| 一类带修理工休假可修系统解的存在唯一性及正则性分析 |
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| 引用本文： | 郭丽娜,任杨莉,张玲玲.一类带修理工休假可修系统解的存在唯一性及正则性分析[J].数学的实践与认识,2013,43(8). |
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| 作者姓名： | 郭丽娜 任杨莉 张玲玲 |
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| 作者单位： | 太原理工大学数学学院,山西太原,030024 |
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| 基金项目： | 数学天元青年基金 11226249，山西省青年基础研究计划项目 2012021015-5，太原理工大学校青年基金 2012L031，山西省自然基础研究计划项目 2012011004-4，国家自然科学专项基金 61250011 |
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| 摘 要： | 考虑一类修理工可多重延误休假的n部件串联可修复系统解的存在唯一性及正则性问题.通过将系统模型方程转化为一组算子积分方程,利用不动点理论讨论该系统局部解的存在唯一性问题,再由一致先验估计和连续延拓讨论系统整体解的存在唯一性问题,继而分析解的正则性问题.为解决复杂可修复系统解的存在唯一性及正则性提供了可行性方法,并且方法同样适用于排队论系统和其他类似系统.
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| 关 键 词： | 可修复系统 多重休假 局部解 整体解 解的正则性 不动点理论 |
The Unique Existence and Regularity of the Solution of a Repairable System with Repairman Vacation |
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| GUO Li-na
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REN Yang-li
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ZHANG Ling-ling.The Unique Existence and Regularity of the Solution of a Repairable System with Repairman Vacation[J].Mathematics in Practice and Theory,2013,43(8). |
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| Authors: | GUO Li-na REN Yang-li ZHANG Ling-ling |
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| Abstract: | The unique existence and regularity of the solution of a series repairable system with repairman following delayed-multiple vacation strategy is considered in this paper.The local solution of the system is discussed by transforming the system equations into operator integral equations and by using the fixed point theory.Then the global solution of the system is studied by a a uniform priori estimate and continuous extension.The regularity of the system solution is also analyzed at the end of the paper.This paper provides a practical method for the study of the unique existence and regularity of solutions for complex repairable systems with more than three variables.And this method can be also applied to the study of analogous systems,such as queueing systems. |
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| Keywords: | Keywords repairable system multiple vacations local solution global solution regularity of solution fixed point theory |
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