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Analysis of an ND-policy Geo/G/1 queue and its application to wireless sensor networks

Author

Listed:
  • Renbin Liu

    (Chongqing University of Technology
    University of Pretoria)

  • Attahiru Sule Alfa

    (University of Pretoria
    University of Manitoba)

  • Miaomiao Yu

    (Sichuan University of Science and Engineering)

Abstract

In this paper, we consider a discrete-time Geo/G/1 queue controlled by the combination of the N and D policies (called ND-policy). In this system, when there are N waiting customers or the service time backlog of all waiting customers exceeds a given threshold D, whichever emerges first, the idle server immediately resumes its service. Under this policy, since the service times of the customers arriving during the idle period, conditioned on the number of these customers, are dependent, and stochastically different from the service times of the customers arriving during the busy period, the customers in the system are classified into two types. Based on this classification, we first derive the probability generating functions and means of the queue length, idle and busy periods, service time backlog, waiting time and sojourn time, where the busy period is first studied in the discrete-time queues involving the D-policy. Next, by analyzing some results and flaws in the work of Gu et al. (J Syst Sci Complex, 2016. doi: 10.1007/s11424-016-4180-y ), we theoretically show the discrepancies that could arise if the conditional dependency of the service times of the customers arriving during the idle period is ignored. Finally, the numerical examples are provided to study the effects of different parameters on the mean queue length. Through an energy consumption optimization problem in wireless sensor networks, the application of our queueing model in the real world is illustrated, and the flaws that resulted from the results by Gu et al. (J Syst Sci Complex, 2016. doi: 10.1007/s11424-016-4180-y ) are numerically revealed.

Suggested Citation

  • Renbin Liu & Attahiru Sule Alfa & Miaomiao Yu, 2019. "Analysis of an ND-policy Geo/G/1 queue and its application to wireless sensor networks," Operational Research, Springer, vol. 19(2), pages 449-477, June.
    • Handle: RePEc:spr:operea:v:19:y:2019:i:2:d:10.1007_s12351-017-0304-y
    DOI: 10.1007/s12351-017-0304-y
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    References listed on IDEAS

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    1. Lotfi Tadj & Gautam Choudhury, 2005. "Optimal design and control of queues," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 13(2), pages 359-412, December.
    2. 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.
    3. J. George Shanthikumar, 1988. "On Stochastic Decomposition in M / G /1 Type Queues with Generalized Server Vacations," Operations Research, INFORMS, vol. 36(4), pages 566-569, August.
    4. K. R. Balachandran, 1973. "Control Policies for a Single Server System," Management Science, INFORMS, vol. 19(9), pages 1013-1018, May.
    5. O. J. Boxma, 1976. "Note--Note on a Control Problem of Balachandran and Tijms," Management Science, INFORMS, vol. 22(8), pages 916-917, April.
    6. Jewgeni H. Dshalalow, 1996. "On applications of excess level processes to (N,D)-policy bulk queueing systems," International Journal of Stochastic Analysis, Hindawi, vol. 9, pages 1-12, January.
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    Cited by:

    1. Zhang, Changzhen & Yang, Jun & Wang, Ning, 2023. "Timely reliability modeling and evaluation of wireless sensor networks with adaptive N-policy sleep scheduling," Reliability Engineering and System Safety, Elsevier, vol. 235(C).

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