doi: 10.3934/jimo.2019007

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

Received  February 2018 Revised  October 2018 Published  March 2019

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.

Citation: Gopinath Panda, Veena Goswami. Effect of information on the strategic behavior of customers in a discrete-time bulk service queue. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019007
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. EconomouA. 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. LiuY. 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. MaW.-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. PandaV. 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.

[21]

G. PandaV. GoswamiA. 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.
[25]

T. YangJ. 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. ZhangJ. 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. ZhangJ. 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. EconomouA. 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. LiuY. 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. MaW.-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. PandaV. 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.

[21]

G. PandaV. GoswamiA. 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.
[25]

T. YangJ. 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. ZhangJ. 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. ZhangJ. 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.

Figure 1.  Various time epochs in a late-arrival system with delayed access (LAS-DA)
Figure 2.  State transition diagram for the original model with maximum batch size $ b $
Figure 3.  State transition diagram for an observable batch service queueing model with maximum batch size $ b $
Figure 4.  State transition diagram for the unobservable batch service queueing model with maximum batch size $ b $
Figure 6.  Effect of customer arrivals on the benefit function under different information policies with parameters $\mu = 0.15, b = 10, R = 30, C = 1$
Figure 7.  Effect of service rate on the benefit function under different information policies with parameters $\lambda = 0.75, b = 10, R = 30, C = 1$
Figure 8.  Equilibrium strategy vs batch size under observable policy for $\lambda = 0.2, \mu = 0.3, R = 10, C = 1$
Figure 9.  Equilibrium strategy vs batch size under unobservable policy for $\lambda = 0.2, \mu = 0.3, R = 5, C = 1$
Figure 10.  Effect of batch size on the benefit function under different information policies with parameters $\lambda = 0.75, \mu = 0.25, R = 30, C = 1$
Figure 11.  Dependence of performance measures on customer arrivals under the observable policy with parameters $ \mu = 0.15, b = 10, R = 30, C = 1$
Figure 12.  Comparison of average system lengths with respect to $b$ for $\lambda = 0.75, \mu = 0.25, R = 30, C = 1$
Figure 13.  Comparison of average system lengths with respect to $\lambda$ for $b = 10, \mu = 0.15, R = 30, C = 1$
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