Advertisement

Approximate and Bound Analysis

  • Simonetta Balsamo
  • Vittoria de Nitto Personé
  • Raif Onvural
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 31)

Abstract

In this chapter we deal with approximate and bound methods to analyze queueing networks with blocking and to evaluate various performance indices. Section 6.1 introduces the basic ideas of the approximate method proposed in the literature. Sections 6.2 and 6.3 present some approximate solution techniques for closed and open networks with blocking, respectively. Section 6.4 deals with bound approximation methods.

Keywords

Queue Length Maximum Relative Error Queueing Network Queue Length Distribution Queue Network Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akyildiz, I.F. “On the exact and approximate throughput analysis of closed queueing networks with blocking” IEEE Trans. on Soft. Eng., Vol. 14 (1988) 62–71.CrossRefGoogle Scholar
  2. Akyildiz, I.F. “Mean value analysis of blocking queueing networks”, IEEE Trans. on Soft. Eng. Vol. 14 (1988) 418–129.CrossRefGoogle Scholar
  3. Akyildiz, I.F., and H.G. Perros, Special Issue on Queueing Networks with Finite Capacity Queues, Performance Evaluation, Vol. 10(1989).Google Scholar
  4. Altiok, T., and H.G. Perros “Open networks of queues with blocking: split and merge configurations” IEE Trans. 9 (1986) 251–261.CrossRefGoogle Scholar
  5. Altiok, T., and H.G. Perros “Approximate analysis of arbitrary configurations of queueing networks with blocking” Ann. Oper. Res. 9 (1987) 481–509.CrossRefGoogle Scholar
  6. Balsamo, S. “Decomposability for General Markovian Networks”, in Mathematical Computer Performance and Reliability, (G. Iazeolla, P.J. Courtois, A. Hordijk Eds.), North Holland, 1984.Google Scholar
  7. Balsamo, S., and B. Pandolfi “Bounded Aggregation in Markovian Networks” in Computer Performance and Reliability (G. Iazeolla, P.J. Courtois, O. Boxma Eds.), North Holland, 1988.Google Scholar
  8. Balsamo, S., and G. Iazeolla “An extension of Norton’s Theorem for Queueing Networks” IEEE Transactions on Software Engineering, Vol.8 (1982) 298–305.CrossRefGoogle Scholar
  9. Balsamo, S., and G. Iazeolla “Synthesis of Queueing Networks with Block and Statedependent Routing”, Computer Systems Science and Engineering, Vol.1 (1986) 194–199.Google Scholar
  10. Balsamo, S., and A. Rainero “Approximate Performance Analysis of Queueing Networks with Blocking: A Comparison” UDMI/05/98/RR, Dept. Math and Comp. Sci., University of Udine, March 1998.Google Scholar
  11. Boxma, O., and A.G. Konheim “Approximate analysis of exponential queueing systems with blocking” Acta Informatica, Vol. 15 (1981) 19–66.CrossRefGoogle Scholar
  12. Boucherie, R. “Norton’s Equivalent for queueing networks comprised of quasireversible components linked by state-dependent routing” Performance Evaluation, Vol. 32 (1998) 83–99.CrossRefGoogle Scholar
  13. Boucherie, R., and N. Van Dijk “A generalization of Norton’s theorem for queueing networks” Queueing Systems, Vol. 13 (1993) 251–289.CrossRefGoogle Scholar
  14. Bouchouch, A., Y. Frein and Y. Dallery “Performance evaluation of closed tandem queueing networks with finite buffers” Performance Evaluation, Vol. 26 (1996) 115–132.CrossRefGoogle Scholar
  15. Brandwajn, A., and Y.L. Jow “An approximation method for tandem queueing systems with blocking” Operations Research, Vol. 1 (1988) 73–83.CrossRefGoogle Scholar
  16. Chandy, K.M., U. Herzog and L. Woo “Parametric analysis of queueing networks” IBM Journal of Research and Development, Vol.1 (1975), 36–42.CrossRefGoogle Scholar
