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Examples of Queueing Models

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Point Process Theory and Applications

Part of the book series: Probability and its Applications ((PA))

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In the first section the classical GI/G/1 model is treated with the emphasis of finding when there is equilibrium (stationarity). For the simplest case, the M/M/1 model, stationarity is discussed in detail, not just for the length of the queue but also involving the time since most the recent arrival and the time since the present service started. The second section deals with the description of some PDMP models of queueing networks that are not just (homogeneous) Markov chains.

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Chapter 11, Queueing

  1. Asmussen, S. (1987). Applied Probability and Queues. Wiley, Chichester. 2nd edition, Springer, New York (2003).

    MATH  Google Scholar 

  2. Baccelli, F. and Brémaud, P. (1994). Elements of Queueing Theory. Springer, New York.

    MATH  Google Scholar 

  3. Brémaud, P. (1981). Point Processes and Queues: Martingale Dynamics. Springer, Berlin.

    MATH  Google Scholar 

  4. Chao, X., Miyazawa, M. and Pinedo, M. (1999). Queueing Networks. Customers, Signals and Product Form Solutions. Wiley.

    Google Scholar 

  5. Chen, H. and Yao, D. (2001). Fundamentals of Queueing Networks: Performance, Asymptotics and Optimization. Springer, New York.

    MATH  Google Scholar 

  6. Dai, J. (1995a). On positive Harris recurrence of multiclass queueing networks: A unified approach via fluid limits. Ann. Appl. Probab. 5, 49–77.

    MATH  MathSciNet  Google Scholar 

  7. Dai, J. (1995b). Stability of open queueing networks via fluid models. In Stochastic Networks (F.P. Kelly and R.J. Williams, eds.). Springer, New York, 71–90.

    Google Scholar 

  8. Franken, P., König, D., Arndt, U. and Schmidt, V. (1982). Queues and Point Processes, Akademie-Verlag, Berlin and Wiley, Chichester.

    MATH  Google Scholar 

  9. Jackson, J.R. (1957). Networks of waiting lines. Operations Research 5, 518–521.

    Article  MathSciNet  Google Scholar 

  10. Kalashnikov, V.V. (1994). Mathematical Methods in Queueing Theory. Kluwer, Dordrecht.

    Google Scholar 

  11. Kelly, F.P. (1979). Reversibility and Stochastic Networks. Wiley, Chichester.

    MATH  Google Scholar 

  12. Robert, P. (2003). Stochastic Networks and Queues. Springer, Berlin.

    MATH  Google Scholar 

  13. Serfozo, R. (1999). Introduction to Stochastic Networks. Springer, New York.

    MATH  Google Scholar 

  14. Walrand, J. (1988). An Introduction to Queueing Networks. Prentice-Hall.

    Google Scholar 

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© 2006 Birkhäuser Boston

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(2006). Examples of Queueing Models. In: Point Process Theory and Applications. Probability and its Applications. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4463-6_11

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