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.

Key Features

  • 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

Table of Contents



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


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"...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