A Tutorial Exposition of Various Methods for Analyzing Capacitated Networks
Ali Muhammad Ali Rushdi, Omar Mutab Alsalami
Journal of Advances in Mathematics and Computer Science · pp. 1–23 · Published 12 Aug 2020
10.9734/jamcs/2020/v35i630288Abstract
In order to assess the performance indexes of some practical systems having fixed channel capacities, such as telecommunication networks, power transmission systems or commodity pipeline systems, we propose various types of techniques for analyzing a capacitated network. These include Karnaugh maps, capacity-preserving network reduction rules associated with delta-star transformations, and a generalization of the max-flow min-cut theorem. All methods rely on recognizing the network capacity function as a random pseudo-Boolean function of link successes; a fact that allows the expected value of this function to be easily obtainable from its sum-of-products expression. This network capacity has certain advantages for representation of nonbinary discrete random functions, mostly employed in the analysis of flow networks. Five tutorial examples demonstrate the afore-mentioned methods and illustrate their computational advantages over the exhaustive state enumeration method.
References (42)
- 1 Flows in networks
- 2 Boolean Methods in Operations Research and Related Areas [DOI]
- 3 Boolean Functions: Theory, Algorithms, and Applications
- 4 On reliability evaluation of a capacitated‐flow network in terms of minimal pathsets [DOI]
- 5 Reliability evaluation of a limited-flow network in terms of minimal cutsets [DOI]
- 6 Risk analysis in engineering
- 7 Digital Logic And Computer Design
- 8 Computing Maximum Flow with Augmenting Electrical Flows [DOI]
- 9 Applied Combinatorics
- 10 Reliability Evaluation of a Flow Network [DOI]
- 11 Network Flow Algorithms [DOI]
- 12 A Simple Method to Verify All d -Minimal Path Candidates of a Limited-Flow Network and its Reliability [DOI]
- 13 Evaluating Reliability/Survivability of Capacitated Wireless Networks [DOI]
- 14 Karnaugh-Map Utility in Medical Studies: The Case of Fetal Malnutrition [DOI]
- 15 Utilization of Karnaugh Maps in Multi-Value Qualitative Comparative Analysis [DOI]
- 16 Reliability Analysis of a Commodity-Supply Multi-State System Using the Map Method [DOI]
- 17 System-Reliability Evaluation Techniques for Complex/Large SystemsߞA Review [DOI]
- 18 Recent Developments in Computing of System-Reliability [DOI]
- 19 Uncertainty Analysis of Fault-Tree Outputs [DOI]
- 20 Using variable-entered karnaugh maps to solve boolean equations [DOI]
- 21 Switching-Algebraic Analysis of System Reliability [DOI]
- 22 Efficient Solution of Boolean Equations Using Variable-Entered Karnaugh Maps
- 23 Map Calculation of the Shapley-Shubik Voting Powers: An Example of the European Economic Community [DOI]
- 24 Calculation of Banzhaf Voting Indices Utilizing Variable-Entered Karnaugh Maps [DOI]
- 25 Handling Generalized Type-2 Problems of Digital Circuit Design via the Variable-Entered Karnaugh Map [DOI]
- 26 Integration of Reliability and Capacity in Performance Measure of a Telecommunication Network [DOI]
- 27 Symbolic Reliability Analysis with the Aid of Variable-Entered Karnaugh Maps [DOI]
- 28 How to Hand-Check a Symbolic Reliability Expression [DOI]
- 29 Efficient Estimation of Stochastic Flow Network Reliability [DOI]
- 30 Maximizing the Mean Number of Communicating Vertex Pairs in Series-Parallel Networks [DOI]
- 31 A Novel Method for Compact Listing of All Particular Solutions of a System of Boolean Equations [DOI]
- 32 Karnaugh-map Utilization in Coincidence Analysis [DOI]
- 33 Efficient algorithms for reliability analysis of planar networks - a survey [DOI]
- 34 A Classification Tree Based Approach for the Development of Minimal Cut and Path Vectors of a Capacitated Network [DOI]
- 35 A New Method for Boolean Function Simplification [DOI]
- 36 Review of Pseudo-Boolean Methods with Applications to Digital Filter Design [DOI]
- 37 An Alternative Index for the Reliability of Telecommunication Networks [DOI]
- 38 Design of a Digital Circuit for Integer Factorization via Solving the Inverse Problem of Logic [DOI]
- 39 Star-delta transformations of bidirectional branches in probabilistic flow networks [DOI]
- 40 Selective Deduction with the Aid of the Variable-Entered Karnaugh Maps [DOI]
- 41 Research on reliability index of a large communication network with domain partition and interconnection
- 42 Indexes of a telecommunication network [DOI]
Cited by 7
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O. M. Alsalami, A. Rushdi · Journal of Engineering Research and Reports · 2020
Mariem H. Lafta, Zahir Al-Khafaji · Lecture Notes in Networks and Systems · 2026
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