A Stackelberg game is used to study the service pricing and the strategic behavior of customers in an unreliable and totally unobservable M/M/1 queue under a reward-cost structure. At the first stage, the server manager, acting as a leader, chooses a service price and, at the second stage, a customer, arriving at the system and acting as a follower, chooses to join the system or an outside opportunity, knowing only the service price imposed by the server manager and the system parameters. We show that the constructed game admits an equilibrium and we give explicit forms of server manager and customers equilibrium behavioral strategies. The results of the proposed model show that the assumption that customers are risk-neutral is fundamental for the standard approach usually used. Moreover, we determine the socially optimal price that maximizes the social welfare and we compare it to the Stackelberg equilibrium. We illustrate, by numerical examples, the effect of some system parameters on the equilibrium service price and the revenue of the server manager.
Keywords: Queueing, unreliable server, pricing, strategic behavior, Stackelberg game, equilibrium
@article{RO_2022__56_1_213_0,
author = {Meziani, Kamel and Rahmoune, Fazia and Radjef, Mohammed Said},
title = {The service pricing strategies and the strategic behavior of customers in an unobservable {Markovian} queue with unreliable server},
journal = {RAIRO. Operations Research},
pages = {213--237},
year = {2022},
publisher = {EDP-Sciences},
volume = {56},
number = {1},
doi = {10.1051/ro/2021181},
mrnumber = {4376284},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ro/2021181/}
}
TY - JOUR AU - Meziani, Kamel AU - Rahmoune, Fazia AU - Radjef, Mohammed Said TI - The service pricing strategies and the strategic behavior of customers in an unobservable Markovian queue with unreliable server JO - RAIRO. Operations Research PY - 2022 SP - 213 EP - 237 VL - 56 IS - 1 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ro/2021181/ DO - 10.1051/ro/2021181 LA - en ID - RO_2022__56_1_213_0 ER -
%0 Journal Article %A Meziani, Kamel %A Rahmoune, Fazia %A Radjef, Mohammed Said %T The service pricing strategies and the strategic behavior of customers in an unobservable Markovian queue with unreliable server %J RAIRO. Operations Research %D 2022 %P 213-237 %V 56 %N 1 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ro/2021181/ %R 10.1051/ro/2021181 %G en %F RO_2022__56_1_213_0
Meziani, Kamel; Rahmoune, Fazia; Radjef, Mohammed Said. The service pricing strategies and the strategic behavior of customers in an unobservable Markovian queue with unreliable server. RAIRO. Operations Research, Tome 56 (2022) no. 1, pp. 213-237. doi: 10.1051/ro/2021181
[1] and , Equilibrium threshold strategies and social benefits in the fully observable Markovian queues with partial breakdowns and interruptible setup/closedown policy. Qual. Technol. Quant. Manage. 17 (2020) 685–722. | DOI
[2] and , Dynamic Noncooperative Game Theory. SIAM (1998). | MR | Zbl | DOI
[3] and , Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes. Eur. J. Oper. Res. 218 (2012) 708–715. | MR | Zbl | DOI
[4] and , The effect of catastrophes on the strategic customer behavior in queueing systems. Nav. Res. Logistics (NRL) 60 (2013) 571–587. | MR | DOI
[5] and , State dependent pricing with a queue. IIE Trans. 33 (2001) 847–860. | DOI
[6] and , Monopoly pricing when customers queue. IIE Trans. 36 (2004) 569–581. | DOI
[7] and , Equilibrium balking strategies in the single server queue with setup times and breakdowns. Oper. Res. 15 (2015) 213–231.
