Section: New Results

Agent-based modeling and applications to Smart Energy and Transportation Systems

• Renewable energy sources, such as wind, are characterized by non-dispatchability, high volatility, and non-perfect forecasts. Energy storage or electric loads that have a flexible consumption are viewed as a way to mitigate these effects. In [9] , [19] , we study centralized and distributed algorithms for solving this problem. We provide theoretical bounds on the trade-off between energy loss and the use of reserves. We develop a centralized algorithm that attains this bound in [9] . In [19] , we study a distributed optimization problem by modeling a two-stage electricity market. We show that the market is efficient: the players' selfish responses to prices coincide with a socially optimal policy. We develop a distributed solution technique based on the Alternating Direction Method of Multipliers (ADMM) and trajectorial forecasts to compute the Nash-equilibrium.

• Bike-sharing systems are becoming important for urban transportation. In these systems, users arrive at a station, pick up a bike, use it for a while, and then return it to another station of their choice. In [8] , we propose a stochastic model of an homogeneous bike-sharing system and study the effect of the randomness of user choices on the number of problematic stations. Even in a homogeneous city, the system exhibits a poor performance: the minimal proportion of problematic stations is of the order of the inverse of the capacity. We show that simple incentives, such as suggesting users to return to the least loaded station among two stations, improve the situation by an exponential factor.

• In [10] , we discuss the validation of an agent-based model of emergent city systems with heterogeneous agents. We transform our model into an analytically tractable discrete Markov model, and we examine the city size distribution. We show that the Markov chains lead to a power-law distribution when the ranges of migration options are randomly distributed across the agent population. We also identify sufficient conditions under which the Markov chains produce the Zipf's Law, which has never been done within a discrete framework. The conditions under which our simplified model yields the Zipf's Law are in agreement with, and thus validate, the configurations of the original heterogeneous agent-based model.