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On the strong convergence of a modified Hestenes-Stiefel method for nonconvex optimization
Equilibrium joining probabilities in observable queues with general service and setup times
1. | Department of Mathematics, Beijing Jiaotong University, 100044 Beijing |
2. | Department of Mathematics, University of Northern Iowa, Cedar Falls, IA 50614-0506 |
References:
[1] |
E. Altman and R. Hassin, Non-threshold equilibrium for customers joining an M/G/1 queue, in "ISDG2002, Vol. I, II" (St. Petersburg), St. Petersburg State Univ. Inst. Chem., St. Petersburg, (2002), 56-64. |
[2] |
J. R. Artalejo, A. Economou and M. J. Lopez-Herrero, Analysis of a multiserver queue with setup times, Queueing Systems, 51 (2005), 53-76.
doi: 10.1007/s11134-005-1740-6. |
[3] |
W. Bischof, Analysis of M/G/1-queues with setup times and vacations under six different service disciplines, Queueing Systems, 39 (2001), 265-301.
doi: 10.1023/A:1013992708103. |
[4] |
A. Borthakur and G. Choudhury, A multiserver Poisson queue with a general startup time under $N$-policy, Calcutta Statistical Association Bulletin, 49 (1999), 199-213. |
[5] |
O. Boudali and A. Economou, Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes, European Journal of Operational Research, 218 (2012), 708-715.
doi: 10.1016/j.ejor.2011.11.043. |
[6] |
A. Burnetas, Customer equilibrium and optimal strategies in Markovian queues in series, Annals of Operations Research, 208 (2013), 515-529.
doi: 10.1007/s10479-011-1010-4. |
[7] |
A. Burnetas and A. Economou, Equilibrium customer strategies in a single server Markovian queue with setup times, Queueing Systems, 56 (2007), 213-228.
doi: 10.1007/s11134-007-9036-7. |
[8] |
G. Choudhury, On a batch arrival Poisson queue with a random setup and vacation period, Computers $&$ Operations Research, 25 (1998), 1013-1026.
doi: 10.1016/S0305-0548(98)00038-0. |
[9] |
G. Choudhury, An $M^X$/G/1 queueing system with a setup period and a vacation period, Queueing Systems, 36 (2000), 23-38.
doi: 10.1023/A:1011089403694. |
[10] |
A. Economou and S. Kanta, On balking strategies and pricing for the single server Markovian queue with compartmented waiting space, Queueing Systems, 59 (2008), 237-269.
doi: 10.1007/s11134-008-9083-8. |
[11] |
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. |
[12] |
A. Economou and S. Kanta, Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue, Naval Research Logistics, 58 (2011), 107-122.
doi: 10.1002/nav.20444. |
[13] |
A. Economou, A. Gomez-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. |
[14] |
A. Economou and A. Manou, Equilibrium balking strategies for a clearing queueing system in alternating environment, Annals of Operations Research, 208 (2013), 489-514.
doi: 10.1007/s10479-011-1025-x. |
[15] |
N. M. Edelson and K. Hildebrand, Congestion tolls for Poisson queueing processes, Econometrica, 43 (1975), 81-92.
doi: 10.2307/1913415. |
[16] |
P. Guo and R. Hassin, Strategic behavior and social optimization in Markovian vacation queues, Operations Research, 59 (2011), 986-997.
doi: 10.1287/opre.1100.0907. |
[17] |
P. Guo and R. Hassin, Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers, European Journal of Operational Research, 222 (2012), 278-286.
doi: 10.1016/j.ejor.2012.05.026. |
[18] |
R. Hassin and M. Haviv, Equilibrium threshold strategies: the case of queues with priorities, Operations Research, 45 (1997), 966-973.
doi: 10.1287/opre.45.6.966. |
[19] |
R. Hassin and M. Haviv, "To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems," International Series in Operations Research & Management Science, 59, Kluwer Academic Publishers, Boston, MA, 2003.
