2,008 research outputs found

    A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

    Full text link
    In this paper we propose a LWR-like model for traffic flow on networks which allows one to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the destination is not assigned a priori, and can be chosen by the drivers during the journey, taking decisions at junctions. The model is then used to describe three possible behaviors of drivers, associated to three different ways to solve the route choice problem: 1. Drivers ignore the presence of the other vehicles; 2. Drivers react to the current distribution of traffic, but they do not forecast what will happen at later times; 3. Drivers take into account the current and future distribution of vehicles. Notice that, in the latter case, we enter the field of differential games, and, if a solution exists, it likely represents a global equilibrium among drivers. Numerical simulations highlight the differences between the three behaviors and suggest the existence of multiple Wardrop equilibria

    A Switching Fluid Limit of a Stochastic Network Under a State-Space-Collapse Inducing Control with Chattering

    Full text link
    Routing mechanisms for stochastic networks are often designed to produce state space collapse (SSC) in a heavy-traffic limit, i.e., to confine the limiting process to a lower-dimensional subset of its full state space. In a fluid limit, a control producing asymptotic SSC corresponds to an ideal sliding mode control that forces the fluid trajectories to a lower-dimensional sliding manifold. Within deterministic dynamical systems theory, it is well known that sliding-mode controls can cause the system to chatter back and forth along the sliding manifold due to delays in activation of the control. For the prelimit stochastic system, chattering implies fluid-scaled fluctuations that are larger than typical stochastic fluctuations. In this paper we show that chattering can occur in the fluid limit of a controlled stochastic network when inappropriate control parameters are used. The model has two large service pools operating under the fixed-queue-ratio with activation and release thresholds (FQR-ART) overload control which we proposed in a recent paper. We now show that, if the control parameters are not chosen properly, then delays in activating and releasing the control can cause chattering with large oscillations in the fluid limit. In turn, these fluid-scaled fluctuations lead to severe congestion, even when the arrival rates are smaller than the potential total service rate in the system, a phenomenon referred to as congestion collapse. We show that the fluid limit can be a bi-stable switching system possessing a unique nontrivial periodic equilibrium, in addition to a unique stationary point

    Wardrop Equilibrium in Discrete-Time Selfish Routing with Time-Varying Bounded Delays

    Get PDF
    This paper presents a multi-commodity, discrete- time, distributed and non-cooperative routing algorithm, which is proved to converge to an equilibrium in the presence of heterogeneous, unknown, time-varying but bounded delays. Under mild assumptions on the latency functions which describe the cost associated to the network paths, two algorithms are proposed: the former assumes that each commodity relies only on measurements of the latencies associated to its own paths; the latter assumes that each commodity has (at least indirectly) access to the measures of the latencies of all the network paths. Both algorithms are proven to drive the system state to an invariant set which approximates and contains the Wardrop equilibrium, defined as a network state in which no traffic flow over the network paths can improve its routing unilaterally, with the latter achieving a better reconstruction of the Wardrop equilibrium. Numerical simulations show the effectiveness of the proposed approach

    Data-Driven Estimation in Equilibrium Using Inverse Optimization

    Get PDF
    Equilibrium modeling is common in a variety of fields such as game theory and transportation science. The inputs for these models, however, are often difficult to estimate, while their outputs, i.e., the equilibria they are meant to describe, are often directly observable. By combining ideas from inverse optimization with the theory of variational inequalities, we develop an efficient, data-driven technique for estimating the parameters of these models from observed equilibria. We use this technique to estimate the utility functions of players in a game from their observed actions and to estimate the congestion function on a road network from traffic count data. A distinguishing feature of our approach is that it supports both parametric and \emph{nonparametric} estimation by leveraging ideas from statistical learning (kernel methods and regularization operators). In computational experiments involving Nash and Wardrop equilibria in a nonparametric setting, we find that a) we effectively estimate the unknown demand or congestion function, respectively, and b) our proposed regularization technique substantially improves the out-of-sample performance of our estimators.Comment: 36 pages, 5 figures Additional theorems for generalization guarantees and statistical analysis adde

    Modeling rationality to control self-organization of crowds: An environmental approach

    Full text link
    In this paper we propose a classification of crowd models in built environments based on the assumed pedestrian ability to foresee the movements of other walkers. At the same time, we introduce a new family of macroscopic models, which make it possible to tune the degree of predictiveness (i.e., rationality) of the individuals. By means of these models we describe both the natural behavior of pedestrians, i.e., their expected behavior according to their real limited predictive ability, and a target behavior, i.e., a particularly efficient behavior one would like them to assume (for, e.g., logistic or safety reasons). Then we tackle a challenging shape optimization problem, which consists in controlling the environment in such a way that the natural behavior is as close as possible to the target one, thereby inducing pedestrians to behave more rationally than what they would naturally do. We present numerical tests which elucidate the role of rational/predictive abilities and show some promising results about the shape optimization problem

    Proposal of a risk model for vehicular traffic: A Boltzmann-type kinetic approach

    Get PDF
    This paper deals with a Boltzmann-type kinetic model describing the interplay between vehicle dynamics and safety aspects in vehicular traffic. Sticking to the idea that the macroscopic characteristics of traffic flow, including the distribution of the driving risk along a road, are ultimately generated by one-to-one interactions among drivers, the model links the personal (i.e., individual) risk to the changes of speeds of single vehicles and implements a probabilistic description of such microscopic interactions in a Boltzmann-type collisional operator. By means of suitable statistical moments of the kinetic distribution function, it is finally possible to recover macroscopic relationships between the average risk and the road congestion, which show an interesting and reasonable correlation with the well-known free and congested phases of the flow of vehicles.Comment: 23 pages, 3 figures, Commun. Math. Sci., 201
    • …
    corecore