Related papers: Continuum Equilibria and Global Optimization for R…
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…
The concept of Wardrop equilibrium plays an important role in congested traffic problems since its introduction in the early 50's. As shown in [2], when we work in two-dimensional cartesian and increasingly dense networks, passing to the…
We revisit the classic problem of determining optimal routes in a graph for transporting two given distributions defined on its nodes, originally studied by Wardrop and Beckmann in the 1950s. The global congestion profile at any given time…
This paper introduces GODDeS: a fully distributed self-organizing decision-theoretic routing algorithm designed to effectively exploit high quality paths in lossy ad-hoc wireless environments, typically with a large number of nodes. The…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Due to their inherent complexity, engineered wireless multihop ad hoc communication networks represent a technological challenge. Having no mastering infrastructure the nodes have to selforganize themselves in such a way that for example…
This paper studies the problem of congestion control and scheduling in ad hoc wireless networks that have to support a mixture of best-effort and real-time traffic. Optimization and stochastic network theory have been successful in…
We study a network design problem (NDP) where the planner aims at selecting the optimal single-link intervention on a transportation network to minimize the travel time under Wardrop equilibrium flows. Our first result is that, if the delay…
In this work, we construct a novel numerical method for solving the multi-marginal optimal transport problems with Coulomb cost. This type of optimal transport problems arises in quantum physics and plays an important role in understanding…
We consider the traffic assignment problem in nonatomic routing games where the players' cost functions may be subject to random fluctuations (e.g., weather disturbances, perturbations in the underlying network, etc.). We tackle this…
We study transportation networks controlled by dynamical feedback tolls. We consider a multiscale transportation network model whereby the dynamics of the traffic flows are intertwined with those of the drivers' route choices. The latter…
Many physical systems -- such as optical waveguide lattices and dense neuronal or vascular networks -- can be modeled by metric graphs, where slender "wires" (edges) support wave or diffusion equations subject to Kirchhoff conditions at the…
The effective design and management of public transport systems are essential to ensure the best service for users. The performance of a transport system will depend heavily on user behaviour. In the common-lines problem approach, users…
In this Doctoral Dissertation we propose new variational principles for traffic assignment problems. So to find equillibrium we have to solve large-scale convex optimization problem of special (multilevel) type. We propose different…
In this paper, we reveal the relationship between entropy rate and the congestion in complex network and solve it analytically for special cases. Finding maximizing entropy rate will lead to an improvement of traffic efficiency, we propose…
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…
In the classical Monge-Kantorovich problem, the transportation cost only depends on the amount of mass sent from sources to destinations and not on the paths followed by this mass. Thus, it does not allow for congestion effects. Using the…
The equilibrium properties of allocation algorithms for networks with a large number of nodes with finite capacity are investigated. Every node is receiving a flow of requests and when a request arrives at a saturated node, i.e. a node…
This paper studies the problem of scheduling in single-hop wireless networks with real-time traffic, where every packet arrival has an associated deadline and a minimum fraction of packets must be transmitted before the end of the deadline.…
We aim to solve a topology optimization problem where the distribution of material in the design domain is represented by a density function. To obtain candidates for local minima, we want to solve the first order optimality system via…