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Analysis of an M/G/1 Stochastic Clearing Queue in a 3-Phase Environment

Author

Listed:
  • Zhang Xiaoyan

    (School of Science, Nanjing University of Science and Technology, Nanjing210094, China)

  • Liu Liwei

    (School of Science, Nanjing University of Science and Technology, Nanjing210094, China)

  • Jiang Tao

    (School of Science, Nanjing University of Science and Technology, Nanjing210094, China)

Abstract

This paper studies a single server M/G/1 stochastic clearing queue operating in a 3-phase environment, where the time length of the first and third phase are assumed to follow exponential distributions, and the time length of the second phase is a constant value. At the completion of phase 1, the system moves to phase 2, and after a fixed time length, the system turns to phase 3. At the end of phase 3, all present customers in the system are forced to leave the system, then the system moves to phase 1 and restarts a new service cycle. Using the supplementary variable technique, we obtain the distribution for the stationary queue at an arbitrary epoch. We also derive the sojourn time distribution and the length of the server’s working time in a cycle.

Suggested Citation

  • Zhang Xiaoyan & Liu Liwei & Jiang Tao, 2015. "Analysis of an M/G/1 Stochastic Clearing Queue in a 3-Phase Environment," Journal of Systems Science and Information, De Gruyter, vol. 3(4), pages 374-384, August.
    • Handle: RePEc:bpj:jossai:v:3:y:2015:i:4:p:374-384:n:8
    DOI: 10.1515/JSSI-2015-0374
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    References listed on IDEAS

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    1. Economou, Antonis & Fakinos, Demetrios, 2003. "A continuous-time Markov chain under the influence of a regulating point process and applications in stochastic models with catastrophes," European Journal of Operational Research, Elsevier, vol. 149(3), pages 625-640, September.
    2. Epaminondas G. Kyriakidis & Theodosis D. Dimitrakos, 2005. "Computation of the Optimal Policy for the Control of a Compound Immigration Process through Total Catastrophes," Methodology and Computing in Applied Probability, Springer, vol. 7(1), pages 97-118, March.
    3. Boudali, Olga & Economou, Antonis, 2012. "Optimal and equilibrium balking strategies in the single server Markovian queue with catastrophes," European Journal of Operational Research, Elsevier, vol. 218(3), pages 708-715.
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