Flow Networks : 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

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.