Traveling itinerary problem in a scheduled multimodal transportation network for a fixed sequence of cities.

Developing an efficient and economical journey plan in multimodal transportation networks is of significant and fast-growing importance, but it is still an annoying experience for a traveler. This paper aims to find the journey plan at a combined cross-border and inter-regional level when visiting a sequence of cities while utilizing several transport modes to reduce travel costs and planning time. We study a traveling itinerary problem in a scheduled multimodal transportation network with constraints on both arcs and nodes as a new extension of the shortest path problem. We formulate a 0-1 integer linear programming model for the traveling itinerary problem and develop an exact algorithm that finds a combined cross-border and inter-regional low costs journey plan. We present case studies based on real-world transport data to illustrate the usefulness and computational efficiency of the proposed approaches. We compare the results with the previously proposed approach to demonstrate the benefits of multimodal journeys. Finally, we compare the results with the solution obtained by the general-purpose 0-1 integer linear programming solver to evaluate the computational time.

Study of travellers' preferences towards travel offer categories and incentives in the journey planning context.

Nowadays, efforts to encourage changes in travel behaviour towards eco-friendly and active modes of transport are intensifying. A promising solution is to increase the use of sustainable public transport modes. Currently, a significant challenge related to this solution is the implementation of journey planners that will inform travellers about available travel solutions and facilitate decision-making by using personalisation techniques. This paper provides some valuable hints to journey planner developers on how to define and prioritise the travel offer categories and incentives to meet the travellers' expectations. The analysed data were obtained from a survey conducted in several European countries as part of the H2020 RIDE2RAIL project. The results confirm that travellers prefer to minimise travel time and stay on time. Also, incentives such as price discounts or class upgrades may play a crucial role in influencing the choices among travel solutions. By applying the regression analysis, it was found that preferences of travel offer categories and incentives are correlated with some demographic or travel-related factors. The results also show that subsets of significant factors strongly differ for particular travel offer categories and incentives, what underlines the importance of personalised recommendations in journey planners.

Large-scale test data set for location problems.

Designers of location algorithms share test data sets (benchmarks) to be able to compare performance of newly developed algorithms. In previous decades, the availability of locational data was limited. Big data has revolutionised the amount and detail of information available about human activities and the environment. It is expected that integration of big data into location analysis will increase the resolution and precision of input data. Consequently, the size of solved problems will significantly increase the demand on the development of algorithms that will be able to solve such problems. Accessibility of realistic large scale test data sets, with the number of demands points above 100,000, is very limited. The presented data set covers entire area of Slovakia and consists of the graph of the road network and almost 700,000 connected demand points. The population of 5.5 million inhabitants is allocated to the locations of demand points considering the residential population grid to estimate the size of the demand. The resolution of demand point locations is 100 m. With this article the test data is made publicly available to enable other researches to investigate their algorithms. The second area of its utilisation is the design of methods to eliminate aggregation errors that are usually present when considering location problems of such size. The data set is related to two research articles: "A Versatile Adaptive Aggregation Framework for Spatially Large Discrete Location-Allocation Problem" (Cebecauer and Buzna, 2017) [1] and "Effects of demand estimates on the evaluation and optimality of service centre locations" (Cebecauer et al., 2016) [2].

Controlling congestion on complex networks: fairness, efficiency and network structure.

We consider two elementary (max-flow and uniform-flow) and two realistic (max-min fairness and proportional fairness) congestion control schemes, and analyse how the algorithms and network structure affect throughput, the fairness of flow allocation, and the location of bottleneck edges. The more realistic proportional fairness and max-min fairness algorithms have similar throughput, but path flow allocations are more unequal in scale-free than in random regular networks. Scale-free networks have lower throughput than their random regular counterparts in the uniform-flow algorithm, which is favoured in the complex networks literature. We show, however, that this relation is reversed on all other congestion control algorithms for a region of the parameter space given by the degree exponent γ and average degree 〈k〉. Moreover, the uniform-flow algorithm severely underestimates the network throughput of congested networks, and a rich phenomenology of path flow allocations is only present in the more realistic α-fair family of algorithms. Finally, we show that the number of paths passing through an edge characterises the location of a wide range of bottleneck edges in these algorithms. Such identification of bottlenecks could provide a bridge between the two fields of complex networks and congestion control.

Geometric Correlations Mitigate the Extreme Vulnerability of Multiplex Networks against Targeted Attacks.

We show that real multiplex networks are unexpectedly robust against targeted attacks on high-degree nodes and that hidden interlayer geometric correlations predict this robustness. Without geometric correlations, multiplexes exhibit an abrupt breakdown of mutual connectivity, even with interlayer degree correlations. With geometric correlations, we instead observe a multistep cascading process leading into a continuous transition, which apparently becomes fully continuous in the thermodynamic limit. Our results are important for the design of efficient protection strategies and of robust interacting networks in many domains.

