# Flow Networks

## 1st Edition

**Analysis and optimization of repairable flow networks, networks with disturbed flows, static flow networks and reliability networks**

Repairable flow networks are a new area of research, which analyzes the repair and flow disruption caused by failures of components in static flow networks. This book addresses a gap in current network research by developing the theory, algorithms and applications related to repairable flow networks and networks with disturbed flows. The theoretical results presented in the book lay the foundations of a new generation of ultra-fast algorithms for optimizing the flow in networks after failures or congestion, and the high computational speed creates the powerful possibility of optimal control of very large and complex networks in real time. Furthermore, the possibility for re-optimizing the network flows in real time increases significantly the yield from real production networks and reduces to a minimum the flow disruption caused by failures. The potential application of repairable flow networks reaches across many large and complex systems, including active power networks, telecommunication networks, oil and gas production networks, transportation networks, water supply networks, emergency evacuation networks, and supply networks.

The book reveals a fundamental flaw in classical algorithms for maximising the throughput flow in networks, published since the creation of the theory of flow networks in 1956. Despite the years of intensive research, the classical algorithms for maximising the throughput flow leave highly undesirable directed loops of flow in the optimised networks. These flow loops are associated with wastage of energy and resources and increased levels of congestion in the optimised networks.

- Includes theory and practical examples to build a deep understanding of the issues
- Written by the leading scholar and researcher in this emerging field
- Features powerful software tools for analysis, optimization and control of repairable flow networks

Students, researchers, and professionals in engineering, computing, and mathematics who work with networks.

Dedication

Preface

1. Flow Networks – Existing Analysis Approaches and Limitations

1.1 Repairable Flow Networks and Static Flow Networks

1.2 Repairable Flow Networks and Stochastic Flow Networks

1.3 Networks with Disturbed Flows and Stochastic Flow Networks

1.4 Performance of Repairable Flow Networks

2. Flow Networks and Paths – Basic Concepts, Conventions and Algorithms

2.1 Basic Concepts and Conventions: Data Structures for Representing Flow Networks

2.2 Pseudo-Code Conventions Used in the Algorithms

2.3 Efficient Representation of Flow Networks with Complex Topology

2.4 Paths: Algorithms Related to Paths in Flow Networks

2.5 Determining the Smallest-Cost Paths from the Source

2.6 Topological Sorting of Networks Without Cycles

2.7 Transforming Flow Networks

3. Key Concepts, Results and Algorithms Related to Static Flow Networks

3.1 Path Augmentation in Flow Networks

3.2 Bounding the Maximum Throughput Flow by the Capacity of s–t Cuts

3.3 A Necessary and Sufficient Condition for a Maximum Throughput Flow in a Static Network: The Max-Flow Min-Cut Theorem

3.4 Classical Augmentation Algorithms for Determining the Maximum Throughput Flow in Networks

3.5 General Push-Relabel Algorithm for Maximising the Throughput Flow in a Network

3.6 Applications

3.7 Successive Shortest-Path Algorithm for Determining the Maximum Throughput Flow at a Minimum Cost

4. Maximising the Throughput Flow in Single- and Multi-Commodity Networks: Removing Parasitic Directed Loops of Flow in Networks Optimised by Classical Algorithms

4.1 Eliminating Parasitic Directed Loops of Flow in Networks Optimised by Classical Algorithms

4.2 A Two-Stage Augmentation Algorithm for Determining the Maximum Throughput Flow in a Network

4.3 A New, Efficient Algorithm for Maximising the T

- No. of pages:
- 320

- Language:
- English

- Copyright:
- © 2013

- Published:
- 1st February 2013

- Imprint:
- Elsevier

- Print ISBN:
- 9780123983961

- Electronic ISBN:
- 9780123984067

Prof. Todinov’s background is Engineering, Mathematics and Computer Science. He holds a PhD and a higher doctorate (DEng) from the University of Birmingham. His name is associated with key results in the areas: Reliability and Risk, Flow networks, Probability, Statistics of inhomogeneous media, Theory of phase transformations, Residual stresses and Probabilistic fatigue and fracture.
M.Todinov pioneered research on: the theory of repairable flow networks and networks with disturbed flows, risk-based reliability analysis – driven by the cost of system failure, fracture initiated by flaws in components with complex shape, reliability dependent on the relative configurations of random variables and optimal allocation of a fixed budget to achieve a maximal risk reduction.
A sample of M.Todinov’s results include: introducing the hazard stress function for modelling the probability of failure of materials and deriving the correct alternative of the Weibull model; stating a theorem regarding the exact upper bound of properties from multiple sources and a theorem regarding variance of a distribution mixture; the formulation and proof of the necessary and sufficient conditions of the Palmgren-Miner rule and Scheil’s additivity rule; deriving the correct alternative of the Johnson-Mehl-Avrami-Kolmogorov equation and stating the dual network theorems for static flows networks and networks with disturbed flows.

Department of Mechanical Engineering and Mathematical Sciences, Oxford Brookes University, Oxford, UK

"...a solid publication targeted at graduate students and academia, as well as industry researchers...useful mainly due to the presentation of models and algorithms applicable to real network problems." *--IEEE Communications Magazine,*December 2014