Transient Model for Jackson Networks and Its Approximation

  • Ahmed M. Mohamed
  • Lester Lipsky
  • Reda Ammar
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3144)


Jackson networks have been very successful in so many areas in modeling parallel and distributed systems. However, the ability of Jackson networks to predict performance with system changes remains an open question, since they do not apply to systems where there are population size constraints. Also, the product-form solution of Jackson networks assumes steady state systems with exponential service centers and FCFS queueing discipline. In this paper, we present a transient model for Jackson networks. The model is applicable under any population size. This model can be used to study the transient behavior of Jackson networks and if the number of tasks to be executed is large enough, the model accurately approaches the product-form solution (steady state solution). Finally, an approximation to the transient model using the steady state solution is presented.


Percentage Error Steady State Solution Service Center Performance Behavior Steady State 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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Mohamed, A., Lipsky, L., Ammar, R.: Performance Modeling of a Cluster of Workstations. In: The 4th International Conference on Communications in Computing (CIC 2003), Las Vegas, NV (2003)Google Scholar
  2. 2.
    Mohamed, A., Lipsky, L., Ammar, R.: Transient Model for Jackson Networks and its Application in Cluster Computing. Sub. to J. of Cluster Computing (November 2003)Google Scholar
  3. 3.
    Mohamed, A., Ammar, R., Lipsky, L.: Efficient Data Allocation for a Cluster of Workstations. In: 16th International Conference on Parallel and Distributed Computing Systems (PDCS 2003), Reno, NV (2003)Google Scholar
  4. 4.
    Buyya, R.: High Performance Cluster Computing: Architecture and Systems, vol. 1. Prentice Hall PTR, NJ (1999)Google Scholar
  5. 5.
    Buzen, J.P.: Queueing Network Models of Multiprogramming, Ph.D. Thesis, Div. Of Engr. and Physics, Harvard University (1971)Google Scholar
  6. 6.
    Buzen, J.: Computational Algorithms for Closed Queueing. Comm. ACM 16(9) (September 1973)Google Scholar
  7. 7.
    Chen, R.J.: A Hybrid Solution of Fork/Join Synchronization in Parallel Queues. IEEE Trans. Parallel and Distributed Systems 12(8), 829–845 (2001)CrossRefGoogle Scholar
  8. 8.
    Foster, I., Kesselman, C.: The Grid: Blueprint for a New Computing Infrastructure. Morgan Kaufmann, San Francisco (1998)Google Scholar
  9. 9.
    Gordon, W.J., Newell, G.: Closed Queueing Systems with Exponential Servers. JORSA 15, 254–265 (1967)zbMATHGoogle Scholar
  10. 10.
    Jackson, J.: Jopshop-Like Queueing Systems. J. TIMS 10, 131–142 (1963)Google Scholar
  11. 11.
    Lipsky, L.: QUEUEING THEORY: A Linear Algebraic Approach. McMillan and Company, New York (1992)zbMATHGoogle Scholar
  12. 12.
    Lipsky, L., Church, J.D.: Applications of a Queueing Network Model for a Computer System. Computing Surveys 9, 205–221 (1977)zbMATHCrossRefGoogle Scholar
  13. 13.
    Moore, F.: Computational Model of a Closed Queueing Network with Exponential Servers. IBM J. of Res. and Develop., 567–572 (November 1962)Google Scholar
  14. 14.
    Muntz, R., Baskett, F., Chandy, K.: Open, closed and Mixed Networks of Queues with Different Classes of Customers. JACM 22, 248–260 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Tehranipour, A., Lipsky, L.: The Generalized M/G/C//N-Queue as a Model for Time-Sharing Systems. In: ACM-IEEE Joint Symposium on Applied Computing, Fayetteville, AR (April 1990)Google Scholar
  16. 16.
    Trividi, K.S.: Probability & Statistics with Reliability, Queueing and Computer Science Applications. Prentice-Hall, Inc., New Jersey (1982)Google Scholar
  17. 17.
    Qin, A., Sholl, H., Ammar, R.: Micro Time Cost Analysis of Parallel Computations. IEEE Trans. Computers 40(5), 613–628 (1991)CrossRefGoogle Scholar
  18. 18.
    Yan, Y., Zhang, X., Song, Y.: An Effective and Practical Performance Prediction Model for Parallel Computing on Nondedicated Heterogeneous Networks of Workstations. J. Parallel Distributed Computing 38(1), 63–80 (1996)CrossRefGoogle Scholar
  19. 19.
    Zhang, T., Kang, S., Lipsky, L.: On The Performance of Parallel Computers: Order Statistics and Amdahl’s Law. International Journal Of Computers And Their Applications 3(2) (August 1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Ahmed M. Mohamed
    • 1
  • Lester Lipsky
    • 1
  • Reda Ammar
    • 1
  1. 1.Dept. of Computer Science and EngineeringUniversity of ConnecticutStorrsUSA

Personalised recommendations