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    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/62717


    Title: A duality relation between the workload and attained waiting time in FCFS G/G/s queues
    Authors: 姚怡慶
    Yao,Yi-Ching
    Contributors: 統計系
    Keywords: Duality;reverse time;sample path;workload process
    Date: 2013.03
    Issue Date: 2013-12-19 11:56:38 (UTC+8)
    Abstract: Sengupta (1989) showed that, for the first-come-first-served (FCFS) G/G/I queue, the workload and attained waiting time of a Customer in service have the same stationary distribution. Sakasegawa and Wolff (1990) derived a sample path version of this result, showing that the empirical distribution of the workload values over a busy period of a given sample path is identical to that of the attained waiting time values over the same period. For a given sample path of an FCFS GIG/s queue, we construct a dual sample path of a dual queue which is FCFS G/G/s in reverse time. It is shown that the workload process on the original sample path is identical to the total attained waiting time process on the dual sample path. As an application of this duality relation, we show that, for a time-stationary FCFS M/M/s/k queue, the workload process is equal in distribution to the time-reversed total attained waiting time process.
    Relation: Journal of Applied Probability, 50(1), 300-307
    Data Type: article
    DOI link: http://dx.doi.org/10.1239/jap/1363784441
    DOI: 10.1239/jap/1363784441
    Appears in Collections:[Department of Statistics] Periodical Articles

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