  17. Cheng, D.W. “Analysis of a tandem queue with state dependent general blocking: a GSMP perspective” Performance Evaluation, Vol. 17 (1993) 169–173.CrossRefGoogle Scholar
  18. Courtois, P.J. Decomposability: Queueing and Computer System Applications, Academic Press, Inc, New York, 1977.Google Scholar
  19. Courtois, P.J., and P. Semal “Computable bounds for conditional steady-state probabilities in large Markov chains and queueing models” IEEE Journal on SAC, Vol. 4 (1986) 920–936.Google Scholar
  20. Dallery, Y., and Y. Frein “A decomposition method for the approximate analysis of closed queueing networks with blocking” Proc. First Int. Workshop on Queueing Networks with Blocking, (H.G. Perros and T. Altiok Eds.) North Holland, 1989.Google Scholar
  21. Dallery, Y., and Y. Frein “On decomposition methods for tandem queueing networks with blocking” Operations Research, Vol. 14 (1993) 386–399.CrossRefGoogle Scholar
  22. Frein, Y., and Y. Dallery “Analysis of cyclic queueing networks with finite buffers and blocking before service” Performance Evaluation, Vol. 10 (1989) 197–210.CrossRefGoogle Scholar
  23. Gershwin, S. “An efficient decomposition method for the approximate evaluation of tandem queues with finite storage space and blocking” Operations Research, Vol. 35 (1987) 291–305.CrossRefGoogle Scholar
  24. Gordon, W.J., and G.F. Newell “Cyclic queueing systems with restricted queues” Oper. Res., Vol. 15 (1967) 286–302.CrossRefGoogle Scholar
  25. Hillier, F.S., and R.W. Boling “Finite queues in series with exponential or Erlang service times — a numerical approach” Operations Research, Vol. 15 (1967) 286–303.CrossRefGoogle Scholar
  26. Konhein, A.G., and M. Reiser “A queueing model with finite waiting room and blocking” SIAM J. of Computing, Vol. 7 (1978) 210–229.CrossRefGoogle Scholar
  27. Kouvatsos, D., and I.U. Awan “Arbitrary closed queueing networks with blocking and multiple job classes” Proc. Third International Workshop on Queueing Networks with Finite Capacity, Bradford, UK, 6–7 July, 1995.Google Scholar
  28. Kouvatsos, D., and S.G. Denazis “Entropy maximized queueing networks with blocking and multiple job classes” Performance Evaluation, Vol. 17 (1993) 189–205.CrossRefGoogle Scholar
  29. Kouvatsos, D., and N.P. Xenios “MEM for arbitrary queueing networks with multiple general servers and repetitive-service blocking” Performance Evaluation Vol. 10 (1989) 106–195.CrossRefGoogle Scholar
  30. Kritzinger, P. S., van Wyk, and A. Krzesinski “A generalization of Norton’s theorem for multiclass queueing networks” Performance Evaluation, Vol. 2 (1982) 98–107.CrossRefGoogle Scholar
  31. Jun, K.P., and H.G. Perros “An approximate analysis of open tandem queueing networks with blocking and general service times” Europ. Journal of Operations Research, Vol. 46 (1990) 123–135.CrossRefGoogle Scholar
  32. Lee, H.S., and S. M. Pollock “Approximation analysis of open acyclic exponential queueing networks with blocking” Operations Research, Vol. 38 (1990) 1123–1134.CrossRefGoogle Scholar
  33. Lee, H.S., A. Bouhchouch, Y. Dallery and Y. Frein “Performance Evaluation of open queueing networks with arbitrary configurations and finite buffers” Proc. Third International Workshop on Queueing Networks with Finite Capacity, Bradford, UK, 6–7 July, 1995.Google Scholar
  34. Liu, X.G., and J.A. Buzacott “A balanced local flow technique for queueing networks with blocking” Proc. First Int. Workshop on Queueing Networks with Blocking (H. Perros and T. Altiok Eds.) North Holland, 1989, 87–104.Google Scholar
