Complex networks have been studied intensively for a decade, but research still focuses on the limited case of a single, non-interacting network. Modern systems are coupled together and therefore should be modelled as interdependent networks. A fundamental property of interdependent networks is that failure of nodes in one network may lead to failure of dependent nodes in other networks. This may happen recursively and can lead to a cascade of failures. In fact, a failure of a very small fraction of nodes in one network may lead to the complete fragmentation of a system of several interdependent networks. A dramatic real-world example of a cascade of failures (‘concurrent malfunction’) is the electrical blackout that affected much of Italy on 28 September 2003: the shutdown of power stations directly led to the failure of nodes in the Internet communication network, which in turn caused further breakdown of power stations. Here we develop a framework for understanding the robustness of interacting networks subject to such cascading failures. We present exact analytical solutions for the critical fraction of nodes that, on removal, will lead to a failure cascade and to a complete fragmentation of two interdependent networks. Surprisingly, a broader degree distribution increases the vulnerability of interdependent networks to random failure, which is opposite to how a single network behaves. Our findings highlight the need to consider interdependent network properties in designing robust networks.

http://absimage.aps.org/image/MAR10/MWS_MAR10-2009-001087.pdf

Catastrophic cascade of failures in interdependent networks

https://nottingham-repository.worktribe.com/preview/1141382/network%20connectivity.pdf

Multi-vehicle synchronized arc routing problem to restore post-disaster network connectivity

Network restoration and recovery in humanitarian operations: Framework, literature review, and research directions

The number of arc routing publications has increased significantly in the last decade. Such an increase justifies a second annotated bibliography, a sequel to Corberan and Prins Networks 56 2010, 50-69, discussing arc routing studies from 2010 onwards. These studies are grouped into three main sections: single vehicle problems, multiple vehicle problems and applications. Each main section catalogs problems according to their specifics. Section 2 is therefore composed of four subsections, namely: the Chinese Postman Problem, the Rural Postman Problem, the General Routing Problem GRP and Arc Routing Problems ARPs with profits. Section 3, devoted to the multiple vehicle case, begins with three subsections on the Capacitated Arc Routing Problem CARP and then delves into several variants of multiple ARPs, ending with GRPs and problems with profits. Section 4 is devoted to applications, including distribution and collection routes, outdoor activities, post-disaster operations, road cleaning and marking. As new applications emerge and existing applications continue to be used and adapted, the future of arc routing research looks promising. © 2017 Wiley Periodicals, Inc. NETWORKS, Vol. 703, 144-194 2017

An updated annotated bibliography on arc routing problems

After a disaster, restoring accessibility in the affected area is critical for response operations. We study two arc routing problems for clearing blocked roads. The first problem minimizes the time to reconnect the road network, while the second maximizes the total benefit gained by reconnecting network components within a time limit. For each problem, we develop a mixed integer programming formulation and two versions of a heuristic algorithm. We conduct computational experiments on Istanbul data and instances adapted from the literature. The heuristics achieve near-optimal or optimal solutions quickly in most of the tested instances.

Arc routing problems to restore connectivity of a road network

Multi-vehicle prize collecting arc routing for connectivity problem

Minimizing latency in post-disaster road clearance operations

Natural disasters impact transportation networks adversely and cause road sections to be damaged or blocked. The road network may even become disconnected, impeding accessibility between disaster-stricken areas and critical locations such as hospitals, relief aid depots and transportation hubs. In the immediate response phase, a set of blocked edges should be selected and restored to reconnect the transportation network. While locations of the disrupted roads can be identified using drone or satellite images, an accurate estimation of time to restore a road segment can be carried out only after expert observations on the field. In this article, we study a post-disaster road restoration problem modeled on an undirected edge-weighted graph with k blocked edges, where the unblocking time of a blocked edge is revealed online once the road restoration team visits an end-node of that blocked edge. The objective is to minimize the time at which the road network is reconnected. We first investigate the worst-case performance of online algorithms against offline optimal solutions by means of the competitive ratio. We prove that any online deterministic algorithm cannot achieve a competitive ratio better than 2 k − 1 . We also provide an optimal online algorithm that is proven to achieve this lower bound. In addition, to achieve good performance on realistic instances, we implement an algorithm that solves a mixed integer programming model each time new information is revealed. Since model solution is prohibitively time-consuming, we also propose a novel polynomial time online algorithm. We compare these two algorithms with two other benchmark online algorithms on both Istanbul road network instances and several other city instances from the literature. Our experiments show that the proposed polynomial time online algorithm performs superior to the benchmark ones and obtains solutions close to the offline optimum on all the tested instances.

An online optimization approach to post-disaster road restoration

We study how to allocate and route search-and-rescue teams to areas with trapped victims in a coordinated manner after a disaster. We propose two online strategies for these time-critical decisions considering the uncertainty about the operation times required to rescue the victims and the condition of the roads that may delay the operations. First, we follow the theoretical competitive analysis approach that takes a worst-case perspective and prove lower bounds on the competitive ratio of the two variants of the defined online problem with makespan and weighted latency objectives. Then, we test the proposed online strategies and observe their good performance against the offline optimal solutions on randomly generated instances.

/pdf/online-routing-and-scheduling-of-search-and-rescue-teams-2h6nkh7a12.pdf

Vahid Akbari

Papers

Multi-vehicle synchronized arc routing problem to restore post-disaster network connectivity

Multi-vehicle prize collecting arc routing for connectivity problem

Minimizing latency in post-disaster road clearance operations

An online optimization approach to post-disaster road restoration

Online routing and scheduling of search-and-rescue teams