Response time distributions in queueing network models

  • Peter G. Harrison
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 729)


Time delays in queueing networks are assuming increasing importance with the proliferation of transaction processing and time-critical real time systems. Mean values are insufficient and it is necessary to estimate time intervals that are not exceeded with a specified probability, i.e. quantiles. This paper presents results on time delay distributions in single server queues of various types and extends these to networks of queues. In particular, the class of Jackson networks that permit exact solution are analysed in both the open and closed cases, and approximation techniques for more general networks are proposed.


  1. [1]
    E.G. Coffman Jnr, R.R. Muntz, H. Trotter Waiting time distribution for processor-sharing systems JACM 17, pp 123–30, 1970Google Scholar
  2. [2]
    H. Daduna Passage times for overtake-free paths in Gordon-Newell networks Adv. Appl. Prob. 14, pp672–86, 1982Google Scholar
  3. [3]
    E. Gelenbe, P. Glynn, K. Sigman Queues with negative arrivals J. Appl. Prob. 28, pp245–50, 1991Google Scholar
  4. [4]
    P.G. Harrison An enhanced approximation by pair-wise analysis of servers for time delay distributions in queueing networks IEEE Transactions on Computers C-35, 1, pp 54–61, 1986Google Scholar
  5. [5]
    P.G. Harrison Laplace transform inversion and passage time distributions in Markov processes J. Appl. Prob. 27, pp 74–87, 1990Google Scholar
  6. [6]
    P.G. Harrison On non-uniform packet switched delta networks and the hot-spot effect IEE Proceedings E 138, 3, pp 123–30, 1991Google Scholar
  7. [7]
    P.G. Harrison, N.M. Patel Performance Modelling of Communication Networks and Computer Architectures Addison-Wesley, 1993Google Scholar
  8. [8]
    P.G. Harrison, E. Pitel Sojourn times in single server queues with negative customers J. Appl. Prob., 1993 (to appear)Google Scholar
  9. [9]
    F.P. Kelly, P.K. Pollett Sojourn times in closed queueing networks Adv. Appl. Prob. 15, 638–56, 1983Google Scholar
  10. [10]
    I. Mitrani Response time problems in communication networks J. Roy. Stat. Soc. B-47, 3, pp 396–406, 1985Google Scholar
  11. [11]
    I. Mitrani Modelling of Computer and Communication Systems Cambridge University Press, 1987Google Scholar
  12. [12]
    E. Pitel Queues with negative customers and their applications PhD Thesis, Department of Computing, Imperial College, University of London, 1994 (in preparation)Google Scholar
  13. [13]
    L. Takacs Introduction to the theory of queues Oxford University Press, 1962Google Scholar

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Peter G. Harrison
    • 1
  1. 1.Department of ComputingImperial CollegeLondonEngland

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