Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics and Stochastic Analysis
Volume 2008, Article ID 518214, 25 pages
http://dx.doi.org/10.1155/2008/518214
Research Article

A Fluid Model for a Relay Node in an Ad Hoc Network: Evaluation of Resource Sharing Policies

1Korteweg-de Vries Institute, University of Amsterdam, Plantage Muidergracht 24, 1018 Amsterdam, The Netherlands
2CWI, P.O. Box 94079, 1090 Amsterdam, The Netherlands
3EURANDOM, Eindhoven, The Netherlands
4University of Twente, P.O. Box 217, 7500 , Enschede, The Netherlands

Received 3 August 2007; Accepted 6 May 2008

Academic Editor: Hans Daduna

Copyright © 2008 Michel Mandjes and Werner Scheinhardt. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. T. Bheemarjuna Reddy, I. Karthigeyan, B. S. Manoj, and C. Siva Ram Murthy, “Quality of service provisioning in ad hoc wireless networks: a survey of issues and solutions,” Ad Hoc Networks, vol. 4, no. 1, pp. 83–124, 2006. View at Publisher · View at Google Scholar
  2. F. Roijers, H. van den Berg, and M. Mandjes, “Fluidflow modeling of a relay node in an IEEE 802.11 wireless ad-hoc network,” in Proceedings of the 20th International Teletraffic Congress on Managing Traffic Performance in Converged Networks, pp. 321–334, Ottawa, Canada, June 2007. View at Publisher · View at Google Scholar
  3. H. van den Berg, M. Mandjes, and F. Roijers, “Performance modeling of a bottleneck node in an IEEE 802.11 ad-hoc network,” in Proceedings of the 5th International Conference on Ad-Hoc, Mobile, and Wireless Networks, T. Kunz and S. S. Ravi, Eds., vol. 4104 of Lecture Notes in Computer Science, pp. 321–336, Ottawa, Canada, August 2006. View at Publisher · View at Google Scholar
  4. M. Mandjes and F. Roijers, “A fluid system with coupled input and output, and its application to bottlenecks in ad hoc networks,” Queueing Systems, vol. 56, no. 2, pp. 79–92, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. D. Anick, D. Mitra, and M. M. Sondhi, “Stochastic theory of a data-handling system with multiple sources,” The Bell System Technical Journal, vol. 61, no. 8, pp. 1871–1894, 1982. View at Google Scholar · View at MathSciNet
  6. L. Kosten, “Stochastic theory of data-handling systems with groups of multiple sources,” in Performance of Computer-Communication Systems, H. Rudin and W. Bux, Eds., pp. 321–331, Elsevier, Amsterdam, The Netherlands, 1984. View at Google Scholar · View at MathSciNet
  7. M. Mandjes, D. Mitra, and W. Scheinhardt, “Models of network access using feedback fluid queues,” Queueing Systems, vol. 44, no. 4, pp. 365–398, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. P. Sonneveld, “Some properties of the generalized eigenvalue problem Mx=λ(ΓcI)x,where M is the infinitesimal generator of a Markov process, and Γ is a real diagonal matrix,” Department of Applied Mathematical Analysis, Delft University of Technology, Delft, The Netherlands, 2004. View at Google Scholar · View at MathSciNet
  9. E. A. van Doorn, A. A. Jagers, and J. S. J. de Wit, “A fluid reservoir regulated by a birth-death process,” Stochastic Models, vol. 4, no. 3, pp. 457–472, 1988. View at Google Scholar · View at MathSciNet
  10. A. I. Elwalid and D. Mitra, “Analysis and design of rate-based congestion control of high-speed networks—I: stochastic fluid models, access regulation,” Queueing Systems, vol. 9, no. 1-2, pp. 29–64, 1991. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. S. Asmussen, Ruin Probabilities, vol. 2 of Advanced Series on Statistical Science and Applied Probability, World Scientific, River Edge, NJ, USA, 2000. View at MathSciNet
  12. J. Abate and W. Whitt, “Numerical inversion of Laplace transforms of probability distributions,” ORSA Journal on Computing, vol. 7, no. 1, pp. 36–43, 1995. View at Google Scholar · View at MathSciNet
  13. P. den Iseger, “Numerical transform inversion using Gaussian quadrature,” Probability in the Engineering and Informational Sciences, vol. 20, no. 1, pp. 1–44, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. M. Mandjes and A. Ridder, “Finding the conjugate of Markov fluid processes,” Probability in the Engineering and Informational Sciences, vol. 9, no. 2, pp. 297–315, 1995. View at Google Scholar · View at MathSciNet
  15. M. Mandjes and B. Zwart, “Large deviations of sojourn times in processor sharing queues,” Queueing Systems, vol. 52, no. 4, pp. 237–250, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. G. Fayolle and R. Iasnogorodski, “Two coupled processors: the reduction to a Riemann-Hilbert problem,” Zeitschrift für Wahrscheinlichkeitstheorie und Verwandte Gebiete, vol. 47, no. 3, pp. 325–351, 1979. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  17. J. W. Cohen, “Some results on regular variation for distributions in queueing and fluctuation theory,” Journal of Applied Probability, vol. 10, pp. 343–353, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  18. A. G. Pakes, “On the tails of waiting-time distributions,” Journal of Applied Probability, vol. 12, no. 3, pp. 555–564, 1975. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  19. A. P. Zwart and O. J. Boxma, “Sojourn time asymptotics in the M/G/1 processor sharing queue,” Queueing Systems, vol. 35, no. 1–4, pp. 141–166, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  20. J. Crowcroft, R. Gibbens, F. Kelly, and S. Östring, “Modelling incentives for collaboration in mobile ad hoc networks,” Performance Evaluation, vol. 57, no. 4, pp. 427–439, 2004. View at Publisher · View at Google Scholar
  21. J. P. Göbel, A. Krzesinski, and M. Mandjes, “Analysis of an ad hoc network with autonomously moving nodes,” in Proceedings of the Australasian Telecommunication Networks and Applications Conference (ATNAC '07), pp. 41–46, Christchurch, New Zealand, December 2007. View at MathSciNet