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Effect of information on the strategic behavior of customers in a discrete-time bulk service queue
1. | School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar, India |
2. | School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar, India |
We consider the equilibrium and socially optimal behavior of strategic customers in a discrete-time queue with bulk service. The service batch size varies from a single customer to a maximum of 'b' customers. We study the equilibrium and socially optimal balking strategies under two information policies: observable and unobservable. In the former policy, a service provider discloses the queue length information to arriving customers and conceals it in the latter policy. The effect of service batch size and other queueing parameters on the equilibrium strategies under both information policies are compared and illustrated with numerical experiments.
References:
[1] |
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. |
[2] |
O. Bountali and A. Economou,
Equilibrium joining strategies in batch service queueing systems, European Journal of Operational Research, 260 (2017), 1142-1151.
doi: 10.1016/j.ejor.2017.01.024. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
N. M. Edelson and D. K. Hilderbrand,
Congestion Tolls for Poisson Queuing Processes, Econometrica, 43 (1975), 81-92.
doi: 10.2307/1913415. |
[7] |
S. Gao and J. Wang,
Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations, RAIRO-Operations Research, 50 (2016), 119-129.
doi: 10.1051/ro/2015019. |
[8] |
V. Goswami and G. Panda,
Optimal information policy in discrete-time queues with strategic customers, Journal of Industrial & Management Optimization, 15 (2019), 689-703.
doi: 10.3934/jimo.2018065. |
[9] |
R. Hassin, Rational Queueing, CRC press, 2016.
doi: 10.1201/b20014.![]() ![]() |
[10] |
R. Hassin and M. Haviv, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems, Springer Science & Business Media, 2003.
doi: 10.1007/978-1-4615-0359-0. |
[11] |
J. J. Hunter, Mathematical Techniques of Applied Probability: Discrete Time Models: Basic
Theory, vol. 1, Academic Press, 1983. |
[12] |
Y. Kerner,
Equilibrium joining probabilities for an M/G/1 queue, Games and Economic Behavior, 71 (2011), 521-526.
doi: 10.1016/j.geb.2010.06.002. |
[13] |
J. Liu and J. Wang,
Strategic joining rules in a single server Markovian queue with Bernoulli vacation, Operational Research, 17 (2017), 413-434.
doi: 10.1007/s12351-016-0231-3. |
[14] |
Z. Liu, Y. Ma and Z. G. Zhang,
Equilibrium mixed strategies in a discrete-time markovian queue under multiple and single vacation policies, Quality Technology & Quantitative Management, 12 (2015), 369-382.
doi: 10.1080/16843703.2015.11673387. |
[15] |
Y. Ma, W.-q. Liu and J.-h. Li,
Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations, Applied Mathematical Modelling, 37 (2013), 3861-3878.
doi: 10.1016/j.apm.2012.08.017. |
[16] |
Y. Ma and Z. Liu, Pricing Analysis in Geo/Geo/1 Queueing System, Mathematical Problems in Engineering, 2015 (2015), Art. ID 181653, 5 pp.
doi: 10.1155/2015/181653. |
[17] |
J. Medhi, Stochastic Models in Queueing Theory, Academic Press, 2003.
![]() |
[18] |
P. Naor,
The regulation of queue size by levying tolls, Econometrica, 37 (1969), 15-24.
doi: 10.2307/1909200. |
[19] |
G. Panda, V. Goswami and A. D. Banik, Equilibrium and socially optimal balking strategies in Markovian queues with vacations and sequential abandonment, Asia-Pacific Journal of Operational Research, 33 (2016), 1650036, 34pp.
doi: 10.1142/S0217595916500366. |
[20] |
G. Panda, V. Goswami and A. D. Banik, Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations, RAIRO-Operations Research, 51 (2017), 685-707. Google Scholar |
[21] |
G. Panda, V. Goswami, A. D. Banik and D. Guha,
Equilibrium balking strategies in renewal input queue with Bernoulli-schedule controlled vacation and vacation interruption, Journal of Industrial and Management Optimization, 12 (2016), 851-878.
doi: 10.3934/jimo.2016.12.851. |
[22] |
W. Sun and S. Li,
Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations, TOP, 22 (2014), 694-715.
doi: 10.1007/s11750-013-0288-6. |
[23] |
F. Wang, J. Wang and F. Zhang, Equilibrium customer strategies in the Geo/Geo/1 queue with single working vacation, Discrete Dynamics in Nature and Society, 2014 (2014), Art. ID 309489, 9 pp.
doi: 10.1155/2014/309489. |
[24] | M. E. Woodward, Communication and Computer Networks: Modelling with discrete-time queues, IEEE Computer Soc. Press, 1994. Google Scholar |
[25] |
T. Yang, J. Wang and F. Zhang,
Equilibrium Balking Strategies in the Geo/Geo/1 Queues with Server Breakdowns and Repairs, Quality Technology & Quantitative Management, 11 (2014), 231-243.
doi: 10.1080/16843703.2014.11673341. |
[26] |
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. |
[27] |
F. Zhang, J. Wang and B. Liu,
Equilibrium joining probabilities in observable queues with general service and setup times, Journal of Industrial and Management Optimization, 9 (2013), 901-917.
