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July  2015, 11(3): 715-731. doi: 10.3934/jimo.2015.11.715

Optimal balking strategies in an M/G/1 queueing system with a removable server under N-policy

1. 

College of Science, Yanshan University, Qinhuangdao, 066004, China, China

2. 

Department of Intelligence and Informatics, Konan University, Kobe 658-8501

Received  February 2013 Revised  June 2014 Published  October 2014

In this paper, we consider the balking behavior of customers in an M/G/1 queueing system with a removable server under N-policy, where the server may be turned off when no customers are present, and be turned on when the queue length reaches size $N$. Arriving customers decide whether to join the system or balk, based on a linear reward-cost structure that incorporates their desire for service, as well as their unwillingness for waiting. For the unobservable and partially observable queues, we first analyze the stationary behavior of the system; then derive the equilibrium mixed strategies and compare them to the socially optimal strategies. We take the number $N$ as a decision variable and discuss the optimal operations policy in equilibrium states. Finally, we present two examples to demonstrate some of the phenomena in the considered models.
Citation: Ruiling Tian, Dequan Yue, Wuyi Yue. Optimal balking strategies in an M/G/1 queueing system with a removable server under N-policy. Journal of Industrial & Management Optimization, 2015, 11 (3) : 715-731. doi: 10.3934/jimo.2015.11.715
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show all references

References:
[1]

Queueing Systems, 56 (2007), 213-228. doi: 10.1007/s11134-007-9036-7.  Google Scholar

[2]

Performance Evaluation, 68 (2011), 967-982. doi: 10.1016/j.peva.2011.07.001.  Google Scholar

[3]

Econometrica, 43 (1975), 81-92. doi: 10.2307/1913415.  Google Scholar

[4]

Operations Research Letters, 36 (2008), 696-699. doi: 10.1016/j.orl.2008.06.006.  Google Scholar

[5]

Queueing Systems, 59 (2008), 237-269. doi: 10.1007/s11134-008-9083-8.  Google Scholar

[6]

Operations Research, 59 (2011), 986-997. doi: 10.1287/opre.1100.0907.  Google Scholar

[7]

European Journal of Operational Research, 222 (2012), 278-286. doi: 10.1016/j.ejor.2012.05.026.  Google Scholar

[8]

Operations Research Letters, 41 (2013), 277-284. doi: 10.1016/j.orl.2013.02.005.  Google Scholar

[9]

Management Science, 53 (2007), 962-970. doi: 10.1287/mnsc.1060.0686.  Google Scholar

[10]

Kluwer Academic Publishers, Boston, 2003. doi: 10.1007/978-1-4615-0359-0.  Google Scholar

[11]

Queueing Systems, 55 (2007), 239-249. doi: 10.1007/s11134-007-9020-2.  Google Scholar

[12]

Games and Economic Behavior, 71 (2011), 521-526. doi: 10.1016/j.geb.2010.06.002.  Google Scholar

[13]

Computers & Industrial Engineering, 66 (2013), 751-757. doi: 10.1016/j.cie.2013.09.023.  Google Scholar

[14]

Econometrica, 37 (1969), 15-24. doi: 10.2307/1909200.  Google Scholar

[15]

Games and Economic Behavior, 59 (2007), 345-363. doi: 10.1016/j.geb.2006.08.008.  Google Scholar

[16]

Journal of Computational Information Systems, 4 (2008), 2167-2172. Google Scholar

[17]

North-Holland, Amsterdam, 1991.  Google Scholar

[18]

Springer, New York, 2006.  Google Scholar

[19]

Journal of Information and Computational Science, 9 (2012), 2827-2841. Google Scholar

[20]

Journal of Industrial and Management Optimization, 9 (2013), 901-917. doi: 10.3934/jimo.2013.9.901.  Google Scholar

[21]

Applied Mathematical Modelling, 37 (2013), 8264-8282. doi: 10.1016/j.apm.2013.03.049.  Google Scholar

[22]

Journal of Industrial and Management Optimization, 8 (2012), 861-875. doi: 10.3934/jimo.2012.8.861.  Google Scholar

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