r-Extreme Signalling for Congestion Control

In many "smart city" applications, congestion arises in part due to the nature of signals received by individuals from a central authority. In the model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015], each agent uses one out of multiple resources at each time instant. The per-use cost of a resource depends on the number of concurrent users. A central authority has up-to-date knowledge of the congestion across all resources and uses randomisation to provide a scalar or an interval for each resource at each time. In this paper, the interval to broadcast per resource is obtained by taking the minima and maxima of costs observed within a time window of length r, rather than by randomisation. We show that the resulting distribution of agents across resources also converges in distribution, under plausible assumptions about the evolution of the population over time

Distributionally Robust Optimisation in Congestion Control

The effects of real-time provision of travel-time information on the behaviour of drivers are considered. The model of Marecek et al. [arXiv:1406.7639, Int. J. Control 88(10), 2015] is extended to consider uncertainty in the response of a driver to an interval provided per route. Specifically, it is suggested that one can optimise over all distributions of a random variable associated with the driver's response with the first two moments fixed, and for each route, over the sub-intervals within the minimum and maximum in a certain number of previous realisations of the travel time per the route

Resource Allocation with Population Dynamics

Many analyses of resource-allocation problems employ simplistic models of the population. Using the example of a resource-allocation problem of Marecek et al. [arXiv:1406.7639], we introduce rather a general behavioural model, where the evolution of a heterogeneous population of agents is governed by a Markov chain. Still, we are able to show that the distribution of agents across resources converges in distribution, for suitable means of information provision, under certain assumptions. The model and proof techniques may have wider applicability

Coordinating users of shared facilities via data-driven predictive assistants and game theory

We study data-driven assistants that provide congestion forecasts to users of shared facilities (roads, cafeterias, etc.), to support coordination between them, and increase efficiency of such collective systems. Key questions are: (1) when and how much can (accurate) predictions help for coordination, and (2) which assistant algorithms reach optimal predictions? First we lay conceptual ground for this setting where user preferences are a priori unknown and predictions influence outcomes. Addressing (1), we establish conditions under which self-fulfilling prophecies, i.e., "perfect" (probabilistic) predictions of what will happen, solve the coordination problem in the game-theoretic sense of selecting a Bayesian Nash equilibrium (BNE). Next we prove that such prophecies exist even in large-scale settings where only aggregated statistics about users are available. This entails a new (nonatomic) BNE existence result. Addressing (2), we propose two assistant algorithms that sequentially learn from users' reactions, together with optimality/convergence guarantees. We validate one of them in a large real-world experiment.Comment: Extended version, including supplement, of a paper at the 35th Conference on Uncertainty in Artificial Intelligence, 201

On Distributed Dynamic Pricing of Multiscale Transportation Networks

We study transportation networks controlled by dynamic feedback congestion tolls. We focus on a multiscale model whereby the dynamics of the traffic flows are intertwined with those of the routing choices. The latter are influenced by the current congestion through the network as well as by decentralized congestion-dependent tolls controlled by the system planner. We prove that a class of decentralized monotone congestion-dependent tolls allow for globally stabilising the transportation network around a generalized Wardrop equilibrium. In particular, our results imply that using decentralized marginal cost tolls, stability of the dynamic transportation network is guaranteed to be around the social optimum traffic assignment. This is particularly remarkable as such feedback tolls can be computed in a fully local way without the need for any global information about the network structure, its state, or the exogenous network loads. Through numerical simulations, we also compare the performance of such decentralized dynamic feedback tolls with constant off-line (and centrally) optimized tolls both in the asymptotic and in the transient regime and we investigate their robustness to information delays