Skip to main content

Advertisement

Log in

Quantitative Stability Estimates in Queues with Server Vacation

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

The derivation of inequalities with exact constants for stochastic models of complex systems is the specific character of the strong stability method. In this paper we obtain quantitative stability estimates for the M/G/1//N system with multiple vacations and exhaustive service.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. A. Aïssani, “An MX/G/1 retrial queue with unreliable server and vacations,” in: Proceedings of the 17th European Simulation Multiconference, Nottingham, UK (2003), pp. 175–180.

    Google Scholar 

  2. D. Aïssani and N.V. Kartashov, “Ergodicity and stability of Markov chains with respect to operator topology in the space of transition kernels,” Dokl. Akad. Nauk Uk. SSR, 12, No. 3, 1–4 (1983).

    Google Scholar 

  3. D. Aïssani and N.V. Kartashov, “Strong stability of imbedded Markov chains in an M/G/1 System,” Theory Probab. Math. Stat., 29, 1–5 (1984).

    Google Scholar 

  4. J. R. Artalejo and G. I. Falin, “Stochastic decomposition for retrial queues,” Oper. Res., 2, No. 2, 329–342 (1994).

    MATH  MathSciNet  Google Scholar 

  5. A. A. Borovkov, Ergodicity and Stability of Stochastic Processes, John Wiley (1998).

  6. R. B. Cooper, Introduction to Queueing Theory, North-Holland, New York (1981).

    Google Scholar 

  7. T.K. Das and M. A. Woltman, “Analysis of asymmetric patrolling repairman systems,” Eur. J. Oper. Res., 64, 45–60 (1990).

    Article  Google Scholar 

  8. B.T. Doshi, “Queueing systems with vacations — A Survey,” Queueing Syst., 1, 129–166 (1986).

    Article  MathSciNet  Google Scholar 

  9. C. F. Ipsen and C. D. Meyer, “Uniform stability of Markov chains,” Siam. J. Matrix, 15, No. 4, 1061–1074 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  10. V. V. Kalashnikov and G. S. Tsitsiashvili, “On the stability of queueing systems with respect to disturbances of their distribution functions,” Queueing Theory and Reliability, 211–217 (1971).

  11. N. V. Kartashov, “Strong stability of Markov chains,” J. Sov. Math, 34, 1493–1498 (1986).

    Article  MATH  Google Scholar 

  12. N.V. Kartashov, Strong Stable Markov Chains, VSP, Utrecht (1996).

    MATH  Google Scholar 

  13. S. T. Rachev, “The problem of stability in queueing theory,” Queueing Syst., 4, 287–318 (1989).

    Article  MATH  MathSciNet  Google Scholar 

  14. F. Rahmoune and D. Aïssani, “Approximation in reparable reliability systems with preventive maintenance,” in: Proceedings of the 5th Multidisciplinary International Conference Quality and Dependability, Bordeaux, France (2005).

    Google Scholar 

  15. T. Saaty, Elements of Queueing Theory and Applications. McGraw–Hill, New York (1961).

    Google Scholar 

  16. A. L. Scherr, An Analysis of Time–Shared Computer Systems, MIT Press, Cambridge (1967).

    MATH  Google Scholar 

  17. D. Stoyan, Comparaison Methods For Queueing Models and Others Stochastic Models, Wiley, New York (1983).

    Google Scholar 

  18. J. Sztrik, Finite source queueing systems and their applications, Technical Report, University of Debrecen, Institute of Mathematics and Inforamatics, Deparatement of Information Technology (2001).

  19. H. Takagi, “M/G/1//N queues with server vacations and exhaustive service,” Oper. Res., 42, No. 5, 926–939 (1994).

    Article  MATH  MathSciNet  Google Scholar 

  20. A. Tedijanito, “Stochastic comparaisons in vacations models,” Commun. Stat.-Stoch. Models, 7, No. 1, 125–135 (1991).

    Article  Google Scholar 

  21. V.M. Zolotarev, “On the continuity of stochastic sequences generated by recurrent processes,” Theory Probab. Appl., 20, 819–832 (1975).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding authors

Correspondence to F. Rahmoune or D. Aïssani.

Additional information

Proceedings of the XXVI International Seminar on Stability Problems for Stochastic Models, Sovata-Bai, Romania, August 27 – September 2, 2006.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rahmoune, F., Aïssani, D. Quantitative Stability Estimates in Queues with Server Vacation. J Math Sci 200, 480–485 (2014). https://doi.org/10.1007/s10958-014-1932-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-014-1932-x

Keywords

Navigation