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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2018, Vol. 35 ›› Issue (1): 16-24.doi: 10.3969/j.issn.1005-3085.2018.01.002

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阈值调控的GI/Geo/1多重工作休假排队

马双凤,   徐秀丽,   靖   欣,   宋晓凤   

  1. 燕山大学理学院，秦皇岛  066004
  • 收稿日期:2016-01-13 接受日期:2016-12-30 出版日期:2018-02-15 发布日期:2018-04-15
  • 通讯作者: 徐秀丽 E-mail: tiannsh@sina.com
  • 基金资助:
    国家自然科学基金(11201408)；河北省自然科学基金(A2013203148).

The GI/Geo/1 Queue with Threshold and Multiple Working Vacations

MA Shuang-feng,  XU Xiu-li,  JING Xin,   SONG Xiao-feng   

  1. College of Science, Yanshan University, Qinhuangdao 066004
  • Received:2016-01-13 Accepted:2016-12-30 Online:2018-02-15 Published:2018-04-15
  • Contact: X. Xu. E-mail address: tiannsh@sina.com
  • Supported by:
    The National Natural Science Foundation of China (11201408); the Natural Science Foundation of Hebei Province (A2013203148).

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摘要： 在随机服务系统中，减少系统能源消耗，提高服务效率，是人们关注的焦点．基于此目的，本文加入阈值和休假中止策略，具体分析了离散时间GI/Geo/1工作休假排队系统．首先，建立了顾客到达前夕二维嵌入马尔可夫链，给出了GI/M/1型结构矩阵．其次，应用矩阵分析方法得到系统稳态队长分布，并进一步求得系统稳态下的平均队长和平均逗留时间等指标．最后，通过Matlab仿真软件，对模型中的性能指标给予刻画和展示，结果表明平均队长和平均逗留时间随阈值的增大而增大，随休假服务率的增加而减少．本文的结果将为交换虚通道以及无线网络等方面的研究提供一定的参考．

关键词: 阈值, GI/Geo/1, 多重工作休假, 矩阵分析

Abstract: In a random service system, people focus on decreasing system's cost and improving service rates. Based on the above purpose, this paper introduces the threshold and vacation interruption strategies into a discrete time GI/Geo/1 working vacation queue. Firstly, the two-dimensional embedded Markov chain before customers arrival instant is established, its transition probability matrix of GI/M/1-type is obtained. Secondly, the stationary queue length distribution is derived by the matrix analysis method, and the expected queue length and mean sojourn time are expressed. Finally, numerical analysis for the performance indices of the system are presented using the Matlab software, which shows that the expected queue length and sojourn time are both increasing with the increase of a threshold but decreasing with the increase of working vacation rates. It is expected that the results obtained here would provide some useful information for the research of SVC systems and wireless networks.

Key words: threshold, GI/Geo/1, multiple working vacations, matrix analysis

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