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Approximate analysis of a queueing–inventory system with early and delayed server vacations

  • Stochastic Systems
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Abstract

We propose a model for a servicing system with perishable inventory and a finite queue of impatient claims where the server can be in one of three states: operational, early and delaying vacations. We develop a method for approximate computation of the system’s characteristics. We show results of numerical experiments.

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References

  1. Krishnamoorthy, A., Lakshmy, B., and Manikandan, R., A Survey on Inventory Models with Positive Service Time, OPSEARCH, 2011, vol. 48, no. 2, pp. 153–169.

    Article  MathSciNet  Google Scholar 

  2. Doshi, B.T., Queueing Systems with Vacations: A Survey, Queueing Syst., 1986, vol. 1, no. 1, pp. 29–66.

    Article  MathSciNet  MATH  Google Scholar 

  3. Tian, N. and Zhang, Z.G., Vacation Queueing Models, Heidelberg: Springer, 2006.

    Book  MATH  Google Scholar 

  4. Ke, J.C., Wu, C.H., and Zhang, Z.G., Recent Developments in Vacation Queueing Models, Int. J. Oper. Res., 2010, vol. 7, no. 4, pp. 3–8.

    Google Scholar 

  5. Daniel, J.K. and Ramanarayanan, R., An (s, S)-Inventory System with Two Servers and Rest Periods to the Server, Naval Res. Logistics, 1988, vol. 35, pp. 119–123.

    Article  MathSciNet  MATH  Google Scholar 

  6. Narayanan, V.C., Deepak, T.G., Krishnamoorthy, A., et al., On an (s, S)-Inventory Policy with Service Time, Vacation to Server and Correlated Lead Time, Quality Technol. Quantit. Manage., 2008, vol. 5, pp. 129–143.

    Article  MathSciNet  Google Scholar 

  7. Sivakumar, B., An Inventory System with Retrial Demands and Multiple Server Vacations, Quality Technol. Quantit. Manage., 2011, vol. 8, pp. 125–146.

    Article  Google Scholar 

  8. Jajaraman, B., Sivakumar, B., and Arivarignan, G., A Perishable Inventory System with Postponed Demands and Multiple Server Vacations, Model. Simul. Eng. (Hindawi Publishing Corporation), 2012, vol. 2012, article ID 620960, 17 p.

    Google Scholar 

  9. Jeganathan, K., Perishable Inventory System at Service Facilities with Multiple Server Vacations and Impatient Customers, J. Statist. Appl. Probab. Lett., 2014, vol. 3, no. 3, pp. 63–73.

    Article  Google Scholar 

  10. Kathiresan, S., Anbazhagan, N., and Jeganathan, K., An Inventory System with Retrial Demands and Working Vacation, Int. J. Sci. Res. Publ., 2014, vol. 4, no. 12, pp. 1–25.

    Google Scholar 

  11. Jeganathan, K., Anbazhagan, N., and Vigneshwaran, B., Perishable Inventory System with Server Interruptions, Multiple Server Vacations and Policy, Int. J. Oper. Res. Inform. Syst., 2015, vol. 6, no. 2, pp. 32–52.

    Article  Google Scholar 

  12. Yadavalli, V.S.S. and Jeganathan, K., Perishable Inventory Model with Two Heterogeneous Servers Including One with Multiple Vacations and Retrial Customers, J. Control Syst. Eng., 2015, vol. 3, no. 1, pp. 10–34.

    Article  Google Scholar 

  13. Padmavathi, I., Sivakumar, B., and Arivarignan, G., A Retrial Inventory System with Single and Modified Multiple Vacation for Server, Ann. Oper. Res., 2015, vol. 233, no. 1, pp. 335–364.

    Article  MathSciNet  MATH  Google Scholar 

  14. Neuts, M.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Baltimore: John Hopkins Univ. Press, 1981.

    MATH  Google Scholar 

  15. Mitrani, I. and Chakka, R., Spectral Expansion Solution for a Class of Markov Models: Application and Comparison with the Matrix-Geometric Method, Perform. Evaluation, 1995, vol. 23, pp. 241–260.

    Article  MATH  Google Scholar 

  16. Chakka, R., Spectral Expansion Solution for Some Finite Capacity Queues, Ann. Oper. Res., 1998, vol. 79, pp. 27–44.

    Article  MathSciNet  MATH  Google Scholar 

  17. Nahmias, S., Perishable Inventory Theory: A Review, Oper. Res., 1982, vol. 30, pp. 680–708.

    Article  MATH  Google Scholar 

  18. Nahmias, S., Perishable Inventory Theory, Heidelberg: Springer, 2011.

    Book  MATH  Google Scholar 

  19. Baron, O., Berman, O., and Perry, D., Continuous Review Inventory Models for Perishable Items Ordered in Batches, Math. Method. Oper. Res., 2010, vol. 72, pp. 217–247.

    Article  MathSciNet  MATH  Google Scholar 

  20. Koroliuk, V.S., Melikov, A.Z., Ponomarenko, L.A., et al., Methods for Analysis of Multi-Channel Queueing Models with Instantaneous and Delayed Feedbacks, Cybernet. Systems Anal., 2016, vol. 52, no. 1, pp. 58–70.

    Article  MathSciNet  MATH  Google Scholar 

  21. Melikov, A.Z., Ponomarenko, L.A., and Bagirova, S.A., Analysis of Queueing-Inventory Systems with Impatience Consume Customers, J. Autom. Inform. Sci., 2016, vol. 48, no. 1, pp. 53–68.

    Article  Google Scholar 

  22. Melikov, A.Z., Ponomarenko, L.A., and Shahmaliyev, M.O., Perishable Queueing-Inventory Models with Repeated Consumer Customers, J. Autom. Inform. Sci., 2016, vol. 48, no. 6, pp. 22–38.

    Article  Google Scholar 

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Authors and Affiliations

  1. Institute of Control Systems, Azerbaijan National Academy of Sciences, Baku, Azerbaijan

    A. Z. Melikov & A. M. Rustamov

  2. International Research and Training Center for Information Technologies and Systems of the National Academy of Sciences of Ukraine, Kiev, Ukraine

    L. A. Ponomarenko

Authors
  1. A. Z. Melikov
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  2. A. M. Rustamov
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  3. L. A. Ponomarenko
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Correspondence to A. Z. Melikov.

Additional information

Original Russian Text © A.Z. Melikov, A.M. Rustamov, L.A. Ponomarenko, 2017, published in Avtomatika i Telemekhanika, 2017, No. 11, pp. 64–78.

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Melikov, A.Z., Rustamov, A.M. & Ponomarenko, L.A. Approximate analysis of a queueing–inventory system with early and delayed server vacations. Autom Remote Control 78, 1991–2003 (2017). https://doi.org/10.1134/S0005117917110054

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  • DOI: https://doi.org/10.1134/S0005117917110054

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