doi: 10.1007/978-1-4615-0359-0. |
[20] |
M. Haviv and Y. Kerner, On balking from an empty queue, Queueing Systems, 55 (2007), 239-249.
doi: 10.1007/s11134-007-9020-2. |
[21] |
Q. M. He and E. Jewkes, Flow time in the $M AP$/G/1 queue with customer batching and setup times, Stochastic Models, 11 (1995), 691-711.
doi: 10.1080/15326349508807367. |
[22] |
Y. Kerner, The conditional distribution of the residual service time in the $M_n$/G/1 queue, Stochastic Models, 24 (2008), 364-375.
doi: 10.1080/15326340802232210. |
[23] |
Y. Kerner, Equilibrium joining probabilities for an M/G/1 queue, Game and Economic Behavior, 71 (2011), 521-526.
doi: 10.1016/j.geb.2010.06.002. |
[24] |
W. Liu, Y. Ma and J. Li, Equilibrium threshold strategies in observable queueing systems under single vacation policy, Applied Mathematical Modelling, 36 (2012), 6186-6202.
doi: 10.1016/j.apm.2012.02.003. |
[25] |
P. Naor, The regulation of queue size by levying tolls, Econometrica, 37 (1969), 15-24.
doi: 10.2307/1909200. |
[26] |
S. Stidham, Jr., "Optimal Design of Queueing Systems," CRC Press, Boca Raton, FL, 2009.
doi: 10.1201/9781420010008. |
[27] |
W. Sun, P. Guo and N. Tian, Equilibrium threshold strategies in observable queueing systems with setup/closedown times, Central European Journal of Operational Research, 18 (2010), 241-268.
doi: 10.1007/s10100-009-0104-4. |
[28] |
H. Takagi, "Queueing Analysis: A Foundation of Performance Evaluation. Vol. 1. Vacation and Priority Systems. Part I," North-Holland, Amsterdam, 1991. |
[29] |
N. Tian and Z.G. Zhang, "Vacation Queueing Models. Theory and Applications," International Series in Operations Research & Management Science, 93, Springer, New York, 2006. |
[30] |
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. |
[31] |
F. Zhang, J. Wang and B. Liu, On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations, Journal of Industrial and Management Optimization, 8 (2012), 861-875.
doi: 10.3934/jimo.2012.8.861. |
show all references
References:
[1] |
E. Altman and R. Hassin, Non-threshold equilibrium for customers joining an M/G/1 queue, in "ISDG2002, Vol. I, II" (St. Petersburg), St. Petersburg State Univ. Inst. Chem., St. Petersburg, (2002), 56-64. |
[2] |
J. R. Artalejo, A. Economou and M. J. Lopez-Herrero, Analysis of a multiserver queue with setup times, Queueing Systems, 51 (2005), 53-76.
doi: 10.1007/s11134-005-1740-6. |
[3] |
W. Bischof, Analysis of M/G/1-queues with setup times and vacations under six different service disciplines, Queueing Systems, 39 (2001), 265-301.
doi: 10.1023/A:1013992708103. |
[4] |
A. Borthakur and G. Choudhury, A multiserver Poisson queue with a general startup time under $N$-policy, Calcutta Statistical Association Bulletin, 49 (1999), 199-213. |
[5] |
O. Boudali and A. Economou, Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes, European Journal of Operational Research, 218 (2012), 708-715.
doi: 10.1016/j.ejor.2011.11.043. |
[6] |
A. Burnetas, Customer equilibrium and optimal strategies in Markovian queues in series, Annals of Operations Research, 208 (2013), 515-529.
doi: 10.1007/s10479-011-1010-4. |
[7] |
A. Burnetas and A. Economou, Equilibrium customer strategies in a single server Markovian queue with setup times, Queueing Systems, 56 (2007), 213-228.
doi: 10.1007/s11134-007-9036-7. |
[8] |
G. Choudhury, On a batch arrival Poisson queue with a random setup and vacation period, Computers $&$ Operations Research, 25 (1998), 1013-1026.
doi: 10.1016/S0305-0548(98)00038-0. |
[9] |
G. Choudhury, An $M^X$/G/1 queueing system with a setup period and a vacation period, Queueing Systems, 36 (2000), 23-38.
