The reliability of two-terminal multistate flow networks is evaluated using two simple (yet useful) methods in this chapter. The Variable-Entered Karnaugh Map (VEKM) and the Multi-Valued Karnaugh Map (MVKM) are the two Karnaugh map variants used in these two methods (MVKM). These two versions are critical in providing not only the visual perspective needed to write better future applications, but also adequate verification tools. We compare these two types of map methods to the exhaustive search method, which ensures conceptual consistency at the cost of computational performance. Our goal is to assess the probability mass function (pmf) in a variety of situations, including flow from a source node to a sink node in a capacitated network with a multistate capacity model for the ties. Each network connection has a different capacity, which is thought to be mutually exclusive. The system’s ability to successfully transmit at least a certain necessary system flow from the source (transmitter) to the sink (receiver) station is entirely dependent on its reliability. In order to achieve all successful states, the max-flow min-cut theorem is crucial. Two demonstrative examples with sufficient descriptions are given to illustrate the applicability of the proposed methods. In terms of pseudo-Boolean functions, the special case of a binary flow network is also considered.
Author (s) Details
Ali Muhammad Ali Rushdi
Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80200, 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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