Modeling Wireless Sensor Networks Using Finite-Source Retrial Queues with Unreliable Orbit

  • Patrick Wüchner
  • János Sztrik
  • Hermann de Meer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6821)

Abstract

Motivated by the need for performance models suitable for modeling and evaluation of wireless sensor networks, we introduce a retrial queueing system with a finite number of homogeneous sources, unreliable servers, orbital search, and unreliable orbit. All random variables involved in model construction are assumed to be independent and exponentially distributed. Providing a generalized stochastic Petri net model of the system, steady-state analysis of the underlying continuous-time Markov chain is performed and steady-state performance measures are computed by the help of the MOSEL-2 tool. The main novelty of this investigation is the introduction of an unreliable orbit and its application to wireless sensor networks. Numerical examples are derived to show the influence of sleep/awake time ratio, message dropping, and message blocking on the senor nodes’ performance.

Keywords

performance evaluation unreliable finite-source retrial queue wireless sensor network energy efficiency self-organization 

References

  1. 1.
    Akyildiz, I.F., Vuran, M.C.: Wireless Sensor Networks. John Wiley & Sons (July 2010)Google Scholar
  2. 2.
    Almasi, B., Bolch, G., Sztrik, J.: Heterogeneous finite-source retrial queues. Journal of Mathematical Sciences 121(5), 2590–2596 (2004)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Almasi, B., Roszik, J., Sztrik, J.: Homogeneous finite-source retrial queues with server subject to breakdowns and repairs. Mathematical and Computer Modelling 42, 673–682 (2005)CrossRefMATHMathSciNetGoogle Scholar
  4. 4.
    Amador, J.: On the distribution of the successful and blocked events in retrial queues with finite number of sources. In: Proc. of the 5th Int’l Conf. on Queueing Theory and Network Applications, pp. 15–22 (2010)Google Scholar
  5. 5.
    Artalejo, J.R.: New results in retrial queueing systems with breakdown of the servers. Statistica Neerlandica 48, 23–36 (1994)CrossRefMATHMathSciNetGoogle Scholar
  6. 6.
    Artalejo, J.R.: Retrial queues with a finite number of sources. J. Korean Math. Soc. 35, 503–525 (1998)MATHMathSciNetGoogle Scholar
  7. 7.
    Artalejo, J.R., Gómez-Corral, A.: Retrial Queueing Systems: A Computational Approach. Springer, Heidelberg (2008)CrossRefMATHGoogle Scholar
  8. 8.
    Artalejo, J.R., Joshua, V.C., Krishnamoorthy, A.: An M/G/1 retrial queue with orbital search by the server. In: Artalejo, J.R., Krishnamoorthy, A. (eds.) Advances in Stochastic Modelling, pp. 41–54. Notable Publications Inc., NJ (2002)Google Scholar
  9. 9.
    Begain, K., Bolch, G., Herold, H.: Practical Performance Modeling – Application of the MOSEL Language. Kluwer Academic Publishers (2001)Google Scholar
  10. 10.
    Bolch, G., Greiner, S., de Meer, H., Trivedi, K.: Queueing Networks and Markov Chains, 2nd edn. John Wiley & Sons, New York (2006)CrossRefMATHGoogle Scholar
  11. 11.
    Chakravarthy, S.R., Krishnamoorthy, A., Joshua, V.C.: Analysis of a multi-server retrial queue with search of customers from the orbit. Performance Evaluation 63(8), 776–798 (2006)CrossRefGoogle Scholar
  12. 12.
    Dressler, F.: Self-Organization in Sensor and Actor Networks. John Wiley & Sons (2007)Google Scholar
  13. 13.
    Dudin, A.N., Krishnamoorthy, A., Joshua, V.C., Tsarenkov, G.V.: Analysis of the BMAP/G/1 retrial system with search of customers from the orbit. Eur. J. Operational Research 157(1), 169–179 (2004)CrossRefMATHGoogle Scholar
  14. 14.
    Falin, G., Templeton, J.: Retrial Queues. Chapman & Hall (1997)Google Scholar
  15. 15.
    Wang, J., Cao, J., Li, Q.: Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Systems 38, 363–380 (2001)CrossRefMATHMathSciNetGoogle Scholar
  16. 16.
    Wüchner, P., de Meer, H., Barner, J., Bolch, G.: A brief introduction to MOSEL-2. In: German, R., Heindl, A. (eds.) Proc. of 13th GI/ITG Conference on Measurement, Modelling and Evaluation of Computer and Communication Systems (MMB 2006), GI/ITG/MMB. University of Erlangen, VDE Verlag (2006)Google Scholar
  17. 17.
    Wüchner, P., de Meer, H., Bolch, G., Roszik, J., Sztrik, J.: Modeling finite-source retrial queueing systems with unreliable heterogeneous servers and different service policies using MOSEL. In: Al-Begain, K., Heindl, A., Telek, M. (eds.) ASMTA 2007 Conference, Prague, Czech Republic, pp. 75–80 (June 2007)Google Scholar
  18. 18.
    Wüchner, P., Sztrik, J., de Meer, H.: Homogeneous finite-source retrial queues with search of customers from the orbit. In: Proc. of 14th GI/ITG Conference on Measurement, Modelling and Evaluation of Computer and Communication Systems (MMB 2008), Dortmund, Germany (March 2008)Google Scholar
  19. 19.
    Wüchner, P., Sztrik, J., de Meer, H.: Finite-source M/M/S retrial queue with search for balking and impatient customers from the orbit. Computer Networks 53(8), 1264–1273 (2009)CrossRefMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2011

Authors and Affiliations

  • Patrick Wüchner
    • 1
  • János Sztrik
    • 2
  • Hermann de Meer
    • 1
  1. 1.Faculty of Informatics and MathematicsUniversity of PassauPassauGermany
  2. 2.Faculty of InformaticsUniversity of DebrecenDebrecenHungary

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