[8] , The impact of information structure on strategic behavior in queueing systems. In: Queueing Theory 2, Advanced Trends. Wiley/ISTE (2021). | DOI
[9] and , Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper. Res. Lett. 36 (2008) 696–699. | MR | Zbl | DOI
[10] and , Congestion tolls for poisson queuing processes. Econ : J Econ. Soc. 43 (1975) 81–92. | MR | Zbl
[11] , , and , Equilibrium balking strategies in the reparable -retrial queue with complete removals. Prob. Eng. Inf. Sci. 35 (2021) 138–157. | MR | DOI
[12] , Rational Queueing. CRC Press (2016). | MR
[13] and , To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Vol. 59. Springer Science & Business Media (2003). | MR | Zbl | DOI
[14] , , and , Non-cooperative spectrum access—the dedicated vs. free spectrum choice. IEEE J. Sel. Areas Commun. 30 (2012) 2251–2261. | DOI
[15] and , Equilibrium balking strategies in the single-server retrial queue with constant retrial rate and catastrophes. Qual. Technol. Quant. Manage. 18 (2021) 156–178. | DOI
[16] , and , Equilibrium customer strategies in Markovian queues with partial breakdowns. Comput. Ind. Eng. 66 (2013) 751–757. | DOI
[17] , and , New results on equilibrium balking strategies in the single-server queue with breakdowns and repairs. Appl. Math. Comput. 241 (2014) 380–388. | MR | DOI
[18] and , Analysis and comparison of queue with -policy and unreliable server. Discrete Dyn. Nat. Soc. 2020 (2020). DOI: . | DOI | MR
[19] , and , Pricing in a transportation station with strategic customers. Prod. Oper. Manage. 26 (2017) 1632–1645. | DOI
[20] , and , Service pricing and customer behavior strategies of stackelberg’s equilibrium in an unobservable Markovian queue with unreliable server and delayed repairs. Int. J. Math. Oper. Res. (2021). DOI: . | DOI | MR
[21] , The regulation of queue size by levying tolls. Econ.: J Econ. Soc. 37 (1969) 15–24. | Zbl
[22] , and , Equilibrium behaviour and social optimization in Markovian queues with impatient customers and variant of working vacations. RAIRO-Oper. Res. 51 (2017) 685–707. | MR | Zbl | Numdam | DOI
[23] , Equilibrium strategies in the almost unobservable queues with catastrophes and repairs. In: Chinese Control Conference (CCC). IEEE (2019 (2019) 1321–1326. | DOI
[24] and , Analysis of equilibrium strategies in Markovian queues with negative customers and working breakdowns. IEEE Access 7 (2019) 159868–159878. | DOI
[25] and , Optimal strategies and pricing analysis in queues with a single working vacation and multiple vacations. RAIRO-Oper. Res. 54 (2020) 1593–1612. | MR | Numdam | DOI
[26] and , Equilibrium analysis of the observable queues with balking and delayed repairs. Appl. Math. Comput. 218 (2011) 2716–2729. | MR | Zbl | DOI
[27] and , Monopoly pricing in a retrial queue with delayed vacations for local area network applications. IMA J. Manage. Math. 27 (2016) 315–334. | MR
[28] , and , Equilibrium strategies of the unobservable queue with balking and delayed repairs. Appl. Math. Comput. 290 (2016) 56–65. | MR | DOI
[29] , and , Strategic behavior in the partially observable Markovian queues with partial breakdowns. Oper. Res. Lett. 45 (2017) 471–474. | MR | DOI
[30] , and , Optimal balking strategies in the M/M/1 queue with multi-phase failures and repairs. Oper. Res. 19 (2019) 435–447.
[31] , Strategic behavior in the constant retrial queue with a single vacation. RAIRO-Oper. Res. 54 (2020) 569–583. | MR | Zbl | Numdam | DOI
[32] and , Strategic joining and information disclosing in Markovian queues with an unreliable server and working vacations. Qual. Technol. Quant. Manage. 18 (2021) 298–325. | DOI
[33] and , Equilibrium customer strategies in Markovian queues with setup times and partial failures. J. Syst. Sci. Complexity 33 (2020) 1163–1178. | MR | DOI
[34] , and , Customers’ strategic behavior in batch arrivals queue. Eur. J. Oper. Res. 247 (2015) 895–903. | MR | DOI
[35] , and , Equilibrium behavioural strategies in an queue. Int. J. Math. Oper. Res. 13 (2018) 377–400. | MR | DOI
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