doi: 10.3934/jimo.2013.9.901. |
show all references
References:
[1] |
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. |
[2] |
O. Bountali and A. Economou,
Equilibrium joining strategies in batch service queueing systems, European Journal of Operational Research, 260 (2017), 1142-1151.
doi: 10.1016/j.ejor.2017.01.024. |
[3] |
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. |
[4] |
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. |
[5] |
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. |
[6] |
N. M. Edelson and D. K. Hilderbrand,
Congestion Tolls for Poisson Queuing Processes, Econometrica, 43 (1975), 81-92.
doi: 10.2307/1913415. |
[7] |
S. Gao and J. Wang,
Equilibrium balking strategies in the observable Geo/Geo/1 queue with delayed multiple vacations, RAIRO-Operations Research, 50 (2016), 119-129.
doi: 10.1051/ro/2015019. |
[8] |
V. Goswami and G. Panda,
Optimal information policy in discrete-time queues with strategic customers, Journal of Industrial & Management Optimization, 15 (2019), 689-703.
doi: 10.3934/jimo.2018065. |
[9] |
R. Hassin, Rational Queueing, CRC press, 2016.
doi: 10.1201/b20014.![]() ![]() |
[10] |
R. Hassin and M. Haviv, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems, Springer Science & Business Media, 2003.
doi: 10.1007/978-1-4615-0359-0. |
[11] |
J. J. Hunter, Mathematical Techniques of Applied Probability: Discrete Time Models: Basic
Theory, vol. 1, Academic Press, 1983. |
[12] |
Y. Kerner,
Equilibrium joining probabilities for an M/G/1 queue, Games and Economic Behavior, 71 (2011), 521-526.
doi: 10.1016/j.geb.2010.06.002. |
[13] |
J. Liu and J. Wang,
Strategic joining rules in a single server Markovian queue with Bernoulli vacation, Operational Research, 17 (2017), 413-434.
doi: 10.1007/s12351-016-0231-3. |
[14] |
Z. Liu, Y. Ma and Z. G. Zhang,
Equilibrium mixed strategies in a discrete-time markovian queue under multiple and single vacation policies, Quality Technology & Quantitative Management, 12 (2015), 369-382.
doi: 10.1080/16843703.2015.11673387. |
[15] |
Y. Ma, W.-q. Liu and J.-h. Li,
Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations, Applied Mathematical Modelling, 37 (2013), 3861-3878.
doi: 10.1016/j.apm.2012.08.017. |
[16] |
Y. Ma and Z. Liu, Pricing Analysis in Geo/Geo/1 Queueing System, Mathematical Problems in Engineering, 2015 (2015), Art. ID 181653, 5 pp.
doi: 10.1155/2015/181653. |
[17] |
J. Medhi, Stochastic Models in Queueing Theory, Academic Press, 2003.
![]() |
[18] |
P. Naor,
The regulation of queue size by levying tolls, Econometrica, 37 (1969), 15-24.
doi: 10.2307/1909200. |
[19] |
G. Panda, V. Goswami and A. D. Banik, Equilibrium and socially optimal balking strategies in Markovian queues with vacations and sequential abandonment, Asia-Pacific Journal of Operational Research, 33 (2016), 1650036, 34pp.
doi: 10.1142/S0217595916500366. |
[20] |
G. Panda, V. Goswami and A. D. Banik, Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations, RAIRO-Operations Research, 51 (2017), 685-707. Google Scholar |
[21] |
G. Panda, V. Goswami, A. D. Banik and D. Guha,
Equilibrium balking strategies in renewal input queue with Bernoulli-schedule controlled vacation and vacation interruption, Journal of Industrial and Management Optimization, 12 (2016), 851-878.
doi: 10.3934/jimo.2016.12.851. |
[22] |
W. Sun and S. Li,
Equilibrium and optimal behavior of customers in Markovian queues with multiple working vacations, TOP, 22 (2014), 694-715.
doi: 10.1007/s11750-013-0288-6. |
[23] |
F. Wang, J. Wang and F. Zhang, Equilibrium customer strategies in the Geo/Geo/1 queue with single working vacation, Discrete Dynamics in Nature and Society, 2014 (2014), Art. ID 309489, 9 pp.
doi: 10.1155/2014/309489. |
[24] | M. E. Woodward, Communication and Computer Networks: Modelling with discrete-time queues, IEEE Computer Soc. Press, 1994. Google Scholar |
[25] |
T. Yang, J. Wang and F. Zhang,
Equilibrium Balking Strategies in the Geo/Geo/1 Queues with Server Breakdowns and Repairs, Quality Technology & Quantitative Management, 11 (2014), 231-243.
doi: 10.1080/16843703.2014.11673341. |
[26] |
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. |
[27] |
F. Zhang, J. Wang and B. Liu,
Equilibrium joining probabilities in observable queues with general service and setup times, Journal of Industrial and Management Optimization, 9 (2013), 901-917.
doi: 10.3934/jimo.2013.9.901. |












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