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Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and N-policy

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Abstract

In this paper, equilibrium strategies and optimal balking strategies of customers in a constant retrial queue with multiple vacations and the N-policy under two information levels, respectively, are investigated. We assume that there is no waiting area in front of the server and an arriving customer is served immediately if the server is idle; otherwise (the server is either busy or on a vacation) it has to leave the system to join a virtual retrial orbit waiting for retrials according to the FCFS rules. After a service completion, if the system is not empty, the server becomes idle, available for serving the next customer, either a new arrival or a retried customer from the virtual retrial orbit; otherwise (if the system is empty), the server starts a vacation. Upon the completion of a vacation, the server is reactivated only if it finds at least N customers in the virtual orbit; otherwise, the server continues another vacation. We study this model at two levels of information, respectively. For each level of information, we obtain both equilibrium and optimal balking strategies of customers, and make corresponding numerical comparisons. Through Particle Swarm Optimization (PSO) algorithm, we explore the impact of parameters on the equilibrium and social optimal thresholds, and obtain the trend in changes, as a function of system parameters, for the optimal social welfare, which provides guiding significance for social planners. Finally, by comparing the social welfare under two information levels, we find that whether the system information should be disclosed to customers depends on how to maintain the growth of social welfare.

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References

  • Balachandran K (1973) Control policies for a single server system. Manag Sci 19(9):1013–1018

    Article  MathSciNet  Google Scholar 

  • Burnetas A, Economou A (2007) Equilibrium customer strategies in a single server Markovian queue with setup times. Queueing Syst 56(3–4):213–228

    Article  MathSciNet  Google Scholar 

  • Chen H, Frank MZ (2001) State dependent pricing with a queue. IIE Trans 33(10):847–860

    Google Scholar 

  • Doshi B (1986) Queueing systems with vacations—a survey. Queueing Syst 1(1):29–66

    Article  MathSciNet  Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science MHS’95, pp 39–43

  • Economou A, Kanta S (2008) Equilibrium balking strategies in the observable single-server queue with breakdowns and repairs. Oper Res Lett 36(6):696–699

    Article  MathSciNet  Google Scholar 

  • Economou A, Kanta S (2011) Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue. Nav Res Logist 58(2):107–122

    Article  MathSciNet  Google Scholar 

  • Edelson NM, Hilderbrand DK (1975) Congestion tolls for Poisson queuing processes. Econometrica 43(1):81–92

    Article  MathSciNet  Google Scholar 

  • Guo P, Hassin R (2011) Strategic behavior and social optimization in Markovian vacation queues. Oper Res 59(4):986–997

    Article  MathSciNet  Google Scholar 

  • Guo P, Hassin R (2012) Strategic behavior and social optimization in Markovian vacation queues: the case of heterogeneous customers. Eur J Oper Res 222(2):278–286

    Article  MathSciNet  Google Scholar 

  • Guo P, Li Q (2013) Strategic behavior and social optimization in partially-observable Markovian vacation queues. Oper Res Lett 41(3):277–284

    Article  MathSciNet  Google Scholar 

  • Hassin R, Haviv M (2003) To queue or not to queue: equilibrium behavior in queueing systems. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  • Johansen SG, Stidham S (1980) Control of arrivals to a stochastic input–output system. Adv Appl Probab 12(4):972–999

    Article  MathSciNet  Google Scholar 

  • Kulkarni VG (1983) A game theoretic model for two types of customers competing for service. Oper Res Lett 2(3):119–122

    Article  MathSciNet  Google Scholar 

  • Kumar BK, Vijayalakshmi G, Krishnamoorthy A, Basha SS (2010) A single server feedback retrial queue with collisions. Comput Oper Res 37(7):1247–1255

    Article  MathSciNet  Google Scholar 

  • Liu W, Ma Y, Li J (2012) Equilibrium threshold strategies in observable queueing systems under single vacation policy. Appl Math Model 36(12):6186–6202

    Article  MathSciNet  Google Scholar 

  • Ma Y, Liu W, Li J (2013) Equilibrium balking behavior in the Geo/Geo/1 queueing system with multiple vacations. Appl Math Model 37(6):3861–3878

    Article  MathSciNet  Google Scholar 

  • Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24

    Article  Google Scholar 

  • Neuts MF (1981) Matrix-geometric solutions in stochastic models. Johns Hopkins University Press, Baltimore

    MATH  Google Scholar 

  • Shanthikumar J (1981) Optimal control of an M/G/1 priority queue via N-control. Am J Math Manag Sci 1(3):191–212

    MathSciNet  MATH  Google Scholar 

  • Stidham S (1985) Optimal control of admission to a queueing system. IEEE Trans Autom Control 30(8):705–713

    Article  MathSciNet  Google Scholar 

  • Sun W, Li S, Cheng-Guo E (2016) Equilibrium and optimal balking strategies of customers in Markovian queues with multiple vacations and N-policy. Appl Math Model 40(1):284–301

    Article  MathSciNet  Google Scholar 

  • Sun W, Li S, Tian N (2017) Equilibrium and optimal balking strategies of customers in unobservable queues with double adaptive working vacations. Qual Technol Quant Manag 14(1):94–113

    Article  Google Scholar 

  • Wang J, Zhang F (2013) Strategic joining in M/M/1 retrial queues. Eur J Oper Res 230(1):76–87

    Article  MathSciNet  Google Scholar 

  • Wang J, Zhang X, Huang P (2017) Strategic behavior and social optimization in a constant retrial queue with the N-policy. Eur J Oper Res 256(3):841–849

    Article  MathSciNet  Google Scholar 

  • Yadin M, Naor P (1963) Queueing systems with a removable service station. J Oper Res Soc 14(4):393–405

    Article  Google Scholar 

  • Zhang F, Wang J, Liu B (2012) On the optimal and equilibrium retrial rates in an unreliable retrial queue with vacations. J Ind Manag Optim 8(4):861–875

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

We are grateful to the anonymous reviewers and editors for their constructive comments and feedback that help us to improve the presentation and quality of this manuscript. This work was supported in part by The National Natural Science Foundation of China (No. 61773014), the Research Fund for the Postgraduate Research and Practice Innovation Program of Jiangsu Province (No. KYCX20_0240), and the Natural Sciences and Engineering Research Council of Canada (No. 315660).

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Authors and Affiliations

  1. School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, Guangxi, China

    Zhen Wang

  2. School of Science, Nanjing University of Science and Technology, Nanjing, 210094, Jiangsu, China

    Liwei Liu

  3. School of Mathematics and Statistics, Carleton University, 1125 Colonel By Drive, Ottawa, ON, K1S 5B6, Canada

    Yiqiang Q. Zhao

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  1. Zhen Wang
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  2. Liwei Liu
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  3. Yiqiang Q. Zhao
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Correspondence to Zhen Wang or Liwei Liu.

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Wang, Z., Liu, L. & Zhao, Y.Q. Equilibrium customer and socially optimal balking strategies in a constant retrial queue with multiple vacations and N-policy. J Comb Optim 43, 870–908 (2022). https://doi.org/10.1007/s10878-021-00814-1

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  • DOI: https://doi.org/10.1007/s10878-021-00814-1

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