Skip to main content

A Diffusion Approximation Analysis of Multilevel Ad Hoc and Sensor Networks

  • Conference paper
  • 594 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNCCN,volume 5793))

Abstract

In this paper we considered the approximation of a queueing system model of wireless ad hoc and sensor networks. In our model we admitted an arbitrary distribution for the duration of each M states that describe the source. Following the Markov Modulated Rate Process (MMRP) as a source model, we used it to introduce a diffusion approximation for the superposition of such aggregated traffic processes. We showed that the diffusion approximation of the aggregated traffic from the Markov modulated sources can illustrate the process of data harvesting by the sensors in different states.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akyildiz, I.F., Su, W., Sankasubramaniam, Y., Cayirci, E.: Wireless Sensor Networks: A Survey. Computer Networks 38, 393–422 (2002)

    Article  Google Scholar 

  2. Feller, W.: An Introduction to Probability Theory and Its Applications, vol. II. John Wiley and Sons, Chichester (1966)

    MATH  Google Scholar 

  3. Heffes, H., Lucatoni, D.M.: A Markov Modulated Characterization of Packetized Voice and Data Traffic and Related Statistical Multiplexer Performance. IEEE J. on Select. Areas in Comm. 4(6), 856–868 (1986)

    Article  Google Scholar 

  4. Hekmat, R.: Ad-Hoc Networks: Fundamental Properties and Network Topologies. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  5. Karl, H., Willig, A.: Protocols and Architectures for Wireless Sensor Networks. John Wiley and Sons, Chichester (2005)

    Book  Google Scholar 

  6. Kobayashi, H.: Application of the Diffusion Approximation to Queueing Networks I: Equilibrium Queue Distributions. J. of the ACM 21(2), 316–328 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  7. Kobayashi, H.: Application of the Diffusion Approximation to Queueing Networks II: Nonequilibrium Distributions and Applications to Computer Modeling. J. of the ACM 21(3), 459–469 (1974)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kobayashi, H., Onozato, Y., Huynh, D.: An Approximation Method for Design and Analysis of an ALOHA System. IEEE Trans. on Commun. 25(1), 148–157 (1977)

    Article  Google Scholar 

  9. Kobayashi, H.: Steady State Approximation Analysis for ATM Multiplexer by Diffusion Process Without Reflection Barrier. In: Proc. the Symp. on Performance Models for Information Communications Networks, pp. 309–320 (1994)

    Google Scholar 

  10. Kobayashi, K., Takahashi, Y.: Steady-State Analysis of ATM Multiplexer with Variable Input Rate Through Diffusion Approximation. Performance Evaluation 23, 163–184 (1995)

    Article  MATH  Google Scholar 

  11. Kochhal, M., Schwiebert, L., Gupta, S.: Role-Based Hierarchical Self-Organization for Wireless Ad Hoc Sensor Networks. In: Proc. of the 2nd ACM Int. Workshop on Wireless Sensor Networks and Applications (WSNA), San Diego, CA, pp. 98–107 (2003)

    Google Scholar 

  12. Ray, S., Starobinski, D., Carruthers, J.B.: Performance of Wireless Networks Networks with Hidden Nodes: A Queueing-theoretic Analysis. Computer Communications 28(10), 1179–1192 (2005)

    Article  Google Scholar 

  13. Simonian, A.: Stationary Analysis of a Fluid Queue with Input Rate Varying as an Ornstein-Uhlenbeck Process. SIAM, J. Appl. Math. 51(3), 828–842 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  14. Tickoo, O., Sikdar, B.: A Queueing Model for Finite Load IEEE 802.11 Random Access MAC. In: Proc. of IEEE ICC, Paris, pp. 175–179 (2004)

    Google Scholar 

  15. Zeng, G., Zhu, H., Chlamtac, I.: A Novel Queueing Model for 802.11 Wireless LANs. In: Proc. of WNCG Wireless Networking Symposium (2003)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Martyna, J. (2009). A Diffusion Approximation Analysis of Multilevel Ad Hoc and Sensor Networks. In: Ruiz, P.M., Garcia-Luna-Aceves, J.J. (eds) Ad-Hoc, Mobile and Wireless Networks. ADHOC-NOW 2009. Lecture Notes in Computer Science, vol 5793. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04383-3_10

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04383-3_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04382-6

  • Online ISBN: 978-3-642-04383-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics