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We study a simple swarming model on a two-dimensional lattice where the self-propelled particles exhibit a tendency to align ferromagnetically. Volume exclusion effects are present: particles can only hop to a neighboring node if the node…
This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network…
An intrinsic branching structure within the transient random walk on a strip in a random environment is revealed. As applications, which enables us to express the hitting time explicitly, and specifies the density of the absolutely…
A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers,…
We analyze a class of Signal-to-Interference-and-Noise-Ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. In contrast to previous studies on the SINR graphs, we consider both a…
Recent microfluidic experiments revealed that large particles advected in a fluidic loop display long-range hydrodynamic interactions. However, the consequences of such couplings on the traffic dynamics in more complex networks remain…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
We study the problem of maintaining a breadth-first spanning tree (BFS tree) in partially dynamic distributed networks modeling a sequence of either failures or additions of communication links (but not both). We present deterministic…
Practical wireless networks are finite, and hence non-stationary with nodes typically non-homo-geneously deployed over the area. This leads to a location-dependent performance and to boundary effects which are both often neglected in…
Navigation in complex and noisy environments is a key issue in diverse fields from biology to engineering. Despite extensive progress in numerical optimization methods for computing navigation policies, insights into how disorder reshapes…
Internet is known to display a highly heterogeneous structure and complex fluctuations in its traffic dynamics. Congestion seems to be an inevitable result of user's behavior coupled to the network dynamics and it effects should be…
The one-dimensional Brownian motion starting from the origin at time $t=0$, conditioned to return to the origin at time $t=1$ and to stay positive during time interval $0 < t < 1$, is called the Bessel bridge with duration 1. We consider…
We study the routing problem for vehicles with limited energy through a network of inhomogeneous charging nodes. This is substantially more complicated than the homogeneous node case studied in [1]. We seek to minimize the total elapsed…
Consider the following random spatial network: in a large disk, construct a network using a stationary and isotropic Poisson line process of unit intensity. Connect pairs of points using the network, with initial / final segments of the…
Liquid diodes are surface structures that facilitate the flow of liquids in a specific direction. When these structures are within the capillary regime, they promote liquid transport without the need for external forces. In nature, they are…
We numerically investigate the transport of a suspended overdamped Brownian particle which is driven through a two-dimensional rectangular array of circular obstacles with finite radius. Two limiting cases are considered in detail, namely,…
Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -- streets, tracks, etc. -- are inherently undirected and directions are only imposed on them to reduce the danger of…
We study the performance of wireless links for a class of Poisson networks, in which packets arrive at the transmitters following Bernoulli processes. By combining stochastic geometry with queueing theory, two fundamental measures are…
Network flows often exhibit a hierarchical tree-like structure that can be attributed to the minimisation of dissipation. The common feature of such systems is a single source and multiple sinks (or vice versa). In contrast, here we study…
We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…