Skip to main content
SpringerLink
Log in

Stochastic comparisons applied to G-Networks with catastrophes

  • Conference paper
  • First Online:
Computer and Information Sciences

Part of the book series: Lecture Notes in Electrical Engineering ((LNEE,volume 62))

  • 811 Accesses

Abstract

We study the transient distribution of some G-networks of queues with customers and signals. After its service completion a cus- tomer moves to another queue and may become a signal. We consider catastrophes where the signal deletes all customers in a queue. Both networks with negative customers and with catastrophes belong to well- known Gelenbe's networks with product form steady-state distribution. As the transient distribution is impossible to obtain, we derive stochas- tic upper and lower bounds on the marginal distribution for each queue following Massey's approach.

partially supported by French research project ANR-SETI06-02

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.-M. Fourneau and L. Kloul and F. Quessette, "Multiple Class G-Networks with Jumps back to Zero", IEEE MASCOTS 95, USA,1995.

    Google Scholar 

  2. E. Gelenbe, "Product form queueing networks with negative and positive customers", Journal of Applied Probability, Vol. 28, pp 656–663, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  3. E. Gelenbe, "G-networks with instantaneous customer movement", Journal of Applied Probability, Vol. 30, No 3, pp 742–748, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  4. E. Gelenbe, "G-Networks with signals and batch removal", Probability in the Engineering and Informational Sciences, Vol. 7, pp 335–342, 1993.

    Article  Google Scholar 

  5. E. Gelenbe and J.M. Fourneau, "G-networks with resets" Performance Evaluation, Vol. 49, No 1/4, pp 179–191, 2002.

    Article  MATH  Google Scholar 

  6. T. Lindvall, "Stochastic monotonicities in Jackson queueing networks", Prob. In the Engineering and Informational Sciences 11, 1–9, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  7. W. A. Massey, "Stochastic orderings for Markov processes on partially ordered spaces", Mathematics of Operations Research, V12, N2, pp 350–367, 1987.

    Article  MATH  MathSciNet  Google Scholar 

  8. W. A. Massey, "A family of bounds for the transient behavior of a Jackson Network", Journal of App. Prob., V23, pp 543–549, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  9. N. Pekergin, H. Taleb-Castel, "Stochastic bounds on the transient behaviors of the G-Network", Studia Informatica, Vol 23, 2002

    Google Scholar 

  10. A. Muller, D. Stoyan, "Comparison methods for Stochastic Models and Risks", J. Wiley and son in Probability and Statistics, 2002.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. INSTITUT TELECOM, TELECOM SudParis, 9, rue Charles Fourier, 91011, Evry Cedex, France

    H. Castel-Taleb

  2. PRiSM, Université de Versailles-Saint-Quentin CNRS, UniverSud, Versailles, France

    J-M. Fourneau

  3. LACL, Université Paris-Est, Val de Marne 61, av. du Général de Gaulle, 94010, Créteil Cedex, France

    N. Pekergin

Authors
  1. H. Castel-Taleb
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J-M. Fourneau
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. N. Pekergin
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. , EEE Dept., Imperial College, Exhibition Road, London, SW72BT, United Kingdom

    Erol Gelenbe

  2. , EEE Dept., Imperial College, Exhibition Rd., London, SW72AZ, United Kingdom

    Ricardo Lent

  3. , EEE Dept., Imperial College, Exhibition Rd., London, SW72AZ, United Kingdom

    Georgia Sakellari

  4. , School of Biomedical Eng., Sci. and Heal, Drexel University, Bossone 702, 3120 Market Street, Philadelphia, 19104, Pennsylvania, USA

    Ahmet Sacan

  5. , Dept. of Computer Engineering, Middle East Technical University, Ankara, 06531, Turkey

    Hakki Toroslu

  6. Fac. Engineering, Dept. Computer Engineering, Middle East Technical University - METU, Ankara, 06531, Turkey

    Adnan Yazici

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media B.V.

About this paper

Cite this paper

Castel-Taleb, H., Fourneau, JM., Pekergin, N. (2011). Stochastic comparisons applied to G-Networks with catastrophes. In: Gelenbe, E., Lent, R., Sakellari, G., Sacan, A., Toroslu, H., Yazici, A. (eds) Computer and Information Sciences. Lecture Notes in Electrical Engineering, vol 62. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-9794-1_11

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-9794-1_11

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-9793-4

  • Online ISBN: 978-90-481-9794-1

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation