Advertisement

Annals of Operations Research

, Volume 9, Issue 1, pp 481–509 | Cite as

Approximate analysis of arbitrary configurations of open queueing networks with blocking

  • T. Altiok
  • H. G. Perros
Real World Issues in Probability Modeling

Abstract

An algorithm for analyzing approximately open exponential queueing networks with blocking is presented. The algorithm decomposes a queueing network with blocking into individual queues with revised capacity, and revised arrival and service processes. These individual queues are then analyzed in isolation. Numerical experience with this algorithm is reported for three-node and four-node queueing networks. The approximate results obtained were compared against exact numerical data, and they seem to have an acceptable error level.

Keywords and phrases

Queueing networks finite queues blocking decomposition approximations 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    T. Altiok, Approximate analysis of exponential tandem queues with blocking, Eur. J. Oper. Res. 11(1982)390.Google Scholar
  2. [2]
    T. Altiok and H.G. Perros, Open networks of queues with blocking: Split and merge configurations, AIIS Trans.Google Scholar
  3. [3]
    P.P. Bocharov and G.P. Rokhas, On an exponential queueing system in series with blocking, Problems of Control and Information Theory 9(1980)441.Google Scholar
  4. [4]
    O.J. Boxma and A.G. Konheim, Approximate analysis of exponential queueing systems with blocking, Acta Informatica 15(1981)19.Google Scholar
  5. [5]
    A. Brandwajn and Y.L. Jow, An approximation method for tandem queues with blocking, manuscript, Amdahl Corp. (1985).Google Scholar
  6. [6]
    P. Caseau and G. Pujolle, Throughput capacity of a sequence of queues with blocking due to finite waiting room, IEEE Trans. Soft. Eng. SE-5 (1979) 631.Google Scholar
  7. [7]
    S.B. Gershwin, An efficient decomposition method for the approximate evaluation of tandem queues with finite storage and blocking, manuscript, Lab. for Information and Decision Sciences, M.I.T. (1983).Google Scholar
  8. [8]
    K. Goto, Y. Takahashi and J. Hasegawa, An approximate analysis on controlled tandem queues, Proc. Modelling Techniques and Tools for Performance Analysis, Cannes, France (1985).Google Scholar
  9. [9]
    F.S. Hillier and R. Boling, Finite queues in series with exponential or Erlang service times —A numerical approach, Oper. Res. 15(1967)286.Google Scholar
  10. [10]
    A. Hordijk and N. Van Dijk, Networks of queues with blocking, in:Performance '81, ed. F.J. Kylstra (North-Holland, New York, 1981).Google Scholar
  11. [11]
    F.P. Kelly, The throughput of a series of buffers, Adv. Appl. Prob. 14(1982)633.Google Scholar
  12. [12]
    J. Labetoulle and G. Pujolle, Modelling of packet switching communication networks with finite buffer size at each node, in:Computer Performance, eds. Chandy and Reiser (North-Holland, 1977) p. 515.Google Scholar
  13. [13]
    L.-M. Le Ny, Etude analytique de réseaux de files d'attente multiclasses a routage variable, RAIRO Recherche Operationelle 14(1980)331.Google Scholar
  14. [14]
    M.F. Neuts,Matrix-geometric Solutions in Stochastic Models — An Algorithmic Approach (The John Hopkins University Press, Baltimore, 1981).Google Scholar
  15. [15]
    R.O. Onvural and H.G. Perros, On equivalencies of blocking mechanisms in queueing networks with blocking, manucript, Comp. Sci. Dept., N.C. State Univ. (1985).Google Scholar
  16. [16]
    H.G. Perros, A symmetrical exponential open queue network with blocking and feedback, IEEE Trans. Soft. Eng. SE-7 (1981) 395.Google Scholar
  17. [17]
    H.G. Perros and T. Altiok, Approximate analysis of open networks of queues with blocking: Tandem configurations, IEEE Trans. Soft. Eng., to appear.Google Scholar
  18. [18]
    H.G. Perros, Queueing networks with blocking: A bibliography, Performance Evaluation Review, ACM SIGMETRICS 12(1984)8.Google Scholar
  19. [19]
    S.M. Pollock and J.R. Birge, Parallel iteration for multiple servers, manuscript, I and OR Dept. 83-16, Michigan Univ. (1983).Google Scholar
  20. [20]
    R. Suri and G.W. Diehl, A variable buffer-size model and its use in analytic closed queueing networks with blocking, Proc. ACM SIGMETRICS on Measurement and Modelling of Computer Systems (1984) 134.Google Scholar
  21. [21]
    Y. Takahashi, H. Miyahara and T. Hasegawa, An approximation method for open restricted queueing networks, J. Oper. Res. 28(1980)594.Google Scholar
  22. [22]
    D. Yao and J.A. Buzacott, Modelling a class of flexible manufacturing systems with reversible routing, manuscript, I.E. Dept., Columbia Univ. (1983).Google Scholar

Copyright information

© J.C. Baltzer A.G., Scientific Publishing Company 1987

Authors and Affiliations

  • T. Altiok
    • 1
  • H. G. Perros
    • 2
  1. 1.Industrial Engineering DepartmentRutgers UniversityPiscatawayUSA
  2. 2.Computer Science DepartmentNorth Carolina State UniversityRaleighUSA

Personalised recommendations