# American Institute of Mathematical Sciences

• Previous Article
Three concepts of robust efficiency for uncertain multiobjective optimization problems via set order relations
• JIMO Home
• This Issue
• Next Article
A joint dynamic pricing and production model with asymmetric reference price effect
April  2019, 15(2): 689-703. doi: 10.3934/jimo.2018065

## Optimal information policy in discrete-time queues with strategic customers

 1 School of Computer Applications, Kalinga Institute of Industrial Technology, Bhubaneswar-751024, India 2 School of Mathematical Sciences, National Institute of Science Education and Research, Bhubaneswar-752050, India

Received  May 2016 Revised  March 2018 Published  April 2019 Early access  June 2018

This paper studies optimal information revelation policies in discrete-time $Geo/Geo/1$ queue. Revealing the queue length information to arriving customers plays an important role in their decision making, that is, whether to join the system or balk. We consider policies where a service provider discloses information to some customers and conceals it from others, depending upon the number of waiting customers. This partial information disclosure policy helps the service provider minimize the idle period of the system and maximize the revenue.

Citation: Veena Goswami, Gopinath Panda. Optimal information policy in discrete-time queues with strategic customers. Journal of Industrial & Management Optimization, 2019, 15 (2) : 689-703. doi: 10.3934/jimo.2018065
##### 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.   Google Scholar [2] 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.  Google Scholar [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.  Google Scholar [4] A. Di Crescenzo, A probabilistic analogue of the mean value theorem and its applications to reliability theory, Journal of Applied Probability, 36 (1999), 706-719.  doi: 10.1239/jap/1032374628.  Google Scholar [5] N. M. Edelson and D. K. Hilderbrand, Congestion Tolls for Poisson Queuing Processes, Econometrica, 43 (1975), 81-92.  doi: 10.2307/1913415.  Google Scholar [6] 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.  Google Scholar [7] A. Glazer and R. Hassin, On the economics of subscriptions, European Economic Review, 19 (1982), 343-356.  doi: 10.1016/S0014-2921(82)80059-7.  Google Scholar [8] P. Guo, W. Sun and Y. Wang, Equilibrium and optimal strategies to join a queue with partial information on service times, European Journal of Operational Research, 214 (2011), 284-297.  doi: 10.1016/j.ejor.2011.04.011.  Google Scholar [9] 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.  Google Scholar [10] R. Hassin and R. Roet-Green, Equilibrium in a Two Dimensional Queueing Game: When Inspecting the Queue is Costly, Technical report, Tel Aviv University, Israel, 2011. Google Scholar [11] J. J. Hunter, Mathematical Techniques of Applied Probability. Vol. 2, Discrete Time Models: Techniques and Applications, Academic Press, 1983.  Google Scholar [12] J. H. Large and T. W. Norman, Markov perfect Bayesian equilibrium via ergodicity, Working paper. Google Scholar [13] 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.  Google Scholar [14] 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.  Google Scholar [15] 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.  Google Scholar [16] P. Naor, The Regulation of Queue Size by Levying Tolls, Econometrica, 37 (1969), 15-24.  doi: 10.2307/1909200.  Google Scholar [17] R. Shone, V. A. Knight and J. E. Williams, Comparisons between observable and unobservable ${M/M/1}$ queues with respect to optimal customer behavior, European Journal of Operational Research, 227 (2013), 133-141.  doi: 10.1016/j.ejor.2012.12.016.  Google Scholar [18] E. Simhon, Y. Hayel, D. Starobinski and Q. Zhu, Optimal information disclosure policies in strategic queueing games, Operations Research Letters, 44 (2016), 109-113.  doi: 10.1016/j.orl.2015.12.005.  Google Scholar [19] W. Sun, P. Guo and N. Tian, Equilibrium threshold strategies in observable queueing systems with setup/closedown times, Central European Journal of Operations Research, 18 (2010), 241-268.  doi: 10.1007/s10100-009-0104-4.  Google Scholar [20] 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.  Google Scholar [21] J. Wang and F. Zhang, Strategic joining in ${M/M/1}$ retrial queues, European Journal of Operational Research, 230 (2013), 76-87.  doi: 10.1016/j.ejor.2013.03.030.  Google Scholar [22] M. E. Woodward, Communication and Computer Networks: Modelling with Discrete-Time Queues, IEEE Computer Soc. Press, 1994. Google Scholar [23] 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.  Google Scholar [24] 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.  Google Scholar

