This chapter examines different methods for examining capacitated networks, with a focus on evaluating performance indicators for realistic systems with fixed channel capacities, such as telecommunication networks, power transmission systems, and commodity pipeline systems. Karnaugh diagrams, capacity-preserving network reduction rules associated with delta-star transformations, and a generalisation of the max-flow min-cut theorem are among the techniques discussed. Recognizing the problem is the foundation of all approaches. The expected value of the network capacity function can be easily obtained from its sum-of-products expression since it is a random pseudo-Boolean function of connection successes. This network capability has several advantages for representing nonbinary discrete random functions, which are commonly used in flow network analysis. Five tutorial examples explain the above-mentioned methods and show how they outperform the exhaustive state enumeration process in terms of computational efficiency. An appendix adds to the chapter by introducing the idea of a “probability-ready expression” for a Boolean-based coherent pseudo-Boolean function.
Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah, 21589, Saudi Arabia.
Omar Mutab Alsalami
Department of Electrical Engineering, Faculty of Engineering, Taif University, Taif, Kingdom of Saudi Arabia.
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