  35. Liu, X.G., and J.A. Buzacott “A decomposition related throughput propety of tandem queueing networks with blocking” Queueing Systems, Vol. 13 (1993) 361–383.CrossRefGoogle Scholar
  36. Liu, X.G., L. Zwang and J.A. Buzacott “A decomposition method for throughput analysis of cyclic queues with production blocking” in Queueing Networks with Finite Capacity (R. O. Onvural and I.F. Akyildiz Eds.) North Holland, 1993, 253–266.Google Scholar
  37. Mishra, S., and S.C. Fang “A maximum entropy optimization approach to tandem queues with generalized blocking” Performance Evaluation, Vol. 30 (1997) 217–241.CrossRefGoogle Scholar
  38. Mitra, D., and I. Mitrani “ Analysis of a Kanban discipline for cell coordination in production lines I” Management Science, Vol. 36 (1990) 1548–1566.CrossRefGoogle Scholar
  39. Mitra, D., and I. Mitrani “Analysis of a Kanban discipline for cell coordination in production lines II: Stochastic demands” Operations Research, Vol. 36 (1992) 807–823.Google Scholar
  40. Onvural, R.O. “Survey of Closed Queueing Networks with Blocking” ACM Computing Surveys, Vol. 22 (1990) 83–121.CrossRefGoogle Scholar
  41. Onvural, R.O. Special Issue on Queueing Networks with Finite Capacity, Performance Evaluation, Vol. 17 (1993).Google Scholar
  42. Onvural, R.O., and H.G. Perros “Throughput analysis in cyclic queueing networks with blocking” IEEE Trans. on Software Eng., Vol. 15 (1989) 800–808.CrossRefGoogle Scholar
  43. Perros, H.G. “Open queueing networks with blocking” in: Stochastic Analysis of Computer and Communications Systems (Takagi Ed.) North Holland, 1989.Google Scholar
  44. Perros, H.G. Queueing networks with blocking. Oxford University Press, 1994.Google Scholar
  45. Perros, H.G., and T. Altiok “Approximate analysis of open networks of queues with blocking: tandem configurations” IEEE Trans. on Software Eng., Vol. 12 (1986) 450–461.CrossRefGoogle Scholar
  46. Perros, H.G., A. Nilsson and Y.G. Liu “Approximate analysis of product form type queueing networks with blocking and deadlock” Performance Evaluation, Vol. 8 (1988) 19–39.CrossRefGoogle Scholar
  47. Perros, H.G., and P.M. Snyder “A computationally efficient approximation algorithm for analyzing queueing networks with blocking” Performance Evaluation, Vol. 9 (1988/89) 217–224.CrossRefGoogle Scholar
  48. Shanthikumar, G.J., and D.D. Yao “Monotonicity Properties in Cyclic Queueing Networks with Finite Buffers” in First International Workshop on Queueing Networks with Blocking, (Perros and Altiok Eds), Elsevier Science Publishers, North Holland, 1989.Google Scholar
  49. Suri, R., and G.W. Diehl “A variable buffer size model and its use in analytical closed queueing networks with blocking” Management Sci., Vol.32 (1986) 206–225.CrossRefGoogle Scholar
  50. Vantilborgh, H. “Exact aggregation in exponential queueing networks” Journal of the ACM, Vol. 25 (1978) 620–629.CrossRefGoogle Scholar
  51. Yao, D.D., and J.A. Buzacott “Modeling a class of state-dependent routing in flexible manufacturing systems” Ann. Oper. Res., Vol. 3 (1985) 153–167.CrossRefGoogle Scholar
  52. Yao, D.D., and J.A. Buzacott “Modeling a class of flexible manufacturing systems with reversible routing” Oper. Res., Vol. 35 (1987) 87–93.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Simonetta Balsamo
    • 1
  • Vittoria de Nitto Personé
    • 2
  • Raif Onvural
    • 3
  1. 1.Universita’ di VeneziaItaly
  2. 2.Universita’ di Roma “Tor Vergata”Italy
  3. 3.IBMUSA

Personalised recommendations