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Multiclass G-Networks of Processor Sharing Queues with Resets

  • Jean-Michel Fourneau
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5055)

Abstract

We consider an open queueing network of generalized queues with several class of customers and one class of signal. Each queue has an infinite capacity and one server. The service time is exponential. The service discipline is Processor Sharing. After its service completion a customer moves to another queue and may become a signal. When the signal enters a non empty queue it vanishes while it resets the queue when it enters an empty queue. We prove that the steady state distribution for such a network of queues has a product form solution. To the best of our knowledge it is the first multiclass network of generalized queues and resets with product form solution.

Keywords

Service Discipline Processor Sharing Service Completion Negative Customer 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.

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References

  1. 1.
    Artalejo, J.R.: G-networks: a versatile approach for work removal in queueing networks. European J. Op. Res. 126, 233–249 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Baskett, F., Chandy, K., Muntz, R.R., Palacios, F.G.: Open, closed and mixed networks of queues with different classes of customers. Journal ACM 22(2), 248–260 (1975)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Fourneau, J.M.: Computing the steady-state distribution of networks with positive and negative customers. In: 13th IMACS World Congress on Computation and Applied Mathematics, Dublin (1991)Google Scholar
  4. 4.
    Fourneau, J.M., Gelenbe, E., Suros, R.: G-networks with multiple classes of positive and negative customers. Theoretical Computer Science 155, 141–156 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Fourneau, J.M., Kloul, L., Quessette, F.: Multiple class G-networks with jumps back to Zero. IEEE Mascots 95, 28–32 (1995)Google Scholar
  6. 6.
    Fourneau, J.M., Quessette, F.: Computing the Steady-State Distribution of G-networks with Synchronized Partial Flushing. In: Levi, A., Savaş, E., Yenigün, H., Balcısoy, S., Saygın, Y. (eds.) ISCIS 2006. LNCS, vol. 4263, pp. 887–896. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Fourneau, J.M.: Closed G-networks with resets: Product Form solution. In: 4th International Conference on the Quantitative Evaluation of Systems QEST 2007, Edinburgh, pp. 287–296 (2007)Google Scholar
  8. 8.
    Gelenbe, E.: Random neural Networks with Negative and Positive Signals and Product Form Solution. Neural Computation 1(4), 502–510 (1990)CrossRefGoogle Scholar
  9. 9.
    Gelenbe, E.: Product form queueing networks with negative and positive customers. Journal of Applied Probability 28, 656–663 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gelenbe, E., Schassberger, R.: Stability of G-Networks. Probability in the Engineering and Informational Sciences 6, 271–276 (1992)zbMATHGoogle Scholar
  11. 11.
    Gelenbe, E.: G-networks with instantaneous customer movement. Journal of Applied Probability 30(3), 742–748 (1993)zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Gelenbe, E.: G-Networks with signals and batch removal. Probability in the Engineering and Informational Sciences 7, 335–342 (1993)Google Scholar
  13. 13.
    Gelenbe, E.: G-networks: An unifying model for queueing networks and neural networks. Annals of Operations Research 48(1-4), 433–461 (1994)zbMATHCrossRefMathSciNetGoogle Scholar
  14. 14.
    Gelenbe, E.: The first decade of G-networks. European J. Op. Res. 126(2), 231–232 (2000)zbMATHCrossRefMathSciNetGoogle Scholar
  15. 15.
    Gelenbe, E.: G-Networks: multiple class of Positive customers, signals and product form results. In: Calzarossa, M.C., Tucci, S. (eds.) Performance 2002. LNCS, vol. 2459, pp. 1–16. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  16. 16.
    Gelenbe, E., Lent, R., Xu, Z.: Design and performance of cognitive packet networks. Performance Evaluation 46(2-3), 155–176 (2001)zbMATHCrossRefGoogle Scholar
  17. 17.
    Gelenbe, E., Fourneau, J.M.: G-networks with resets. Performance Evaluation 49(1/4), 179–191 (2002)zbMATHCrossRefGoogle Scholar
  18. 18.
    Gelenbe, E., Fourneau, J.M.: Flow Equivalence and Stochastic Equivalence in G-Networks. Computational Management Science 1(2), 179–192 (2004)zbMATHGoogle Scholar
  19. 19.
    Gelenbe, E., Lent, R.: Power-aware ad hoc cognitive packet networks. Ad Hoc Networks 2(3), 205–216 (2004)CrossRefGoogle Scholar
  20. 20.
    Gelenbe, E.: Keeping Viruses Under Control. In: Yolum, p., Güngör, T., Gürgen, F., Özturan, C. (eds.) ISCIS 2005. LNCS, vol. 3733, pp. 304–311. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  21. 21.
    Harrison, P.: Compositional reversed markov processes, with applications to g-networks. Performance Evaluation 57(3), 379–408 (2004)CrossRefGoogle Scholar
  22. 22.
    Jackson, J.R.: Jobshop-like queueing systems. Management Science 10(1), 131–142 (1963)CrossRefGoogle Scholar
  23. 23.
    Mohamed, S., Rubino, G., Varela, M.: Performance evaluation of real-time speech through a packet network: a random neural networks-based approach. Performance Evaluation 57(2), 141–161 (2004)CrossRefGoogle Scholar
  24. 24.
    Pinedo, M., Chao, X., Miyazawa, M.: Queueing Networks: Customers, Signals and Product Form Solutions. J. Wiley, Chichester (1999)zbMATHGoogle Scholar
  25. 25.
    Rubino, G., Tirilly, P., Varela, M.: Evaluating Users’ Satisfaction in Packet Networks Using Random Neural Networks. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4131, pp. 303–312. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  26. 26.
    Wang, Y.: G-Networks and the Modeling of Adversarial Agents. In: Kollias, S., Stafylopatis, A., Duch, W., Oja, E. (eds.) ICANN 2006. LNCS, vol. 4131, pp. 330–339. Springer, Heidelberg (2006)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Jean-Michel Fourneau
    • 1
    • 2
  1. 1.INRIA Project MESCAL, LIG, UJF & CNRSMontbonnotFrance
  2. 2.PRiSMUniversité de Versailles-Saint-Quentin & CNRS & UniverSudVersaillesFrance

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