American Institute of Mathematical Sciences

Advanced
  • Previous Article
    An inexact semismooth Newton method for variational inequality with symmetric cone constraints
  • JIMO Home
  • This Issue
  • Next Article
    Levitin-Polyak well-posedness of a system of generalized vector variational inequality problems
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

Ruiling Tian 1, , Dequan Yue 1, and  Wuyi Yue 2,

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.
Keywords: Queuing system, socially optimal strategy., equilibrium strategy, optimization, balking behavior.
Mathematics Subject Classification: Primary: 60K25; Secondary: 90B2.
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
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

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

[1]

Xiaoyi Zhou, Tong Ye, Tony T. Lee. Designing and analysis of a Wi-Fi data offloading strategy catering for the preference of mobile users. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021038
[2]

Kai Kang, Taotao Lu, Jing Zhang. Financing strategy selection and coordination considering risk aversion in a capital-constrained supply chain. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021042
[3]

Wei Wang, Yang Shen, Linyi Qian, Zhixin Yang. Hedging strategy for unit-linked life insurance contracts with self-exciting jump clustering. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021072
[4]

Sarra Delladji, Mohammed Belloufi, Badreddine Sellami. Behavior of the combination of PRP and HZ methods for unconstrained optimization. Numerical Algebra, Control & Optimization, 2021, 11 (3) : 377-389. doi: 10.3934/naco.2020032
[5]

Eduardo Casas, Christian Clason, Arnd Rösch. Preface special issue on system modeling and optimization. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021008
[6]

M. Grasselli, V. Pata. Asymptotic behavior of a parabolic-hyperbolic system. Communications on Pure & Applied Analysis, 2004, 3 (4) : 849-881. doi: 10.3934/cpaa.2004.3.849
[7]

Luke Finlay, Vladimir Gaitsgory, Ivan Lebedev. Linear programming solutions of periodic optimization problems: approximation of the optimal control. Journal of Industrial & Management Optimization, 2007, 3 (2) : 399-413. doi: 10.3934/jimo.2007.3.399
[8]

Amira Khelifa, Yacine Halim. Global behavior of P-dimensional difference equations system. Electronic Research Archive, , () : -. doi: 10.3934/era.2021029
[9]

Shoufeng Ji, Jinhuan Tang, Minghe Sun, Rongjuan Luo. Multi-objective optimization for a combined location-routing-inventory system considering carbon-capped differences. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021051
[10]

Wenjuan Zhao, Shunfu Jin, Wuyi Yue. A stochastic model and social optimization of a blockchain system based on a general limited batch service queue. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1845-1861. doi: 10.3934/jimo.2020049
[11]

Xianbang Chen, Yang Liu, Bin Li. Adjustable robust optimization in enabling optimal day-ahead economic dispatch of CCHP-MG considering uncertainties of wind-solar power and electric vehicle. Journal of Industrial & Management Optimization, 2021, 17 (4) : 1639-1661. doi: 10.3934/jimo.2020038
[12]

Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021  doi: 10.3934/mcrf.2021014
[13]

Sumon Sarkar, Bibhas C. Giri. Optimal lot-sizing policy for a failure prone production system with investment in process quality improvement and lead time variance reduction. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021048
[14]

Kehan Si, Zhenda Xu, Ka Fai Cedric Yiu, Xun Li. Open-loop solvability for mean-field stochastic linear quadratic optimal control problems of Markov regime-switching system. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021074
[15]

Junichi Minagawa. On the uniqueness of Nash equilibrium in strategic-form games. Journal of Dynamics & Games, 2020, 7 (2) : 97-104. doi: 10.3934/jdg.2020006
[16]

Simone Calogero, Juan Calvo, Óscar Sánchez, Juan Soler. Dispersive behavior in galactic dynamics. Discrete & Continuous Dynamical Systems - B, 2010, 14 (1) : 1-16. doi: 10.3934/dcdsb.2010.14.1
[17]

Enkhbat Rentsen, Battur Gompil. Generalized Nash equilibrium problem based on malfatti's problem. Numerical Algebra, Control & Optimization, 2021, 11 (2) : 209-220. doi: 10.3934/naco.2020022
[18]

Liangliang Ma. Stability of hydrostatic equilibrium to the 2D fractional Boussinesq equations. Discrete & Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021068
[19]

Suzete Maria Afonso, Vanessa Ramos, Jaqueline Siqueira. Equilibrium states for non-uniformly hyperbolic systems: Statistical properties and analyticity. Discrete & Continuous Dynamical Systems, 2021  doi: 10.3934/dcds.2021045
[20]

Anderson L. A. de Araujo, Marcelo Montenegro. Existence of solution and asymptotic behavior for a class of parabolic equations. Communications on Pure & Applied Analysis, 2021, 20 (3) : 1213-1227. doi: 10.3934/cpaa.2021017

2019 Impact Factor: 1.366

Tools

Metrics

  • PDF downloads (78)
  • HTML views (0)
  • Cited by (6)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences