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Analysis of G-Queue with Pseudo-Fault and Multiple Working Vacations

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Abstract

This paper presents a new model of discrete time Geo/Geo/1 repairable queueing system with pseudo-fault, negative customers and multiple working vacations. The authors assume that system service may be interrupted by breakdown or pseudo-fault, this system may become disabled only when it is in a regular busy period, and negative customers adopt two types of typical killing strategies. In this paper, the authors know that the evolution of the system can be described by a two-dimensional Markov chain, and the two-dimensional Markov chain satisfies the condition of quasi birth and death chains. Based on the method of matrix-geometric solution, the authors obtain distributions for the stationary queue length in RCH and RCE strategy, respectively. Moreover, the reliability of the system is analyzed and the number of customers and waiting time of a customer in the system in steady state are obtained. The authors analyze the impact of two killing strategies on the system comparatively. This paper studies the individually and socially optimal behaviors of positive customers, and presents a pricing policy for positive customers, therefore, the authors obtain the socially optimal arrival rate. Various numerical results are provided to show the change of performance measures.

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References

  1. Meisling T, Discrete time queueing theory, Operations Research, 1958, 6: 96–105.

    MathSciNet  MATH  Google Scholar 

  2. Alfa A S, Discrete time queues and matrix-analytic method, Top, 2002, 10(2): 147–185.

    MathSciNet  MATH  Google Scholar 

  3. Zhang Z G and Tian N S, Discrete time Geo/G/1 queue with multiple adaptive vacations, Queueing Systems, 2001, 38(4): 419–429.

    MathSciNet  MATH  Google Scholar 

  4. Sokol N and Scoppola B, Discrete time GI/Geom/1 queueing system with priority, European Journal of Operational Research, 2008, 189(3): 1403–1408.

    MathSciNet  MATH  Google Scholar 

  5. Kalidass K and Kasturi R, A queue with working breakdowns, Computers & Industrial Engineering, 2012, 63(4): 779–783.

    Google Scholar 

  6. Goswami V and Samanta S K, Discrete-time bulk-service queue with two heterogeneous servers, Computers & Industrial Engineering, 2009, 56(4): 1348–1356.

    Google Scholar 

  7. Yu M M, Tang Y H, and Chen S L, Reliability analysis of discrete time two-unit parallel repairable system with single vacation, Journal of System Science and Mathematical Science, 2009, 29(5): 617–629.

    MathSciNet  MATH  Google Scholar 

  8. Atencia I, A discrete-time queueing system with server breakdowns and changes in the repair times, Annals of Operations Research, 2015, 235(1): 37–49.

    MathSciNet  MATH  Google Scholar 

  9. Chaudhry M, Banik A, and Pacheco A, A simple analysis of the batch arrival queue with infinite-buffer and Markovian service process using roots method: GI[X]/C-MSP/1/∞, Article Annals of Operations Research, 2017, 252(1): 135–173.

    MathSciNet  MATH  Google Scholar 

  10. Gelenbe E, Random neural networks with negative and positive signals and product form solution, Neural Computation, 1989, 1(4): 502–510.

    Google Scholar 

  11. Gelenbe E, Product-form queueing networks with negative and positive customers, Journal of Applied Probability, 1991, 28(3): 656–663.

    MathSciNet  MATH  Google Scholar 

  12. Gelenbe E, G-networks with signals and batch removal, Probability in the Engineering and Informotional Sciences, 1993, 7(3): 335–342.

    Google Scholar 

  13. Atencia I and Moreno P, The discrete-time Geo/Geo/1 queue with negative customers and disasters, Computers & Operations Research, 2004, 31(9): 1537–1548.

    MATH  Google Scholar 

  14. Atencia I and Moreno P, A single-server G-queue in discrete-time with geometrical arrival and service process, Performance Evaluation, 2005, 59(1): 85–97.

    Google Scholar 

  15. Ma L, A class of Geom/Geom/1 discrete-time queueing system with negative customers, International Journal of Nonlinear Science, 2008, 5(3): 275–280.

    MathSciNet  MATH  Google Scholar 

  16. Lee D H, Yang W S, and Park H M, Geo/G/1 queues with disasters and general repair times, Applied Mathematical Modelling, 2011, 35(4): 1561–1570.

    MathSciNet  MATH  Google Scholar 

  17. Wang J, Huang Y, and Do T V, A single-server discrete-time queue with correlated positive and negative customer arrivals, Applied Mathematical Modelling, 2013, 37(9): 6212–6224.

    MathSciNet  MATH  Google Scholar 

  18. Choudhury G and Tadj L, An M/G/1 queue with two phases of service subject to the server breakdown and delayed repair, Applied Mathematical Modelling, 2009, 33(6): 2699–2709.

    MathSciNet  MATH  Google Scholar 

  19. Ma Z, Guo Y, Wang P, et al., The Geo/Geo/1+1 queueing system with negative customers, Mathematical Problems in Engineering, 2013, 2013: 1–8.

    MathSciNet  MATH  Google Scholar 

  20. Dimitriou I, A mixed priority retrial queue with negative arrivals, unreliable server and multiple vacations, Applied Mathematical Modelling, 2013, 37(3): 1295–1309.

    MathSciNet  MATH  Google Scholar 

  21. Wu J and Lian Z, A single-server retrial G-queue with priority and unreliable server under bernoulli vacation schedule, Computers & Industrial Engineering, 2013, 64(1): 84–93.

    Google Scholar 

  22. Chae K C, Park H M, and Yang W S, A GI/Geo/1 queue with negative and positive customers, Applied Mathematical Modelling, 2010, 34(6): 1662–1671.

    MathSciNet  MATH  Google Scholar 

  23. Servi L D and Finn S G, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, 2002, 50(1): 41–52.

    Google Scholar 

  24. Baba Y, Analysis of a GI/Geom/1 queue with multiple working vacations, Operations Research Letters, 2005, 33(2): 201–209.

    MathSciNet  MATH  Google Scholar 

  25. Wu D A and Takagi H, M/G/1 queue with multiple working vacations, Performance Evaluation, 2006, 63(7): 654–681.

    Google Scholar 

  26. Yu M and Alfa A, A simple method to obtain the stochastic decomposition structure of the busy period in Geo/Geo/1/N vacation queue, 4 OR — A Quarterly Journal of Operations Research, 2015, 13(4): 361–380.

    MathSciNet  MATH  Google Scholar 

  27. Sun W, Wang Y, and Tian N, Pricing and setup/closedown policies in unobservable queues with strategic customers, 4OR — A Quarterly Journal of Operations Research, 2012, 10(3): 287–311.

    MathSciNet  MATH  Google Scholar 

  28. Ma Z, Wang P, Cui G, et al., The discrete time Geom/Geom/1 repairable queuing system with pseudo-fault and multiple vacations, Journal of Information & Computational Science, 2014, 11(13): 4667–4678.

    Google Scholar 

  29. Papatheou E, Manson G, Barthorpe R J, et al., The use of pseudo-faults for novelty detection in SHM, Journal of Sound and Vibration, 2010, 329(12): 2349–2366.

    Google Scholar 

  30. Hunter J J, Mathematical Techniques of Applied Probability Discrete Time Models: Techniques and Applications, Vol. 2, Academic Press, New York, 1983.

    MATH  Google Scholar 

  31. Gravey A and Hebuterne G, Simultaneity in discrete-time single server queues with Bernoulli inputs, Performance Evaluation, 1992, 14(2): 123–131.

    MathSciNet  MATH  Google Scholar 

  32. Tian N, Xu X, and Ma Z, Discrete Time Queueing Theory, Science Publishers, Beijing, 2008 (in Chinese).

    Google Scholar 

  33. Latouche G and Ramaswami V, Introduction to Matrix Analytic Methods in Stochastic Modeling, Society for Industrial & Applied Mathematics, Philadelphia, 1999.

    MATH  Google Scholar 

  34. Neuts M F, Matrix-Geometric Solutions in Stochastic Models, The Johns Hopkins University Press, Baltimore and London, 1981.

    MATH  Google Scholar 

  35. Hassin R and Haviv M, To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems, Kluwer Academic Publishers, Boston, 2003.

    MATH  Google Scholar 

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Authors and Affiliations

  1. School of Science, Yanshan University, Qinhuangdao, 066004, China

    Zhanyou Ma

  2. LiRen College, Yanshan University, Qinhuangdao, 066004, China

    Li Chen

  3. School of Transportation Science and Engineering, Beihang University, Beijing, 100000, China

    Pengcheng Wang

Authors
  1. Zhanyou Ma
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  2. Li Chen
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  3. Pengcheng Wang
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Corresponding author

Correspondence to Zhanyou Ma.

Additional information

This paper was supported by the National Natural Science Foundation of China under Grant Nos. 61973261, 61872311, the Natural Science Foundation of Hebei Province under Grant No. A2018203088, Key Foundation of Higher Education Science and Technology Research of Hebei Province under Grant No. ZD2017079.

This paper was recommended for publication by Editor WANG Shouyang.

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Ma, Z., Chen, L. & Wang, P. Analysis of G-Queue with Pseudo-Fault and Multiple Working Vacations. J Syst Sci Complex 33, 1144–1162 (2020). https://doi.org/10.1007/s11424-020-8117-0

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  • DOI: https://doi.org/10.1007/s11424-020-8117-0

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