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Reallocatable GSMP with Sequentially Dependent Lifetimes: Clockwise Decomposability and its Applications

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Applied Probability and Stochastic Processes

Part of the book series: International Series in Operations Research & Management Science ((ISOR,volume 19))

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Abstract

In a recent communication, François Beccelli suggested the importance of a general formulation in research when he commented that we see many beautiful flowers in a garden but cannot see ground. Julian Keilson is honored as one of the great pioneers in cultivating the ground of applied probability. I am pleased to have an opportunity to contribute to this book dedicated to him, and I would like to consider queueing network problems under a general formulation.

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References

  1. Baccelli, F., and Bremaud, P. Elements of Queueing Theory. Springer-Verlag, New York, 1994.

    MATH  Google Scholar 

  2. Baskett, F., Chandy, K, M., Muntz, R. R., and Palacios, F. G. Open, closed and mixed networks of queues with different classes of customers. JACM 22, 248–260, 1975.

    Article  MathSciNet  MATH  Google Scholar 

  3. Chandy, K. M., Howard, J. H. Jr., and Towsley, D. F. Product form and local balance in queueing networks. JACM 24, 250–263, 1977.

    Article  MathSciNet  MATH  Google Scholar 

  4. Chandy, K., and Martin, J. A characterization of product form queueing networks. JACM 24, 250–263, 1983.

    Article  Google Scholar 

  5. Chao, X., and Miyazawa, M. On quasi-reversibility and local balance: an alternative derivation of the product-form results. Oper. Res., to appear.

    Google Scholar 

  6. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. II, 2nd ed. John Wiley & Sons, New York, 1971.

    MATH  Google Scholar 

  7. Franken, P., Knig D., Arndt, U., and Schmidt, V. Queues and Point Processes. Wiley, Chichester, 1982.

    MATH  Google Scholar 

  8. Jansen, U. A generalization of insensitivity results by cyclically marked stationary point processes. Elektron. Informationsverarb, u. Kybernet. 19, 307–320, 1983.

    MathSciNet  MATH  Google Scholar 

  9. Jansen U., König, D., and Nawrotzki, K. A criterion of insensitivity for a class of queueing systems with random marked point processes. Math. Oerationsforsch. u. Stat. Ser. Optimization 10, 379–403, 1979.

    Article  MATH  Google Scholar 

  10. Kelly, F. P. Networks of queues. Adv. Appl. Prob. 8, 416–432, 1976.

    Article  MATH  Google Scholar 

  11. Kelly, F. P. Reversibility and Stochastic Networks. Wiley, New York, 1979.

    MATH  Google Scholar 

  12. Miyazawa, M. The derivation of invariance relations in complex queueing systems with stationary inputs. Adv. Appl. Prob. 15, 874–885, 1983.

    Article  MathSciNet  MATH  Google Scholar 

  13. Miyazawa, M. The characterization of the stationary distributions of the supplemented Self-clocking Jump Process. Math. OR 16, 547–565, 1991.

    Article  MathSciNet  MATH  Google Scholar 

  14. Miyazawa, M. Insensitivity and product form decomposability of Reallocatable GSMP. Adv. Appl. Prob. 25, 415–437, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  15. Miyazawa, M. Rate conservation law: a survey. Queueing Syst. 15, 1–58, 1994.

    Article  MathSciNet  MATH  Google Scholar 

  16. Miyazawa, M., Schassberger, R., and Schmidt, V. On the structure of insensitive GSMP with reallocation and with point-process input. Adv. Appl. Prob. 27, 203–225, 1995.

    Article  MathSciNet  MATH  Google Scholar 

  17. Miyazawa, M., and Yamazaki, G. Note on batch arrival LCFS and related symmetric queues. Oper. Res. Lett. 14, 35–41, 1993.

    Article  MathSciNet  MATH  Google Scholar 

  18. Miyazawa, M., and Wolff, R. W. Symmetric queues with batch departures and their network. Adv. Appl. Prob. 28, 308–326, 1996.

    Article  MathSciNet  MATH  Google Scholar 

  19. Schassberger, R. Insensitivity of steady-state distributions of generalized semi-Markov processes with speeds. Adv. Appl. Prob. 10, 836–851, 1978.

    Article  MathSciNet  MATH  Google Scholar 

  20. Schassberger, R. Two remarks on insensitive stochastic models. Adv. Appl. Prob. 18, 791–814, 1986.

    Article  MathSciNet  MATH  Google Scholar 

  21. Serfozo, R. F. Markovian network processes with system-dependent transition rates. Queueing Syst. 5, 5–36, 1989.

    Article  MathSciNet  MATH  Google Scholar 

  22. Serfozo, R. F. Markovian network processes with system-dependent transition rates. Queueing Syst. 5, 5–36, 1993.

    Article  MathSciNet  Google Scholar 

  23. Yamazaki, G, and Miyazawa, M. Decomposability in queues with background states. Queueing Syst., to appear.

    Google Scholar 

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Authors

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J. G. Shanthikumar Ushio Sumita

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© 1999 Springer Science+Business Media New York

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Miyazawa, M. (1999). Reallocatable GSMP with Sequentially Dependent Lifetimes: Clockwise Decomposability and its Applications. In: Shanthikumar, J.G., Sumita, U. (eds) Applied Probability and Stochastic Processes. International Series in Operations Research & Management Science, vol 19. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-5191-1_11

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  • DOI: https://doi.org/10.1007/978-1-4615-5191-1_11

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-7364-3

  • Online ISBN: 978-1-4615-5191-1

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