Resilience of natural gas networks during conflicts, crises and disruptions.

Human conflict, geopolitical crises, terrorist attacks, and natural disasters can turn large parts of energy distribution networks offline. Europe's current gas supply network is largely dependent on deliveries from Russia and North Africa, creating vulnerabilities to social and political instabilities. During crises, less delivery may mean greater congestion, as the pipeline network is used in ways it has not been designed for. Given the importance of the security of natural gas supply, we develop a model to handle network congestion on various geographical scales. We offer a resilient response strategy to energy shortages and quantify its effectiveness for a variety of relevant scenarios. In essence, Europe's gas supply can be made robust even to major supply disruptions, if a fair distribution strategy is applied.

Fair sharing of resources in a supply network with constraints.

This paper investigates the effect of network topology on the fair allocation of network resources among a set of agents, an all-important issue for the efficiency of transportation networks all around us. We analyze a generic mechanism that distributes network capacity fairly among existing flow demands. The problem can be solved by semianalytical methods on a nearest-neighbor graph with one source and sink pair, when transport occurs over shortest paths. For this setup, we uncover a broad range of patterns of intersecting shortest paths as a function of the distance between the source and the sink. When the number of intersections is the maximum and the distance between the source and the sink is large, we find that a fair allocation implies a decrease of at least 50% from the maximum throughput. We also find that the histogram of the flow allocations assigned to the agents decays as a power law with exponent -1. Our semianalytical framework suggests possible explanations for the well-known reduction of the throughput in fair allocations. It also suggests that the combination of network topology and routing rules can lead to highly uneven (but fair) distributions of resources, a remark of caution to network designers.

Decelerated spreading in degree-correlated networks.

While degree correlations are known to play a crucial role for spreading phenomena in networks, their impact on the propagation speed has hardly been understood. Here we investigate a tunable spreading model on scale-free networks and show that the propagation becomes slow in positively (negatively) correlated networks if nodes with a high connectivity locally accelerate (decelerate) the propagation. Examining the efficient paths offers a coherent explanation for this result, while the k-core decomposition reveals the dependence of the nodal spreading efficiency on the correlation. Our findings should open new pathways to delicately control real-world spreading processes.

Robustness of trans-European gas networks.

Here, we uncover the load and fault-tolerant backbones of the trans-European gas pipeline network. Combining topological data with information on intercountry flows, we estimate the global load of the network and its tolerance to failures. To do this, we apply two complementary methods generalized from the betweenness centrality and the maximum flow. We find that the gas pipeline network has grown to satisfy a dual purpose. On one hand, the major pipelines are crossed by a large number of shortest paths thereby increasing the efficiency of the network; on the other hand, a nonoperational pipeline causes only a minimal impact on network capacity, implying that the network is error tolerant. These findings suggest that the trans-European gas pipeline network is robust, i.e., error tolerant to failures of high load links.

Synchronization in symmetric bipolar population networks.

We analyze populations of Kuramoto oscillators with a particular distribution of natural frequencies. Inspired by networks where there are two groups of nodes with opposite behaviors, as for instance, in power-grids where energy is either generated or consumed at different locations, we assume that the frequencies can take only two different values. Correlations between the value of the frequency of a given node and its topological localization are considered in both regular and random topologies. Synchronization is enhanced when nodes are surrounded by nodes of the opposite frequency. The theoretical result presented in this paper is an analytical estimation for the minimum value of the coupling strength between oscillators that guarantees the achievement of a globally synchronized state. This analytical estimation, which is in a very good agreement with numerical simulations, provides a better understanding of the effect of topological localization of natural frequencies on synchronization dynamics.

Transient dynamics increasing network vulnerability to cascading failures.

We study cascading failures in networks using a dynamical flow model based on simple conservation and distribution laws. It is found that considering the flow dynamics may imply reduced network robustness compared to previous static overload failure models. This is due to the transient oscillations or overshooting in the loads, when the flow dynamics adjusts to the new (remaining) network structure. The robustness of networks showing cascading failures is generally given by a complex interplay between the network topology and flow dynamics.

Efficient response to cascading disaster spreading.

We study the effectiveness of recovery strategies for a dynamic model of failure spreading in networks. These strategies control the distribution of resources based on information about the current network state and network topology. In order to assess their success, we have performed a series of simulation experiments. The considered parameters of these experiments are the network topology, the response time delay, and the overall disposition of resources. Our investigations are focused on the comparison of strategies for different scenarios and the determination of the most appropriate strategy. The importance of prompt response and the minimum sufficient quantity of resources are discussed as well.