Related papers: Nash Flows Over Time with Tolls
This paper considers a single link with traffic light boundary conditions at both ends, and investigates the traffic evolution over time with various signal and system configurations. A hydrodynamic model and a modified stochastic domain…
The problem of a car following a lead car driven with constant velocity is considered. To derive the governing equations for the following car dynamics a cost functional that ranks the outcomes of different driving strategies is…
The modelling of traffic flow using methods and models from physics has a long history. In recent years especially cellular automata models have allowed for large-scale simulations of large traffic networks faster than real time. On the…
We introduce a new model to study the oscillations of opposite flows sharing a common bottleneck and moving on two Totally Asymmetric Simple Exclusion Process (TASEP) lanes. We provide a theoretical analysis of the phase diagram, valid when…
A thermodynamically consistent particle-based model for fluid dynamics with continuous velocities and a non-ideal equation of state is presented. Excluded volume interactions are modeled by means of biased stochastic multiparticle…
We derive a thermodynamically consistent model, which describes the time evolution of a two-phase flow in an evolving domain. The movement of the free boundary of the domain is driven by the velocity field of the mixture in the bulk, which…
We study {\em bottleneck routing games} where the social cost is determined by the worst congestion on any edge in the network. In the literature, bottleneck games assume player utility costs determined by the worst congested edge in their…
We propose a many-particle-inspired theory for granular outflows from a hopper and for the escape dynamics through a bottleneck based on a continuity equation in polar coordinates. If the inflow is below the maximum outflow, we find an…
We develop the energy budget equation of the coupled Navier-Stokes-Cahn-Hilliard (NSCH) system. We use the NSCH equations to model the dynamics of liquid droplets in a liquid continuum. Buoyancy effects are accounted for through the…
Deciding that two network flows are essentially the same is an important problem in intrusion detection or in tracing anonymous connections. A stepping stone or an anonymity network may try to prevent flow correlation by delaying the…
Measurements on real traffic have revealed the existence of metastable states with very high flow. Such states have not been observed in the Nagel-Schreckenberg (NaSch) model which is the basic cellular automaton for the description of…
We describe traffic flows in one lane roadways using kinetic theory, with special emphasis on the role of quenched randomness in the velocity distributions. When passing is forbidden, growing clusters are formed behind slow cars and the…
The balanced vehicular traffic model is a macroscopic model for vehicular traffic flow. We use this model to study the traffic dynamics at highway bottlenecks either caused by the restriction of the number of lanes or by on-ramps or…
This paper proposes a dynamic congestion pricing model that takes into account mobile source emissions. We consider a tollable vehicular network where the users selfishly minimize their own travel costs, including travel time, early/late…
We find an approximate Nash equilibrium in a game between decentralized exchanges (DEXs) that compete for order flow by setting dynamic trading fees. We characterize the equilibrium via a coupled system of partial differential equations and…
Measurements of traffic flow show the existence of metastable states of very high throughput. These observations cannot be reproduced by the CA model of Nagel and Schreckenberg (NaSch model), not even qualitatively. Here we present two…
We consider a linear transport equation on the edges of a network with time-varying coefficients. Using methods for non-autonomous abstract Cauchy problems, we obtain well-posedness of the problem and describe the asymptotic profile of the…
There has been much research on network flows over time due to their important role in real world applications. This has led to many results, but the more challenging continuous time model still lacks some of the key concepts and techniques…
The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…
We describe a simple experiment involving spheres rolling down an inclined plane towards a bottleneck and through a gap. Results of the experiment indicate that flow rate can be increased by placing an obstruction at optimal positions near…