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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Artalejo, J.R.: G-networks: a versatile approach for work removal in queueing networks. European J. Op. Res. 126, 233–249 (2000)
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)
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)
Fourneau, J.M., Gelenbe, E., Suros, R.: G-networks with multiple classes of positive and negative customers. Theoretical Computer Science 155, 141–156 (1996)
Fourneau, J.M., Kloul, L., Quessette, F.: Multiple class G-networks with jumps back to Zero. IEEE Mascots 95, 28–32 (1995)
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)
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)
Gelenbe, E.: Random neural Networks with Negative and Positive Signals and Product Form Solution. Neural Computation 1(4), 502–510 (1990)
Gelenbe, E.: Product form queueing networks with negative and positive customers. Journal of Applied Probability 28, 656–663 (1991)
Gelenbe, E., Schassberger, R.: Stability of G-Networks. Probability in the Engineering and Informational Sciences 6, 271–276 (1992)
Gelenbe, E.: G-networks with instantaneous customer movement. Journal of Applied Probability 30(3), 742–748 (1993)
Gelenbe, E.: G-Networks with signals and batch removal. Probability in the Engineering and Informational Sciences 7, 335–342 (1993)
Gelenbe, E.: G-networks: An unifying model for queueing networks and neural networks. Annals of Operations Research 48(1-4), 433–461 (1994)
Gelenbe, E.: The first decade of G-networks. European J. Op. Res. 126(2), 231–232 (2000)
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)
Gelenbe, E., Lent, R., Xu, Z.: Design and performance of cognitive packet networks. Performance Evaluation 46(2-3), 155–176 (2001)
Gelenbe, E., Fourneau, J.M.: G-networks with resets. Performance Evaluation 49(1/4), 179–191 (2002)
Gelenbe, E., Fourneau, J.M.: Flow Equivalence and Stochastic Equivalence in G-Networks. Computational Management Science 1(2), 179–192 (2004)
Gelenbe, E., Lent, R.: Power-aware ad hoc cognitive packet networks. Ad Hoc Networks 2(3), 205–216 (2004)
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)
Harrison, P.: Compositional reversed markov processes, with applications to g-networks. Performance Evaluation 57(3), 379–408 (2004)
Jackson, J.R.: Jobshop-like queueing systems. Management Science 10(1), 131–142 (1963)
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)
Pinedo, M., Chao, X., Miyazawa, M.: Queueing Networks: Customers, Signals and Product Form Solutions. J. Wiley, Chichester (1999)
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)
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)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fourneau, JM. (2008). Multiclass G-Networks of Processor Sharing Queues with Resets. In: Al-Begain, K., Heindl, A., Telek, M. (eds) Analytical and Stochastic Modeling Techniques and Applications. ASMTA 2008. Lecture Notes in Computer Science, vol 5055. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68982-9_16
Download citation
DOI: https://doi.org/10.1007/978-3-540-68982-9_16
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68980-5
Online ISBN: 978-3-540-68982-9
eBook Packages: Computer ScienceComputer Science (R0)