Related papers: Random road networks: the quadtree model
We investigate graph representation learning approaches that enable models to generalize across graphs: given a model trained using the representations from one graph, our goal is to apply inference using those same model parameters when…
Air pollution can be studied in the urban structure regulated by transport networks. Transport networks can be studied as geometric and topological graph characteristics through designed models. Current studies do not offer a comprehensive…
Every human likes choices. But today's fast route planning algorithms usually compute just a single route between source and target. There are beginnings to compute alternative routes, but this topic has not been studied thoroughly. Often,…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
The scientific field of traffic engineering encompasses a rich set of mathematical techniques, as well as researchers with entirely different backgrounds. This paper provides an overview of what is currently the state-of-the-art with…
We present an analysis of the topologies of a class of networks which are optimal in terms of the requirements of having as short a route as possible between any two nodes while yet keeping the congestion in the network as low as possible.…
Road networks are characterised by several structural and geometric properties. Their topological structure determines partially its hierarchical arrangement, but since these are networks that are spatially situated and, therefore,…
We consider two variational models for transport networks, an urban planning and a branched transport model, in which the degree of network complexity and ramification is governed by a small parameter $\varepsilon>0$. Smaller $\varepsilon$…
Structure and dynamics of complex networks usually deal with degree distributions, clustering, shortest path lengths and other graph properties. Although these concepts have been analysed for graphs on abstract spaces, many networks happen…
Generative network models are extremely useful for understanding the mechanisms that operate in network formation and are widely used across several areas of knowledge. However, when it comes to bipartite networks -- a class of network…
We study a minimal model of traffic flows in complex networks, simple enough to get analytical results, but with a very rich phenomenology, presenting continuous, discontinuous as well as hybrid phase transitions between a free-flow phase…
The theory of linear transports along paths in vector bundles, generalizing the parallel transports generated by linear connections, is developed. The normal frames for them are defined as ones in which their matrices are the identity…
In this paper, we introduce and test our algorithm to create a road network representation for city-scale active transportation simulation models. The algorithm relies on open and universal data to ensure applicability for different cities…
Optimal paths connecting randomly selected network nodes and fixed routers are studied analytically in the presence of non-linear overlap cost that penalizes congestion. Routing becomes increasingly more difficult as the number of selected…
There are two prominent paradigms to the modeling of networks: in the first, referred to as the mechanistic approach, one specifies a set of domain-specific mechanistic rules that are used to grow or evolve the network over time; in the…
The objective of this paper is to initiate a qualitative analysis of dynamic flow in traffic networks by using the competitive equilibrium model of multiple market systems. A network is modeled as a dynamic graph where routes (edges) are…
In this paper we will provide an introductory understanding of random graph models, and matchings in the case of Erdos-Renyi random graphs. We will provide a synthesis of background theory to this end. We will further examine pertinent…
We present elements of a typing theory for flow networks, where "types", "typings", and "type inference" are formulated in terms of familiar notions from polyhedral analysis and convex optimization. Based on this typing theory, we develop…
We introduce a class of generative network models that insert edges by connecting the starting and terminal vertices of a random walk on the network graph. Within the taxonomy of statistical network models, this class is distinguished by…
A prominent model for transportation networks is branched transport, which seeks the optimal transportation scheme to move material from a given initial to a final distribution. The cost of the scheme encodes a higher transport efficiency…