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.   Google Scholar [2] 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.  Google Scholar [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.  Google Scholar [4] A. Di Crescenzo, A probabilistic analogue of the mean value theorem and its applications to reliability theory, Journal of Applied Probability, 36 (1999), 706-719.  doi: 10.1239/jap/1032374628.  Google Scholar [5] N. M. Edelson and D. K. Hilderbrand, Congestion Tolls for Poisson Queuing Processes, Econometrica, 43 (1975), 81-92.  doi: 10.2307/1913415.  Google Scholar [6] 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.  Google Scholar [7] A. Glazer and R. Hassin, On the economics of subscriptions, European Economic Review, 19 (1982), 343-356.  doi: 10.1016/S0014-2921(82)80059-7.  Google Scholar [8] P. Guo, W. Sun and Y. Wang, Equilibrium and optimal strategies to join a queue with partial information on service times, European Journal of Operational Research, 214 (2011), 284-297.  doi: 10.1016/j.ejor.2011.04.011.  Google Scholar [9] 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.  Google Scholar [10] R. Hassin and R. Roet-Green, Equilibrium in a Two Dimensional Queueing Game: When Inspecting the Queue is Costly, Technical report, Tel Aviv University, Israel, 2011. Google Scholar [11] J. J. Hunter, Mathematical Techniques of Applied Probability. Vol. 2, Discrete Time Models: Techniques and Applications, Academic Press, 1983.  Google Scholar [12] J. H. Large and T. W. Norman, Markov perfect Bayesian equilibrium via ergodicity, Working paper. Google Scholar [13] 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.  Google Scholar [14] 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.  Google Scholar [15] 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.  Google Scholar [16] P. Naor, The Regulation of Queue Size by Levying Tolls, Econometrica, 37 (1969), 15-24.  doi: 10.2307/1909200.  Google Scholar [17] R. Shone, V. A. Knight and J. E. Williams, Comparisons between observable and unobservable ${M/M/1}$ queues with respect to optimal customer behavior, European Journal of Operational Research, 227 (2013), 133-141.  doi: 10.1016/j.ejor.2012.12.016.  Google Scholar [18] E. Simhon, Y. Hayel, D. Starobinski and Q. Zhu, Optimal information disclosure policies in strategic queueing games, Operations Research Letters, 44 (2016), 109-113.  doi: 10.1016/j.orl.2015.12.005.  Google Scholar [19] W. Sun, P. Guo and N. Tian, Equilibrium threshold strategies in observable queueing systems with setup/closedown times, Central European Journal of Operations Research, 18 (2010), 241-268.  doi: 10.1007/s10100-009-0104-4.  Google Scholar [20] 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.  Google Scholar [21] J. Wang and F. Zhang, Strategic joining in ${M/M/1}$ retrial queues, European Journal of Operational Research, 230 (2013), 76-87.  doi: 10.1016/j.ejor.2013.03.030.  Google Scholar [22] M. E. Woodward, Communication and Computer Networks: Modelling with Discrete-Time Queues, IEEE Computer Soc. Press, 1994. Google Scholar [23] 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.  Google Scholar [24] 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.  Google Scholar
Various time epochs in late-arrival system with delayed access (LAS-DA)
State transition diagram of the $Geo/Geo/1$ model with selective threshold policy $\xi_D$.
Various time epochs in early arrival system (EAS)
Uniformed policy ($\xi_-$) is optimal for the $Geo/Geo/1/30$ queue with $\lambda = 0.5, \mu = 0.6, R = 50.$
Informed policy ($\xi_+$) is optimal for the $Geo/Geo/1/30$ queue with $\lambda = 0.65, \mu = 0.6, R = 50.$
Expected waiting time for different joining probabilities for $\lambda = 0.65, \mu = 0.6, D = 5.$
Expected waiting time for different joining probabilities for $\lambda = 0.5, \mu = 0.6, D = 5.$
