Skip to main content

Discrete time analysis of a state dependent tandem with different customer types

  • Chapter
  • First Online:
Book cover Foundations of Computer Science

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1337))

Abstract

We consider a discrete time model for a transmission line in a meshed network of stations. The line is fed by a state dependent arrival stream of customers of different types. The service regime at the nodes is FCFS with state dependent probabilities. The stationary distribution for the joint queue lengths of the line is of product form. We derive expressions for loss probabilities, end-to-end-delay distribution, and throughput.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. O. Boxma and H. Daduna. Sojourn times in queueing networks. In H. Takagi, editor, Stochastic Analysis of Computer and Communication Systems, pages 401–450, Amsterdam, 1990. IFIP, North-Holland.

    Google Scholar 

  2. H. Bruneel and B. G. Kim. Discrete-Time Models for Communication Systems including ATM. Kluwer Academic Publications, Boston, 1993.

    Google Scholar 

  3. H. Daduna. The joint distribution of sojourn times for a customer traversing a series of queues: The discrete-time case. Preprint 95-3, Institut für Mathematische Stochastik der Universität Hamburg, 1995. Submitted.

    Google Scholar 

  4. H. Daduna. Discrete time queueing networks: Recent developments. Preprint 96-13, Institut für Mathematische Stochastik der Universität Hamburg, 1996. (Tutorial Lecture Notes Performance '96).

    Google Scholar 

  5. H. Daduna. Discrete time analysis of a state dependent tandem system with different customer types. Preprint 97-6, Institut für Mathematische Stochastik der Universität Hamburg, 1997.

    Google Scholar 

  6. H. Daduna. Some results for steady-state and sojourn time distributions in open and closed linear networks of Bernoulli servers with state-dependent service and arrival rates. Performance Evaluation, 30:3–18, 1997.

    Article  Google Scholar 

  7. H. Daduna and R. Schassberger. Delay time distributions and adjusted transfer rates for Jackson networks. Archiv für Elektronik und übertragungstechnik, 47:342–348, 1993.

    Google Scholar 

  8. J. Hsu and P. Burke. Behaviour of tandem buffers with geometric input and markovian output. IEEE Transactions on Communications, 24:358–361, 1976.

    Article  MathSciNet  MATH  Google Scholar 

  9. M. Reiser. Performance evaluation of data communication systems. Proceedings of the IEEE, 70:171–196, 1982.

    Article  Google Scholar 

  10. H. Takagi. Queueing Analysis: A Foundation of Performance Analysis, volume 3. North-Holland, New York, 1993. Discrete-Time Systems.

    Google Scholar 

  11. M. Woodward. Communication and Computer Networks: Modelling with Discrete-Time Queues. IEEE Computer Society Press, Los Alamitos, CA, 1994.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Christian Freksa Matthias Jantzen Rüdiger Valk

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Daduna, H. (1997). Discrete time analysis of a state dependent tandem with different customer types. In: Freksa, C., Jantzen, M., Valk, R. (eds) Foundations of Computer Science. Lecture Notes in Computer Science, vol 1337. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0052097

Download citation

  • DOI: https://doi.org/10.1007/BFb0052097

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63746-2

  • Online ISBN: 978-3-540-69640-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics