Related papers: Continuity, Uniqueness and Long-Term Behavior of N…
Motivated by the dynamic traffic assignment problem, we consider flows over time model with deterministic queuing. Dynamic equilibria, called Nash flows over time, have been studied intensively since their introduction by Koch and Skutella…
We consider a dynamic model of traffic that has received a lot of attention in the past few years. Infinitesimally small agents aim to travel from a source to a destination as quickly as possible. Flow patterns vary over time, and…
Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its…
Modeling traffic in road networks is a widely studied but challenging problem, especially under the assumption that drivers act selfishly. A common approach is the deterministic queuing model, for which the structure of dynamic equilibria…
This paper continues the study of equilibria for flows over time in the fluid queueing model recently considered by Koch and Skutella [10]. We provide a constructive proof for the existence and uniqueness of equilibria in the case of a…
Nash flows over time describe the behavior of selfish users eager to reach their destination as early as possible while traveling along the arcs of a network with capacities and transit times. Throughout the past decade, they have been…
A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…
This paper is concerned with a conservation law model of traffic flow on a network of roads, where each driver chooses his own departure time in order to minimize the sum of a departure cost and an arrival cost. The model includes various…
Different populations of vehicles travel along a network. Each population has its origin, destination and travel costs - which may well be unbounded. Under the only requirement of the continuity of the travel costs, we prove the existence…
We study a dynamic routing game motivated by traffic flows. The base model for an edge is the Vickrey bottleneck model. That is, edges are equipped with a free flow transit time and a capacity. When the inflow into an edge exceeds its…
Flows over time are a natural way to incorporate flow dynamics that arise in various applications such as traffic networks. In this paper we introduce a natural variant of the deterministic fluid queuing model in which users aim to minimize…
Stability of Wardrop equilibria is analyzed for dynamical transportation networks in which the drivers' route choices are influenced by information at multiple temporal and spatial scales. The considered model involves a continuum of…
We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a…
Recent studies on transportation networks have shown that real-time route guidance can inadvertently induce congestion or oscillatory traffic patterns. Nevertheless, such technologies also offer a promising opportunity to manage traffic…
We consider traffic flow dynamics for a network of signalized intersections, where the outflow from every link is constrained to be equal to a given capacity function if the queue length is positive, and equal to the minimum of cumulative…
We introduce a formalism to deal with the microscopic modeling of vehicular traffic on a road network. Traffic on each road is uni-directional, and the dynamics of each vehicle is described by a Follow-the-Leader model. From a mathematical…
Given a network with a continuum of users at some origins, suppose that the users wish to reach specific destinations, but that they are not indifferent to the time needed to reach their destination. They may have several possibilities (of…
We study a network congestion game of discrete-time dynamic traffic of atomic agents with a single origin-destination pair. Any agent freely makes a dynamic decision at each vertex (e.g., road crossing) and traffic is regulated with given…
While many classical traffic models treat the spatial extension of streets continuously or by discretization into cells of a certain length, we will subdivide roads into comparatively long homogeneous road sections of constant capacity with…
This paper is concerned with a fluidodynamic model for traffic flow. More precisely, we consider a single conservation law, deduced from conservation of the number of cars, defined on a road network that is a collection of roads with…