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Retrial queueing system with balking, optional service and vacation

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  • D. Arivudainambi
  • P. Godhandaraman

Abstract

In this study, we propose a single server retrial queueing system with balking, second optional service and single vacation. At the arrival epoch, if the server is busy, the arriving job join the orbit or balks the system whereas if the server is free, then the arriving job starts its service immediately. For each job, the server provides two phases of service. All the jobs demand the first essential service, whereas only some of the jobs demand for the second optional service. If the system is empty, then the server becomes inactive and begins a single vacation. If server comes back from the vacation, it does not go for another vacation even if the system is still empty at that time. The steady state distributions of the server state and the number of jobs in the orbit are obtained along with other performance measures. The effects of various parameters on the system performance are analyzed numerically. A general decomposition law for this retrial queueing system is established. Copyright Springer Science+Business Media New York 2015

Suggested Citation

  • D. Arivudainambi & P. Godhandaraman, 2015. "Retrial queueing system with balking, optional service and vacation," Annals of Operations Research, Springer, vol. 229(1), pages 67-84, June.
    • Handle: RePEc:spr:annopr:v:229:y:2015:i:1:p:67-84:10.1007/s10479-014-1765-5
    DOI: 10.1007/s10479-014-1765-5
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    References listed on IDEAS

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    1. S. W. Fuhrmann & Robert B. Cooper, 1985. "Stochastic Decompositions in the M / G /1 Queue with Generalized Vacations," Operations Research, INFORMS, vol. 33(5), pages 1117-1129, October.
    2. Linn I. Sennott & Pierre A. Humblet & Richard L. Tweedie, 1983. "Technical Note—Mean Drifts and the Non-Ergodicity of Markov Chains," Operations Research, INFORMS, vol. 31(4), pages 783-789, August.
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    Cited by:

    1. Anatoly Nazarov & János Sztrik & Anna Kvach & Tamás Bérczes, 2019. "Asymptotic analysis of finite-source M/M/1 retrial queueing system with collisions and server subject to breakdowns and repairs," Annals of Operations Research, Springer, vol. 277(2), pages 213-229, June.
    2. V., Saravanan & V., Poongothai & P., Godhandaraman, 2023. "Performance analysis of a multi server retrial queueing system with unreliable server, discouragement and vacation model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 214(C), pages 204-226.
    3. Sanga, Sudeep Singh & Jain, Madhu, 2019. "FM/FM/1 double orbit retrial queue with customers’ joining strategy: A parametric nonlinear programing approach," Applied Mathematics and Computation, Elsevier, vol. 362(C), pages 1-1.

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