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Performance Analysis of Closed Queueing Networks

Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 663))

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Abstract

In recent years, many procedures have been developed to analyze stochastic flow lines. Exact methods and closed-form expressions have been proposed for the analysis of closed queueing networks with exponential processing times and infinite buffer spaces. Under the assumption of exponential processing times and finite buffer spaces, many approximate methods have been introduced. Only a few approximate procedures exist which consider general processing times, of which only a fraction additionally assume finite buffer spaces.

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Notes

  1. 1.

    CONWIP = constant work-in-process.

  2. 2.

    See Tempelmeier and Kuhn (1993, p. 1).

  3. 3.

    See Hopp and Spearman (2000, p. 223).

  4. 4.

    See Bolch et al. (2006, p. 245).

  5. 5.

    See Little (1961, pp. 383ff).

  6. 6.

    See Bolch et al. (2006, pp. 384f).

  7. 7.

    See Bolch et al. (2006, pp. 410ff).

  8. 8.

    Marie’s method considers general processing times and works very well. For more details on this procedure, see Sect. 3.3.3.2 on page 35 and Marie (1979).

  9. 9.

    Although the Gordon-Newell Theorem is called a theorem, it allows the evaluation of the performance measures and is, therefore, sorted into this section.

  10. 10.

    See Bolch et al. (2006, pp. 346f).

  11. 11.

    See Baskett et al. (1975) and Bolch et al. (2006, pp. 353ff).

  12. 12.

    See Tempelmeier and Kuhn (1993, p. 76).

  13. 13.

    For a description of Marie’s method, see page 35.

  14. 14.

    See Tempelmeier and Kuhn (1993, p. 71ff).

  15. 15.

    See Sect. 3.1.

  16. 16.

    See Bolch et al. (2006, p. 388).

  17. 17.

    See Bolch et al. (2006, p. 387).

  18. 18.

    For a description of the method and implementation, see Bolch et al. (2006, pp. 410ff).

  19. 19.

    See Sect. 3.1.

  20. 20.

    See also Sauer and Chandy (1981).

  21. 21.

    See also Bolch et al. (2006, pp. 369f).

  22. 22.

    See also Bolch et al. (2006, pp. 422, 427).

  23. 23.

    For this, see Sect. 3.3.3.4.

  24. 24.

    For more information on increasing failure rates, see Marshall and Olkin (2007).

  25. 25.

    See also Bolch et al. (2006, pp. 440ff).

  26. 26.

    See also Chen, George, and Tardif (2001).

  27. 27.

    See the Markov property on page 92.

  28. 28.

    See Stewart (2009, p. 184).

  29. 29.

    See Bolch et al. (2006, pp. 463ff).

  30. 30.

    Bolch et al. (2006, p. 492).

  31. 31.

    See Altiok (1996, p. 30).

  32. 32.

    Here, ρ i (n − 1) is the probability that the server is occupied. As no blocking occurs, the probability that a job receives service equals the probability that the server is busy. In case of blocking, the utilization and the blocking probability would have to be subtracted from the mean work-in-process.

  33. 33.

    Curry and Feldman (2008, pp. 252ff).

  34. 34.

    See also Sect. 3.3.1 on pages 26ff.

  35. 35.

    Dynamic parts routing means that parts follow a probabilistic shortest-queue scheme. For details, see Yao and Buzacott (1985).

  36. 36.

    See Bolch et al. (2006, pp. 505ff).

  37. 37.

    Bottapprox is an approximate method for CQN with exponential processing times and infinite buffers, see Sect. 3.3.1 on page 26.

  38. 38.

    See Bolch et al. (2006, pp. 502–505).

  39. 39.

    See Akyildiz (1987) for details and page 41.

  40. 40.

    See Akyildiz (1987, 1988c, 1989).

  41. 41.

    See Rall (1998, p. 127).

  42. 42.

    See Yao and Buzacott (1986a).

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  1. Department of Supply Chain Management and Production, University of Cologne, Cologne, Germany

    Svenja Lagershausen

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  1. Svenja Lagershausen
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Lagershausen, S. (2013). Literature Review. In: Performance Analysis of Closed Queueing Networks. Lecture Notes in Economics and Mathematical Systems, vol 663. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32214-3_3

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