A Study of Truck Platooning Incentives Using a Congestion Game

We introduce an atomic congestion game with two types of agents, cars and trucks, to model the traffic flow on a road over various time intervals of the day. Cars maximize their utility by finding a trade-off between the time they choose to use the road, the average velocity of the flow at that time, and the dynamic congestion tax that they pay for using the road. In addition to these terms, the trucks have an incentive for using the road at the same time as their peers because they have platooning capabilities, which allow them to save fuel. The dynamics and equilibria of this game-theoretic model for the interaction between car traffic and truck platooning incentives are investigated. We use traffic data from Stockholm to validate parts of the modeling assumptions and extract reasonable parameters for the simulations. We use joint strategy fictitious play and average strategy fictitious play to learn a pure strategy Nash equilibrium of this game. We perform a comprehensive simulation study to understand the influence of various factors, such as the drivers' value of time and the percentage of the trucks that are equipped with platooning devices, on the properties of the Nash equilibrium.Comment: Updated Introduction; Improved Literature Revie

Randomized Consensus with Attractive and Repulsive Links

We study convergence properties of a randomized consensus algorithm over a graph with both attractive and repulsive links. At each time instant, a node is randomly selected to interact with a random neighbor. Depending on if the link between the two nodes belongs to a given subgraph of attractive or repulsive links, the node update follows a standard attractive weighted average or a repulsive weighted average, respectively. The repulsive update has the opposite sign of the standard consensus update. In this way, it counteracts the consensus formation and can be seen as a model of link faults or malicious attacks in a communication network, or the impact of trust and antagonism in a social network. Various probabilistic convergence and divergence conditions are established. A threshold condition for the strength of the repulsive action is given for convergence in expectation: when the repulsive weight crosses this threshold value, the algorithm transits from convergence to divergence. An explicit value of the threshold is derived for classes of attractive and repulsive graphs. The results show that a single repulsive link can sometimes drastically change the behavior of the consensus algorithm. They also explicitly show how the robustness of the consensus algorithm depends on the size and other properties of the graphs

Complexity Reduction for Parameter-Dependent Linear Systems

We present a complexity reduction algorithm for a family of parameter-dependent linear systems when the system parameters belong to a compact semi-algebraic set. This algorithm potentially describes the underlying dynamical system with fewer parameters or state variables. To do so, it minimizes the distance (i.e., H-infinity-norm of the difference) between the original system and its reduced version. We present a sub-optimal solution to this problem using sum-of-squares optimization methods. We present the results for both continuous-time and discrete-time systems. Lastly, we illustrate the applicability of our proposed algorithm on numerical examples

Design of State-based Schedulers for a Network of Control Loops

For a closed-loop system, which has a contention-based multiple access network on its sensor link, the Medium Access Controller (MAC) may discard some packets when the traffic on the link is high. We use a local state-based scheduler to select a few critical data packets to send to the MAC. In this paper, we analyze the impact of such a scheduler on the closed-loop system in the presence of traffic, and show that there is a dual effect with state-based scheduling. In general, this makes the optimal scheduler and controller hard to find. However, by removing past controls from the scheduling criterion, we find that certainty equivalence holds. This condition is related to the classical result of Bar-Shalom and Tse, and it leads to the design of a scheduler with a certainty equivalent controller. This design, however, does not result in an equivalent system to the original problem, in the sense of Witsenhausen. Computing the estimate is difficult, but can be simplified by introducing a symmetry constraint on the scheduler. Based on these findings, we propose a dual predictor architecture for the closed-loop system, which ensures separation between scheduler, observer and controller. We present an example of this architecture, which illustrates a network-aware event-triggering mechanism.Comment: 17 pages, technical repor