Batch Arrival Queueing Model with Unreliable Server

  • Authors

    • M. Seenivasan
    • K. S.Subasri
    https://doi.org/10.14419/ijet.v7i4.10.20910

    Received date: October 4, 2018

    Accepted date: October 4, 2018

    Published date: October 2, 2018

  • Busy State, Idle state, Matrix Geometric Method, Repair State, Stationary distribution, , Server breakdown.

  • Abstract

    The unreliable server with provision of temporary server in the context of application has been investigated. A temporary server is installed when the primary server is over loaded i.e., a fixed queue length of K-policy customers including the customer with the primary server has been build up. The primary server may breakdown while rendering service to the customers; it is sent for the repair. This type of queuing system has been investigated using Matrix Geometric Method to obtain the probabilities of the system steady state.

    AMS subject classification number— 60K25, 60K30 and 90B22.

  • References

    1. Aissani A, Unreliable queueing with repeated orders. Microelectron and Reliability, 33:2093-2106, 1993.
    2. Bhargava C. and M. Jain, Unreliable multi-server queuing system with modified vacation policy, OPSEARCH, doi:http://dx.doi.org/10.1007/s12597-013-0138-1, 2013.
    3. Chakaravarthy S.R., A multi-server synchronous vacation model with thresholds and a probabilistic decision rule, Ero. J. oper. Res., Vol.182, pp. 305-320, 2007.
    4. Eager D. L., Lazowska E. D. and J. Zahorjan, A comparison of receiver-initiated and sender-initiated adaptive load sharing, perf.Eval., Vol.6, pp.53-68, 1986.
    5. Gharbi, N. and M. Ioualalen, Numerical investigation of finite – source multi server system with different vacation policies, J. Comp. Appl. Math., Vol. 234, pp 625-635, 2010.
    6. Haridass M, and R. Arumuganathan , studied analysis of a bulk queue with unreliable server and single vacation, Int. J. Open Prob-lems Compt. Math., Vol. 1, No. 2, 2008
    7. Indra and Vijay Rajan, Studied queueing analysis of markovian queue having two heterogeneous server with catastrophes using ma-trix
    8. geometric technique, international Journal of statistics and systems, vol.12, pp.205-212, 2017.
    9. Jain M. and A. Jain, Working vacations queuing models with mul tiple types of server breakdowns, Appl. Math. model.vol.34,pp.1-13, 2010.
    10. Kalayanraman R. and M. Seenivasan, The stationary analysis of M/M/4/4+1 queueing model, Annamalai university Science Journal 46:103-110,2010.
    11. Kalayanraman R. and M. Seenivasan, The stationary analysis of M/M/5/5+1 queueing model with linear retrial rate, proceeding of the international Conference on Mathematical Science ( ICMS-2014) published by Elsevier, pp.749-753, 2014.
    12. Ke, j.C, Wu C.H. and Z.G Zhang, A Note on a multi server Queue with Vacations of Multiple Groups of Servers, Quant. Tech.Quant.Mgmt., Vol. 10, pp.513-525, 2013.
    13. Krishna Kumar B. and S.P Madheswari, An M/M/2 queuing sys tem with heterogeneous servers and multiple vacations, Math. Comput. Model., Vol. 41, pp. 1415- 1429, 2005.
    14. Kushner H. J, Heavy traffic analysis of controlled Queuing and Communication Networks Springer-Verlag, New York, 2001.
    15. Leite S.C. and M.D. Fragoso, Heavy traffic analysis of state- dependent parallel queues with trigger and an application to web search systems Perf.Eval.,Vol.67, pp.913-928, 2010.
    16. Neuts M.F, Markov chains with applications queueing theory, which have a matrix geometric invariant probability vector, Adv. Appl. Prob., Vol.10, pp.185-212, 1978.
    17. Neuts M.F, Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach. The Johns Hopkins University Press, Balti more, 1981.
    18. Neuts M.F and D. M. Lucantoni, A Markovian queue with N serv-ers subject to breakdowns and repairs, Management Science, 25, 849-861 1979.
    19. Parthasarathy P.R. and R. Sudhesh, Transient solution of a multi server Poisson queue with N-policy, Comput.Math.Appl, Vol.55,pp.550-562, 2008.
    20. Renisagaya Raj. M and B. Chandrasekar,, Matrix – Geometric Method for queueing model with subject to breakdown and N-Policy vacations, Mathematica Aeterna, Vol. 5, pp.917-926, 2015.
    21. Renisagaya Raj. M and B. Chandrasekar, Matrix – Geometric Method for queueing model with state-Dependent arrival of an un-reli able server and PH service, Mathematica Aeterna, Vol. 6, no.1 pp.107-1166, 2016.
    22. Vinod. B, Unreliable queueing system, Comp.oper. Res. 12, 323- 340(1985).

  • Downloads

  • How to Cite

    Seenivasan, M., & S.Subasri, K. (2018). Batch Arrival Queueing Model with Unreliable Server. International Journal of Engineering and Technology, 7(4.10), 269-273. https://doi.org/10.14419/ijet.v7i4.10.20910