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