 [1] Biao Xu, Xiuli Xu, Zhong Yao. Equilibrium and optimal balking strategies for low-priority customers in the M/G/1 queue with two classes of customers and preemptive priority. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1599-1615. doi: 10.3934/jimo.2018113 [2] Pradeep Dubey, Rahul Garg, Bernard De Meyer. Competing for customers in a social network. Journal of Dynamics & Games, 2014, 1 (3) : 377-409. doi: 10.3934/jdg.2014.1.377 [3] Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006 [4] 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, 2020, 16 (3) : 1369-1388. doi: 10.3934/jimo.2019007 [5] Ruopeng Wang, Jinting Wang, Chang Sun. Optimal pricing and inventory management for a loss averse firm when facing strategic customers. Journal of Industrial & Management Optimization, 2018, 14 (4) : 1521-1544. doi: 10.3934/jimo.2018019 [6] Gopinath Panda, Veena Goswami, Abhijit Datta Banik, Dibyajyoti Guha. Equilibrium balking strategies in renewal input queue with Bernoulli-schedule controlled vacation and vacation interruption. Journal of Industrial & Management Optimization, 2016, 12 (3) : 851-878. doi: 10.3934/jimo.2016.12.851 [7] Sin-Man Choi, Ximin Huang, Wai-Ki Ching. Minimizing equilibrium expected sojourn time via performance-based mixed threshold demand allocation in a multiple-server queueing environment. Journal of Industrial & Management Optimization, 2012, 8 (2) : 299-323. doi: 10.3934/jimo.2012.8.299 [8] Ganfu Wang, Xingzheng Ai, Chen Zheng, Li Zhong. Strategic inventory under suppliers competition. Journal of Industrial & Management Optimization, 2020, 16 (5) : 2159-2173. doi: 10.3934/jimo.2019048 [9] Vikram Krishnamurthy, William Hoiles. Information diffusion in social sensing. Numerical Algebra, Control & Optimization, 2016, 6 (3) : 365-411. doi: 10.3934/naco.2016017 [10] Werner Creixell, Juan Carlos Losada, Tomás Arredondo, Patricio Olivares, Rosa María Benito. Serendipity in social networks. Networks & Heterogeneous Media, 2012, 7 (3) : 363-371. doi: 10.3934/nhm.2012.7.363 [11] Yuki Kumagai. Social networks and global transactions. Journal of Dynamics & Games, 2019, 6 (3) : 211-219. doi: 10.3934/jdg.2019015 [12] Nickolas J. Michelacakis. Strategic delegation effects on Cournot and Stackelberg competition. Journal of Dynamics & Games, 2018, 5 (3) : 231-242. doi: 10.3934/jdg.2018015 [13] Gang Chen, Zaiming Liu, Jingchuan Zhang. Analysis of strategic customer behavior in fuzzy queueing systems. Journal of Industrial & Management Optimization, 2020, 16 (1) : 371-386. doi: 10.3934/jimo.2018157 [14] Misha Perepelitsa. A model of cultural evolution in the context of strategic conflict. Kinetic & Related Models, 2021, 14 (3) : 523-539. doi: 10.3934/krm.2021014 [15] Dequan Yue, Wuyi Yue. A heterogeneous two-server network system with balking and a Bernoulli vacation schedule. Journal of Industrial & Management Optimization, 2010, 6 (3) : 501-516. doi: 10.3934/jimo.2010.6.501 [16] Jinyan Wang, Yanni Xiao, Robert A. Cheke. Modelling the effects of contaminated environments in mainland China on seasonal HFMD infections and the potential benefit of a pulse vaccination strategy. Discrete & Continuous Dynamical Systems - B, 2019, 24 (11) : 5849-5870. doi: 10.3934/dcdsb.2019109 [17] Qian Zhao, Yang Shen, Jiaqin Wei. Mean-variance investment and contribution decisions for defined benefit pension plans in a stochastic framework. Journal of Industrial & Management Optimization, 2021, 17 (3) : 1147-1171. doi: 10.3934/jimo.2020015 [18] Yahia Zare Mehrjerdi. A novel methodology for portfolio selection in fuzzy multi criteria environment using risk-benefit analysis and fractional stochastic. Numerical Algebra, Control & Optimization, 2021  doi: 10.3934/naco.2021019 [19] Lianxia Zhao, Jianxin You, Shu-Cherng Fang. A dual-channel supply chain problem with resource-utilization penalty: Who can benefit from sales effort?. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2837-2853. doi: 10.3934/jimo.2020097 [20] Filipe Martins, Alberto A. Pinto, Jorge Passamani Zubelli. Nash and social welfare impact in an international trade model. Journal of Dynamics & Games, 2017, 4 (2) : 149-173. doi: 10.3934/jdg.2017009

2020 Impact Factor: 1.801