (2005), 201-209.
doi: 10.1016/j.orl.2004.05.006. |
[2] |
A. D. Banik, U. C. Gupta and S. S. Pathak, On the GI/M/1/N queue with multiple working vacations-analytic analysis and computation, Applied Mathematical Modelling, 31 (2007), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[3] |
M. A. A. Boon, R. D. van der Mei and E. M. M. Winands, Applications of polling systems, Surveys in Operations Research and Management Science, 16 (2011), 67-82.
doi: 10.1016/j.sorms.2011.01.001. |
[4] |
M. L. Chaudhry and J. G. C. Templeton, A First Course in Bulk Queues, Wiley, New York, 1983. |
[5] |
M. L. Chaudhry, C. M. Harris and W. G. Marchal, Robustness of rootfinding in single-server queueing models, ORSA Journal on Computing, 2 (1990), 273-286. |
[6] |
H. Chen, J. Li and N. Tian, The GI/M/1 queue with phase-type working vacations and vacation interruption, Journal of Applied Mathematics and Computing, 30 (2009), 121-141.
doi: 10.1007/s12190-008-0161-1. |
[7] |
J. L. Dorsman, O. J. Boxma and R. D. van der Mei, On two-queue Markovian polling systems with exhaustive service, Queueing Systems, 78 (2014), 287-311.
doi: 10.1007/s11134-014-9413-y. |
[8] |
B. T. Doshi, Queueing systems with vacations-A survey, Queueing Systems, 1 (1986), 29-66.
doi: 10.1007/BF01149327. |
[9] |
A. Economou, A. Gómez-Corral and S. Kanta, Optimal balking strategies in single-server queues with general service and vacation times, Performance Evaluation, 68 (2011), 967-982.
doi: 10.1016/j.peva.2011.07.001. |
[10] |
A. Economou and S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs, Operations Research Letters, 36 (2008), 696-699.
doi: 10.1016/j.orl.2008.06.006. |
[11] |
N. M. Edelson and D. K. Hilderbrand, Congestion tolls for Poisson queuing processes, Econometrica: Journal of the Econometric Society, 43 (1975), 81-92.
doi: 10.2307/1913415. |
[12] |
V. Goswami and P. V. Laxmi, Analysis of renewal input bulk arrival queue with single working vacation and partial batch rejection, Journal of Industrial and Management Optimization, 6 (2010), 911-927.
doi: 10.3934/jimo.2010.6.911. |
[13] |
P. Guo and P. Zipkin, The effects of the availability of waiting-time information on a balking queue, European Journal of Operational Research, 198 (2009), 199-209.
doi: 10.1016/j.ejor.2008.07.035. |
[14] |
R. Hassin and M. Haviv, To Queue or not to Queue: Equilibrium Behavior in Queueing Systems, Springer, 2003.
doi: 10.1007/978-1-4615-0359-0. |
[15] |
J. Ke, C. Wu and Z. G. Zhang, Recent developments in vacation queueing models: A short survey, International Journal of Operations Research, 7 (2010), 3-8. |
[16] |
J. Keilson and L. D. Servi, Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules, Journal of Applied Probability, 23 (1986), 790-802.
doi: 10.2307/3214016. |
[17] |
G. Latouche and V. Ramaswami, Introduction to Matrix Analytic Methods in Stochastic Modeling, ASA-SIAM Series on Statistics and Applied Probability, SIAM, Philadelphia, PA, 1999.
doi: 10.1137/1.9780898719734. |
[18] |
J. Li and N. Tian, The M/M/1 queue with working vacations and vacation interruptions, Journal of Systems Science and Systems Engineering, 16 (2007), 121-127.
doi: 10.1007/s11518-006-5030-6. |
[19] |
J. Li, N. Tian and Z. Ma, Performance analysis of GI/M/1 queue with working vacations and vacation interruption, Applied Mathematical Modelling, 32 (2008), 2715-2730.
doi: 10.1016/j.apm.2007.09.017. |
[20] |
P. Naor, The regulation of queue size by levying tolls, Econometrica, 37 (1969), 15-24.
doi: 10.2307/1909200. |
[21] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[22] |
L. Takács, Introduction to the Theory of Queues, University Texts in the Mathematical Sciences, Oxford University Press, New York, 1962. |
[23] |
H. Takagi, Analysis and application of polling models, in Performance Evaluation: Origins and Directions, Lecture Notes in Computer Science, 1769, Springer, 2000, 423-442.
doi: 10.1007/3-540-46506-5_18. |
[24] |
L. Tao, Z. Liu and Z. Wang, The GI/M/1 queue with start-up period and single working vacation and Bernoulli vacation interruption, Applied Mathematics and Computation, 218 (2011), 4401-4413.
doi: 10.1016/j.amc.2011.10.017. |
[25] |
L. Tao, Z. Wang and Z. Liu, The GI/M/1 queue with Bernoulli-schedule-controlled vacation and vacation interruption, Applied Mathematical Modelling, 37 (2013), 3724-3735.
doi: 10.1016/j.apm.2012.07.045. |
[26] |
N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications, International Series in Operations Research & Management Science, 93, Springer, New York, 2006. |
[27] |
J. Wang and F. Zhang, Equilibrium analysis of the observable queues with balking and delayed repairs, Applied Mathematics and Computation, 218 (2011), 2716-2729.
doi: 10.1016/j.amc.2011.08.012. |
[28] |
U. Yechiali, On optimal balking rules and toll charges in the GI/M/1 queuing process, Operations Research, 19 (1971), 349-370.
doi: 10.1287/opre.19.2.349. |
[29] |
D. Yue, W. Yue and G. Xu, Analysis of customers' impatience in an M/M/1 queue with working vacations, Journal of Industrial and Management Optimization, 8 (2012), 895-908.
doi: 10.3934/jimo.2012.8.895. |
[30] |
F. Zhang, J. Wang and B. Liu, Equilibrium balking strategies in Markovian queues with working vacations, Applied Mathematical Modelling, 37 (2013), 8264-8282.
doi: 10.1016/j.apm.2013.03.049. |
[31] |
H. Zhang and D. Shi, The M/M/1 queue with Bernoulli-schedule-controlled vacation and vacation interruption, Int. J. Inform. Manage. Sci, 20 (2009), 579-587. |
[32] |
G. Zhao, X. Du and N. Tian, GI/M/1 queue with set-up period and working vacation and vacation interruption, Int. J. Inform. Manage. Sci, 20 (2009), 351-363. |
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