多源多汇网络的极限范围与运行边界
作者:
作者单位:

1.天津大学 电气自动化与信息工程学院;2.天津大学 数学学院

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中图分类号:

O157.5

基金项目:

国家自然科学基金项目(面上项目)


Limit range and operation boundary of multi-source and multi-sink network
Author:
Affiliation:

1.School of Electrical and Information Engineering, Tianjin University;2.School of Mathematics, Tianjin University

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    摘要:

    文中首次得到了多源多汇网络的极限范围与运行边界。首先,定义了临界流,临界流是具有临界性的可行流,现有研究的最大流和堵塞流是临界流中的一部分。其次,首次得到多源多汇网络的所有临界流,并绘制成临界流曲线,它完整刻画了网络传输流量能力的极限范围,最大流流量位于曲线最高点、最小流流量位于曲线最低点。利用临界流确定了网络流的运行边界,在边界内部和边界上都是可行流,边界外都是不可行流。文中提出了多源多汇网络临界流、临界流曲线和运行边界的数学定义及求解方法。最后,展示了临界流曲线和运行边界在规划和运行领域中的用途。多源多汇网络模型更接近于实际网络,其临界流曲线和运行边界的发现,能帮助人们更深入了解实际网络运行的极限范围。

    Abstract:

    The limit range and operation boundary of multi-source and multi-sink network are obtained for the first time. Firstly, the critical flow was defined. The critical flow was a feasible flow with criticality. The maximum flow and blocking flow in existing researches were only part of the critical flow. Secondly, all critical flows of multi-source and multi-sink network were obtained for the first time and plotted as a critical flow curve (CF Curve). CF Curve completely described the limit range of the network transmission flow capacity, where the maximum flow was located at its highest point and the minimum flow was located at its lowest point. The critical flow was also used to determine the network operational boundary, inside which were feasible flows, and outside which were unfeasible flows. The mathematical definitions and solutions method of critical flow, CF Curve and operational boundary of multi-source and multi-sink network were proposed. Finally, the possible applications of the critical flow curve and the operational boundary in planning and operation fields were demonstrated. Since most real networks are the multi-source multi-sink networks, so the proposed of critical flow curve and operation boundary can help us to know the full limit range of network operation.

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历史
  • 收稿日期:2020-08-19
  • 最后修改日期:2020-12-04
  • 录用日期:2020-12-25
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