Abstract
This paper studies the equilibrium behavior of customers in the M/M/1 queue with setup times, breakdowns and repairs. The server is turned off whenever the system is empty. Once a customer arrives to an empty system, the server begins an exponential setup time to start service again. The lifetime of the server is assumed to be exponentially distributed and once the server breaks down, it will be sent for repair immediately, and the repair time is also exponentially distributed. We consider separately the equilibrium threshold strategies for the fully observable case and mixed strategies for the partially observable and fully unobservable cases. Some numerical examples are presented to illustrate the effect of the information levels and several parameters on the customers’ equilibrium and optimal strategies.
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References
Allahverdi A, Ng CT, Cheng TE, Kovalyov MY (2008) A survey of scheduling problems with setup times or costs. Eur J Oper Res 187(3):985–1032
Bischof W (2001) Analysis of M/G/1 queues with setup times and vacations under six different service disciplines. Queueing Syst 39:265–301
Boudali O, Economou A (2012) Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes. Eur J Oper Res 218:708–715
Burnetas A, Economou A (2007) Equilibrium customer strategies in a single server Markovian queue with setup times. Queueing Syst 56:213–228
Chen H, Frank M (2004) Monopoly pricing when customers queue. IIE Trans 36:569–581
Choudhury G (2000) An M X/G/1 queueing system with a setup period and a vacation period. Queueing Syst 36:23–38
Economou A, Kanta S (2008) Equilibrium balking strategies in the observable single server queue with breakdowns and repairs. Oper Res Lett 36:696–699
Economou A, Kanta S (2011) Equilibrium customer strategies and social-profit maximization in the single-server constant retrial queue. Naval Res Logist 58(2):107–122
Edelson NM, Hildebrand K (1975) Congestion tolls for Poisson queueing processes. Econometrica 43:81–92
Hassin R, Haviv M (2003) To queue or not to queue: equilibrium behavior in queueing systems. Kluwer Academic, Boston
Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37:15–24
Reddy GV, Nadarajan R, Arumuganathan R (1998) Analysis of a bulk queue with N-policy multiple vacations and setup times. Comput Oper Res 25(8):957–967
Wang J, Cao J, Li Q (2001) Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Syst 38(2):363–380
Zhang F, Zhu Z (2013) A discrete-time unreliable Geo/G/1 retrial queue with balking customers, second optional service, and general retrial times. Math Probl Eng 2013:1–12, Art ID 832318
Zhang Z, Wang J, Zhang F (2014) Equilibrium customer strategies in the single server constant retrial queue with breakdowns and repairs. Math Probl Eng 2014:1–14, Art ID 379572
Acknowledgments
The authors would like to thank the anonymous referees for their valuable comments and suggestions which are very helpful for us to improve the presentation of the paper. This research is partially supported by NSFC (71371075, 71090403, 71271089), NSFA (KJ2013B162, KJ2014A174), FSYT (2011195). It is also supported by the ISCISI of South China University of Technology and Chaohu University Scientific Research Fund.
Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
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Chen, P., Zhou, Y. Equilibrium balking strategies in the single server queue with setup times and breakdowns. Oper Res Int J 15, 213–231 (2015). https://doi.org/10.1007/s12351-015-0174-0
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DOI: https://doi.org/10.1007/s12351-015-0174-0