Transport on Coupled Spatial Networks

Abstract

Transport processes on spatial networks are representative of a broad class of real world systems which, rather than being independent, are typically interdependent. We propose a measure of utility to capture key features that arise when such systems are coupled together. The coupling is defined in a way that is not solely topological, relying on both the distribution of sources and sinks, and the method of route assignment. Using a toy model, we explore relevant cases by simulation. For certain parameter values, a picture emerges of two regimes. The first occurs when the flows go from many sources to a small number of sinks. In this case, network utility is largest when the coupling is at its maximum and the average shortest path is minimized. The second regime arises when many sources correspond to many sinks. Here, the optimal coupling no longer corresponds to the minimum average shortest path, as the congestion of traffic must also be taken into account. More generally, results indicate that coupled spatial systems can give rise to behavior that relies subtly on the interplay between the coupling and randomness in the source-sink distribution.

Percolation in multiplex networks with overlap

“…[18]. Other examples of multiplexes can be found in transportation networks, where cities can be connected by roads, railways, waterways, or airline connections [10,11,19], or brain networks where different regions of the brain belong at the same time to the functional network of brain activity and to the structural brain network [14].…”

“…In fact, different models of multiplex structure have been formulated [20][21][22][23], critical phenomena and dynamical processes have been characterized on multiplex structures [6,[24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40], and finally new structural measures have been introduced and evaluated in large multiplex data sets [10][11][12][13]. The theoretical interest has been partly sparked by the discovery [6,[24][25][26] that the robustness properties of a multiplex formed by interdependent networks is strongly affected by its multilayer structure.…”

“…Recently, it has become clear that in order to fully investigate the properties of a large variety of complex systems such as energy supply networks [6], complex infrastructures [7][8][9][10][11], social networks [12], climatic systems [13], and brain networks [14], it is necessary to consider their multilayer structure [15]. Each layer corresponds to a network with a specific function, but the entire complex system requires multiple layers operating in a coupled way and forming an interacting set of networks.…”

Statistical mechanics of multiplex networks: Entropy and overlap

“…The offshoot of the network theory fundamental insights is that for us working in statistical mechanics it is now possible -in a sense it is mandatory to move into the field to shed light on the complexity on interdependent networks and multiplexes. In this context, new measures for multiplex [8,16,17] and new models of growing multiplexes [18,19] have been proposed. Moreover, several works have studied dynamical processes taking place on multiplexes and interacting networks and new surprising phenomena have been observed in this context involving percolation [14,[20][21][22], cascades [23], diffusion [24], epidemic spreading [25] and cooperation [26],opinion dynamics [27] and community detection [7,28,29].…”

Suppressing traffic-driven epidemic spreading by use of the efficient routing protocol

“…Epidemic spreading [1,2,3,4,5,6,7,8,9,10,11,12] and traffic dynamics [13,14,15,16,17,18,19,20] on complex networks have attracted much attention in the past decade. For a long time, the two types of dynamical processes have been studied independently.…”