On the Price of Anarchy for flows over time

Dynamic network flows, or network flows over time, constitute an important model for real-world situations where steady states are unusual, such as urban traffic and the Internet. These applications immediately raise the issue of analyzing dynamic network flows from a game-theoretic perspective. In this paper we study dynamic equilibria in the deterministic fluid queuing model in single-source single-sink networks, arguably the most basic model for flows over time. In the last decade we have witnessed significant developments in the theoretical understanding of the model. However, several fundamental questions remain open. One of the most prominent ones concerns the Price of Anarchy, measured as the worst case ratio between the minimum time required to route a given amount of flow from the source to the sink, and the time a dynamic equilibrium takes to perform the same task. Our main result states that if we could reduce the inflow of the network in a dynamic equilibrium, then the Price of Anarchy is exactly e/(e − 1) ≈ 1.582. This significantly extends a result by Bhaskar, Fleischer, and Anshelevich (SODA 2011). Furthermore, our methods allow to determine that the Price of Anarchy in parallel-link networks is exactly 4/3. Finally, we argue that if a certain very natural monotonicity conjecture holds, the Price of Anarchy in the general case is exactly e/(e − 1)

Approximate reduction of heterogenous nonlinear models with differential hulls

We present a model reduction technique for a class of nonlinear ordinary differential equation (ODE) models of heterogeneous systems, where heterogeneity is expressed in terms of classes of state variables having the same dynamics structurally, but which are characterized by distinct parameters. To this end, we first build a system of differential inequalities that provides lower and upper bounds for each original state variable, but such that it is homogeneous in its parameters. Then, we use two methods for exact aggregation of ODEs to exploit this homogeneity, yielding a smaller model of size independent of the number of heterogeneous classes. We apply this technique to two case studies: a multiclass queuing network and a model of epidemics spread

Self-Evaluation Applied Mathematics 2003-2008 University of Twente

This report contains the self-study for the research assessment of the Department of Applied Mathematics (AM) of the Faculty of Electrical Engineering, Mathematics and Computer Science (EEMCS) at the University of Twente (UT). The report provides the information for the Research Assessment Committee for Applied Mathematics, dealing with mathematical sciences at the three universities of technology in the Netherlands. It describes the state of affairs pertaining to the period 1 January 2003 to 31 December 2008

Dynamic Traffic Models in Transportation Science

Traffic assignment models are crucial for traffic planners to be able to predict traffic distributions, especially, in light of possible changes of the infrastructure, e.g., road constructions, traffic light controls, etc. The starting point of the seminar was the observation that there is a trend in the transportation community (science as well as industry) to base such predictions on complex computer-based simulations that are capable of resolving many elements of a real transportation system. On the other hand, within the past few years, the theory of dynamic traffic assignments in terms of equilibrium existence and equilibrium computation has not matured to the point matching the model complexity inherent in simulations. In view of the above, this interdisciplinary seminar brought together leading scientists in the areas traffic simulations, algorithmic game theory and dynamic traffic assignment as well as people from industry with strong scientific background who identified possible ways to bridge the described gap