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The Preemptive Repeat Hybrid Server Interruption Model

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Analytical and Stochastic Modeling Techniques and Applications (ASMTA 2010)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 6148))

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Abstract

We analyze a discrete-time queueing system with server interruptions and a hybrid preemptive repeat interruption discipline. Such a discipline encapsulates both the preemptive repeat identical and the preemptive repeat different disciplines. By the introduction and analysis of so-called service completion times, we significantly reduce the complexity of the analysis. Our results include a.o. the probability generating functions and moments of queue content and delay. Finally, by means of some numerical examples, we assess how performance measures are affected by the specifics of the interruption discipline.

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References

  1. White, H., Christie, L.: Queuing with preemptive priorities or with breakdown. Operations Research 66(1), 79–95 (1958)

    Article  MathSciNet  Google Scholar 

  2. Avi-Itzhak, B., Naor, P.: Some queuing problems with the service station subject to breakdown. Operations Research 11(3), 303–319 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  3. Thiruvengadam, K.: Queuing with breakdowns. Operations Research 11(1), 62–71 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  4. Gaver Jr., D.: A waiting line with interrupted service, including priorities. Journal of the Royal Statistical Society B24, 73–90 (1962)

    MathSciNet  Google Scholar 

  5. Fiems, D., Steyaert, B., Bruneel, H.: Discrete-time queues with generally distributed service times and renewal-type server interruptions. Performance Evaluation 55(3-4), 277–298 (2004)

    Article  Google Scholar 

  6. Kim, K., Chae, K.: Discrete-time queues with discretionary priorities. European Journal of Operational Research 200(2), 473–485 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  7. Federgruen, A., Green, L.: Queueing systems with service interruptions. Operations Research 34(5), 752–768 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  8. Bruneel, H.: A general treatment of discrete-time buffers with one randomly interrupted output line. European Journal of Operational Research 27(1), 67–81 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  9. Lee, D.: Analysis of a single server queue with semi-Markovian service interruption. Queueing Systems 27(1-2), 153–178 (1997)

    Article  MATH  Google Scholar 

  10. Núñez Queija, R.: Sojourn times in a processor sharing queue with service interruptions. Queueing Systems 34(1-4), 351–386 (2000)

    Article  MATH  Google Scholar 

  11. Balciog̃lu, B., Jagerman, D.L., Altiok, T.: Approximate mean waiting time in a GI/D/1 queue with autocorrelated times to failures. IIE Transactions 39(10), 985–996 (2007)

    Google Scholar 

  12. Fiems, D., Maertens, T., Bruneel, H.: Queueing systems with different types of interruptions. European Journal of Operations Research 188, 838–845 (2008)

    Article  MATH  Google Scholar 

  13. Mitrany, I., Avi-Itzhak, B.: A many-server queue with service interruptions. Operations Research 16, 628–638 (1968)

    Article  MATH  Google Scholar 

  14. Neuts, M., Lucantoni, D.: Markovian queue with N-servers subject to breakdowns and repairs. Management Science 25(9), 849–861 (1979)

    Article  MathSciNet  Google Scholar 

  15. Fiems, D.: Analysis of discrete-time queueing systems with vacations. PhD thesis, Ghent University (2004)

    Google Scholar 

  16. Bruneel, H.: Performance of discrete-time queuing-systems. Computers & Operations Research 20(3), 303–320 (1993)

    Article  MATH  Google Scholar 

  17. Takagi, H.: Queueing Analysis; A foundation of performance evaluation. Vacation and priority systems, part 1, vol. 1. Elsevier Science Publishers, Amsterdam (1991)

    MATH  Google Scholar 

  18. Takagi, H.: Queueing Analysis; A foundation of performance evaluation. Discrete-time systems, vol. 3. Elsevier Science Publishers, Amsterdam (1993)

    Google Scholar 

  19. Fiems, D., Bruneel, H.: A note on the discretization of Little’s result. Operations Research Letters 30(1), 17–18 (2002)

    Article  MATH  MathSciNet  Google Scholar 

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Demoor, T., Fiems, D., Walraevens, J., Bruneel, H. (2010). The Preemptive Repeat Hybrid Server Interruption Model. In: Al-Begain, K., Fiems, D., Knottenbelt, W.J. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2010. Lecture Notes in Computer Science, vol 6148. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13568-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-13568-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13567-5

  • Online ISBN: 978-3-642-13568-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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