Equilibrium joining strategies in the single-server constant retrial queues with Bernoulli vacations

Sun, Ke; Wang, Jinting

doi:10.1051/ro/2019087

Sun, Ke ; Wang, Jinting

RAIRO. Operations Research, Tome 55 (2021), pp. S481-S502

Résumé

We consider the equilibrium joining strategies in an M/M/1 constant retrial queue with Bernoulli vacations. There is no buffer in front of the server, thus an arriving customer will be served immediately if the server is available, and blocked ones wait in a queue if the server is busy or under vacation. The queue length information of orbit is observable to customers upon their arrivals. Then, blocked customers decide whether to join the orbit or not based on a reward-cost structure and their information level. After completing service, the server begins a vacation or remains available and it becomes available again when a vacation ends. The available server seeks to serve the customer in the head of the orbit queue. During the seeking process, an external arrival can interrupt it and obtain service. Our goal is to explore equilibrium behavior of customers in two information cases, fully observable case and almost observable case, which corresponding to whether blocked arrivals can differentiate the state of unavailable server. We obtain the threshold strategies of blocked customers in two information cases and provide numerical experiments to characterize the influence of different parameters on the equilibrium joining strategies.

MR Zbl

DOI : 10.1051/ro/2019087

Classification : 60K25, 90B22, 91A13
Keywords: Queueing, constant retrial rate, Bernoulli vacations, Nash equilibrium, threshold strategies, partial information

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     author = {Sun, Ke and Wang, Jinting},
     title = {Equilibrium joining strategies in the single-server constant retrial queues with {Bernoulli} vacations},
     journal = {RAIRO. Operations Research},
     pages = {S481--S502},
     year = {2021},
     publisher = {EDP-Sciences},
     volume = {55},
     doi = {10.1051/ro/2019087},
     mrnumber = {4223094},
     zbl = {1469.60293},
     language = {en},
     url = {https://www.numdam.org/articles/10.1051/ro/2019087/}
}

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Sun, Ke; Wang, Jinting. Equilibrium joining strategies in the single-server constant retrial queues with Bernoulli vacations. RAIRO. Operations Research, Tome 55 (2021), pp. S481-S502. doi: 10.1051/ro/2019087

Bibliographie
Cité par

J. R. Artalejo, A. Gómez-Corral and M. F. Neuts, Analysis of multiserver queues with constant retrial rate. Eur. J. Oper. Res. 135 (2001) 569–581. | MR | Zbl | DOI

K. Avrachenkov and U. Yechiali, Retrial networks with finite buffers and their application to internet data traffic. Prob. Eng. Inf. Sci. 22 (2008) 519–536. | MR | Zbl | DOI

K. Avrachenkov and U. Yechiali, On tandem blocking queues with a common retrial queue. Comput. Oper. Res. 37 (2010) 1174–1180. | MR | Zbl | DOI

A. Burnetas and A. Economou, Equilibrium customer strategies in a single server Markovian queue with setup times. Queueing Syst. 56 (2007) 213–228. | MR | Zbl | DOI

J. W. Cohen, Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommun. Rev. 18 (1957) 49–100.

A. Economou and S. Kanta, Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper. Res. Lett. 36 (1957) 696–699. | MR | Zbl | DOI

A. Economou and S. Kanta, Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue. Naval Res. Logist. 58 (2011) 107–122. | MR | Zbl | DOI

N. M. Edelson and K. Hildebrand, Congestion tolls for Poisson queuing processes. Econometrica 43 (1975) 81–92. | MR | Zbl | DOI

G. Falin, A survey of retrial queues. Queueing Syst. 7 (1990) 127–167. | MR | Zbl | DOI

G. I. Falin and J. G. Templeton, Retrial Queues. Chapman and Hall, London (1997). | Zbl

G. Fayolle, A simple telephone exchange with delayed feedbacks. Proceeding of the International Seminar on Teletraffic Analysis and Computer Performance Evaluation, Amsterdam (1986) 245–253.

R. Hassin, Rational Queueing. Chapman & Hall/CRC Series in Operations Research (2016). | MR | Zbl | DOI

R. Hassin and M. Haviv, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems. Kluwer Academic Publishers, Netherlands (2003). | MR | Zbl | DOI

J. Keilson and L. D. Servi, Oscillating random walk models for $G I / G / 1$ vacation systems with Bernoulli schedules. J. Appl. Prob. 23 (1986) 790–802. | MR | Zbl | DOI

B. K. Kumar and D. Arivudainambi, The $M / G / 1$ retrial queue with Bernoulli schedules and general retrial times. Comput. Math. Appl. 43 (2002) 15–30. | MR | Zbl | DOI

B. K. Kumar and S. P. Madheswari, Analysis of an $M / M / N$ queue with Bernoulli service schedule. Int. J. Oper. Res. 5 (2009) 48–72. | Zbl | DOI

B. K. Kumar, D. Arivudainambi and A. Vijayakumar, On the $M^{(x)} / G / 1$ retrial queue with Bernoulli schedules and general retrial times. Asia-Pac. J. Oper. Res. 19 (2002) 177. | MR | Zbl

B. K. Kumar, R. Rukmani and V. Thangaraj, An $M / M / C$ retrial queueing system with Bernoulli vacations. J. Syst. Sci. Syst. Eng. 18 (2009) 222. | DOI

B. K. Kumar, R. Rukmani and S. A. Lakshmi, Performance analysis of an $M / G / 1$ queueing system under Bernoulli vacation schedules with server setup and close down periods. Comput. Ind. Eng. 66 (2013) 1–9. | DOI

V. G. Kulkarni, A game theoretic model for two types of customer’s competing for service. Oper. Res. Lett. 2 (1983) 119–122. | MR | Zbl | DOI

T. Li, L. Zhang and S. Gao, An $M / G / 1$ retrial queue with balking customers and Bernoulli working vacation interruption. Qual. Technol. Quant. Manage. 16 (2018) 511–530. | DOI

J. Liu and J. Wang, Strategic joining rules in a single server Markovian queue with Bernoulli vacation. Oper. Res. 17 (2017) 413–434.

M. Martin and J. Artalejo, Analysis of an $M / G / 1$ queue with two types of impatient units. Adv. Appl. Prob. 27 (1995) 840–861. | MR | Zbl | DOI

P. Naor, The regulation of queue size by levying tolls. Econometrica 37 (1969) 15–24. | Zbl | DOI

N. Tian and Z. G. Zhang, Vacation Queueing Models: Theory and Applications. Springer Science & Business Media 93 (2006). | MR | Zbl

J. Wang and F. Zhang, Strategic joining in $M / M / 1$ retrial queues. Eur. J. Oper. Res. 37 (2013) 76–87. | MR | Zbl | DOI

F. Wang, J. Wang and F. Zhang, Strategic behavior in the single-server constant retrial queue with individual removal. Qual. Technol. Quant. Manage. 12 (2015) 325–342. | DOI

J. Wang, X. Zhang and P. Huang, Strategic behavior and social optimization in the constant retrial queue with $N$ -policy. Eur. J. Oper. Res. 256 (2017) 841–849. | MR | Zbl | DOI

Z. Zhang, J. Wang and F. Zhang, Equilibrium customer strategies in the single-server constant retrial queue with breakdowns and repairs. Math. Probl. Eng. 2014 (2014) 379572. | MR | Zbl | DOI

W. Zhou, Analysis of a single-server retrial queue with FCFS orbit and Bernoulli vacation. Appl. Math. Comput. 161 (2005) 353–364. | MR | Zbl

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