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

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dc.contributor.author Liu, Renbin
dc.contributor.author Alfa, Attahiru Sule
dc.contributor.author Yu, Miaomiao
dc.date.accessioned 2019-05-28T15:04:32Z
dc.date.available 2019-05-28T15:04:32Z
dc.date.issued 2019
dc.description.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. en_ZA
dc.description.department Electrical, Electronic and Computer Engineering en_ZA
dc.description.librarian hb2019 en_ZA
dc.description.sponsorship In part by the NRF funds for the SARChI Chair in Advanced Sensor Networks (South Africa) and the National Natural Science Foundation of China (No. 71301111). en_ZA
dc.description.uri http://link.springer.com/journal/12351 en_ZA
dc.identifier.citation Liu, R., Alfa, A.S. & Yu, M. Analysis of an ND-policy Geo/G/1 queue and its application to wireless sensor networks. Operational Research (2019). https://doi.org/10.1007/s12351-017-0304-y. NYP. en_ZA
dc.identifier.issn 1109-2858 (print)
dc.identifier.issn 1866-1505 (online)
dc.identifier.other 10.1007/s12351-017-0304-y
dc.identifier.uri http://hdl.handle.net/2263/69229
dc.language.iso en en_ZA
dc.publisher Springer en_ZA
dc.rights © Springer-Verlag Berlin Heidelberg 2017. The original publication is available at : http://link.springer.com/journal/12351. en_ZA
dc.subject ND-policy en_ZA
dc.subject Queue length en_ZA
dc.subject Service time backlog en_ZA
dc.subject Busy period en_ZA
dc.subject Energy consumption optimization en_ZA
dc.title Analysis of an ND-policy Geo/G/1 queue and its application to wireless sensor networks en_ZA
dc.type Postprint Article en_ZA


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