doi: 10.1023/A:1011089403694. |
[10] |
A. Economou and S. Kanta, On balking strategies and pricing for the single server Markovian queue with compartmented waiting space, Queueing Systems, 59 (2008), 237-269.
doi: 10.1007/s11134-008-9083-8. |
[11] |
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. |
[12] |
A. Economou and S. Kanta, Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue, Naval Research Logistics, 58 (2011), 107-122.
doi: 10.1002/nav.20444. |
[13] |
A. Economou, A. Gomez-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. |
[14] |
A. Economou and A. Manou, Equilibrium balking strategies for a clearing queueing system in alternating environment, Annals of Operations Research, 208 (2013), 489-514.
doi: 10.1007/s10479-011-1025-x. |
[15] |
N. M. Edelson and K. Hildebrand, Congestion tolls for Poisson queueing processes, Econometrica, 43 (1975), 81-92.
doi: 10.2307/1913415. |
[16] |
P. Guo and R. Hassin, Strategic behavior and social optimization in Markovian vacation queues, Operations Research, 59 (2011), 986-997.
doi: 10.1287/opre.1100.0907. |
[17] |
P. Guo and R. Hassin, Strategic behavior and social optimization in Markovian vacation queues: The case of heterogeneous customers, European Journal of Operational Research, 222 (2012), 278-286.
doi: 10.1016/j.ejor.2012.05.026. |
[18] |
R. Hassin and M. Haviv, Equilibrium threshold strategies: the case of queues with priorities, Operations Research, 45 (1997), 966-973.
doi: 10.1287/opre.45.6.966. |
[19] |
R. Hassin and M. Haviv, "To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems," International Series in Operations Research & Management Science, 59, Kluwer Academic Publishers, Boston, MA, 2003.
doi: 10.1007/978-1-4615-0359-0. |
[20] |
M. Haviv and Y. Kerner, On balking from an empty queue, Queueing Systems, 55 (2007), 239-249.
doi: 10.1007/s11134-007-9020-2. |
[21] |
Q. M. He and E. Jewkes, Flow time in the $M AP$/G/1 queue with customer batching and setup times, Stochastic Models, 11 (1995), 691-711.
doi: 10.1080/15326349508807367. |
[22] |
Y. Kerner, The conditional distribution of the residual service time in the $M_n$/G/1 queue, Stochastic Models, 24 (2008), 364-375.
doi: 10.1080/15326340802232210. |
[23] |
Y. Kerner, Equilibrium joining probabilities for an M/G/1 queue, Game and Economic Behavior, 71 (2011), 521-526.
doi: 10.1016/j.geb.2010.06.002. |
[24] |
W. Liu, Y. Ma and J. Li, Equilibrium threshold strategies in observable queueing systems under single vacation policy, Applied Mathematical Modelling, 36 (2012), 6186-6202.
doi: 10.1016/j.apm.2012.02.003. |
[25] |
P. Naor, The regulation of queue size by levying tolls, Econometrica, 37 (1969), 15-24.
doi: 10.2307/1909200. |
[26] |
S. Stidham, Jr., "Optimal Design of Queueing Systems," CRC Press, Boca Raton, FL, 2009.
doi: 10.1201/9781420010008. |
[27] |
W. Sun, P. Guo and N. Tian, Equilibrium threshold strategies in observable queueing systems with setup/closedown times, Central European Journal of Operational Research, 18 (2010), 241-268.
doi: 10.1007/s10100-009-0104-4. |
[28] |
H. Takagi, "Queueing Analysis: A Foundation of Performance Evaluation. Vol. 1. Vacation and Priority Systems. Part I," North-Holland, Amsterdam, 1991. |
[29] |
N. Tian and Z.G. Zhang, "Vacation Queueing Models. Theory and Applications," International Series in Operations Research & Management Science, 93, Springer, New York, 2006. |
[30] |
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. |
[31] |
F. Zhang, J. Wang and B. Liu, On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations, Journal of Industrial and Management Optimization, 8 (2012), 861-875.
doi: 10.3934/jimo.2012.8.861. |
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