Skip to main content
SpringerLink
Log in

Reliability analysis of complex communication systems

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

This paper deals with a first-come, first-served (FCFS) queueing model to analyze the asymptotic behavior of a heterogeneous finite-source communication system with a single processor. Each source and the processor are assumed to operate in independent random environments, allowing the arrival and service processes to be Markov-modulated ones. Each message is characterized by its own exponentially distributed source and processing time with parameter, depending on the state of the corresponding environment, that is, the arrival and service rates are subject to random fluctuations. Assuming that the arrival rates of the messages are many times greater than their service rates (“fast” arrival), it is shown that the time to the first system failure converges in distribution, under appropriate norming, to an exponentially distributed random variable. Some simple examples are considered to illustrate the effectiveness of the method proposed by comparing the approximate results to the exact ones.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. V. Anisimov, “Switching processes: Averaging principle, diffusion approximation, and applications,”Act. Appl. Math.,40, 95–141 (1995).

    Article  MATH  Google Scholar 

  2. V. V. Anisimov, “Asymptotic analysis of switching queueing systems under conditions of low and heavy loading; matrix-analytic methods in stochastic models,” in:Lecture Notes in Pure and Application Mathematical Series,183, Marcel Dekker (1996).

  3. V. V. Anisimov and J. Sztrik, “Asymptotic analysis of some controlled finite-source queueing systems,”Act. Cybern.,9, 27–38 (1989).

    MATH  Google Scholar 

  4. D. P. Gaver, P. A. Jacobs, and G. Latouche, “Finite birth-and-death models in randomly changing environments,”Adv. Appl. Probab.,16, 715–731 (1984).

    Article  MATH  Google Scholar 

  5. I. B. Gertsbakh, “Asymptotic methods in reliability theory: A review,”Adv. Appl. Probab.,16, 147–175 (1984).

    Article  MATH  Google Scholar 

  6. I. B. Gertsbakh,Statistical Reliability Theory, Marcel Dekker, New York (1989).

    MATH  Google Scholar 

  7. P. Harrison and N. M. Patel,Performance Modeling of Communication Networks and Computer Architectures, Addison-Wesley (1993).

  8. J. Keilson,Markov Chain Models—Rarity and Exponentiality, Springer, Berlin (1979).

    MATH  Google Scholar 

  9. D. D. Kouvatsos, R. Fretwell, and J. Sztrik, “Bounds on the effects of correlation in a stable MMPP/MMPP/1/N queue: An asymptotic approach,” in:Proceedings of Second Workshop on Performance Modeling and Evaluation of ATM Networks, Chapman and Hall, London (1995), pp. 261–281.

    Google Scholar 

  10. I. N. Kovalenko, “Rare events in queueing systems; A survey,”Queueing Syst.,16, 1–49 (1994).

    Article  MATH  Google Scholar 

  11. I. Mitrani,Modeling of Computer and Communication Systems, Cambridge Univ. Press, Cambridge (1987).

    Google Scholar 

  12. T. E. Stern and A. I. Elwalid, “Analysis of separable Markov-modulated rate models for information-handling systems,”Adv. Appl. Probab.,23, 105–139 (1989).

    Article  Google Scholar 

  13. J. Sztrik, “Modeling of a multiprocessor system in a randomly changing environment,”Perform. Evaluat.,17, 1–11 (1993).

    Article  MATH  Google Scholar 

  14. J. Sztrik and D. D. Kouvatsos, “Asymptotic analysis of a heterogeneous multiprocessor system in a randomly changing environment,”IEEE Trans. Soft. Engineer.,17, 1069–1075 (1991).

    Article  Google Scholar 

  15. J. Sztrik and L. Lukashuk, “Modeling of a communication system evolving in a random environment,”Acta Cybern.,10, 85–91 (1991).

    Google Scholar 

  16. J. Sztrik and R. Rigo, “On a closed communication system with fast sources and operating in Markovian environments,”J. Inform. Process. Cybernet, EIK,29, 241–246 (1993).

    MATH  Google Scholar 

  17. H. Takagi, “Bibliography on performance evaluation,” in:Stochastic Analysis of Computer and Communication Systems, North-Holland, Amsterdam (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Debrecen, P.O. Box 12, 4010, Debrecen, Hungary

    J. Sztrik

Authors
  1. J. Sztrik
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Supported by the Hungarian National Foundation for Scientific Research (grant No. OTKA T14974/95).

Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part II.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sztrik, J. Reliability analysis of complex communication systems. J Math Sci 99, 1476–1484 (2000). https://doi.org/10.1007/BF02673723

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02673723

Keywords

Search

Navigation