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We study dynamic network flows and introduce a notion of instantaneous dynamic equilibrium (IDE) requiring that for any positive inflow into an edge, this edge must lie on a currently shortest path towards the respective sink. We measure…
We consider flows over time within the deterministic queueing model and study the solution concept of instantaneous dynamic equilibrium (IDE) in which flow particles select at every decision point a currently shortest path. The length of…
We study a dynamic traffic assignment model, where agents base their instantaneous routing decisions on real-time delay predictions. We formulate a mathematically concise model and define dynamic prediction equilibrium (DPE) in which no…
We study a dynamic routing game motivated by traffic flows. The base model for an edge is the Vickrey bottleneck model. That is, edges are equipped with a free flow transit time and a capacity. When the inflow into an edge exceeds its…
Dynamic user equilibrium (DUE) is a Nash-like solution concept describing an equilibrium in dynamic traffic systems over a fixed planning period. DUE is a challenging class of equilibrium problems, connecting network loading models and…
We study a network congestion game of discrete-time dynamic traffic of atomic agents with a single origin-destination pair. Any agent freely makes a dynamic decision at each vertex (e.g., road crossing) and traffic is regulated with given…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
This paper analyzes the use of variable speed limits to optimize travel time reliability for commuters. The investigation focuses on a traffic corridor with a bottleneck subject to the capacity drop phenomenon. The optimization criterion is…
We consider dynamic equilibria for flows over time under the fluid queuing model. In this model, queues on the links of a network take care of flow propagation. Flow enters the network at a single source and leaves at a single sink. In a…
This paper is concerned with dynamic user equilibrium with elastic travel demand (E-DUE) when the trip demand matrix is determined endogenously. We present an infinite-dimensional variational inequality (VI) formulation that is equivalent…
Dynamic user equilibrium (DUE) is the most widely studied form of dynamic traffic assignment, in which road travelers engage in a non-cooperative Nash-like game with departure time and route choices. DUE models describe and predict the…
Flows over time have received substantial attention from both an optimization and (more recently) a game-theoretic perspective. In this model, each arc has an associated delay for traversing the arc, and a bound on the rate of flow entering…
Predicting selfish behavior in public environments by considering Nash equilibria is a central concept of game theory. For the dynamic traffic assignment problem modeled by a flow over time game, in which every particle tries to reach its…
A fluid queuing network constitutes one of the simplest models in which to study flow dynamics over a network. In this model we have a single source-sink pair and each link has a per-time-unit capacity and a transit time. A dynamic…
Long-term traffic flow forecasting plays a crucial role in intelligent transportation as it allows traffic managers to adjust their decisions in advance. However, the problem is challenging due to spatio-temporal correlations and complex…
This paper is concerned with the existence of the simultaneous route-and-departure choice dynamic user equilibrium (SRDC-DUE) in continuous time, first formulated as an infinite-dimensional variational inequality in Friesz et al. (1993). In…
We study an infinite-horizon discrete-time optimal stopping problem under non-exponential discounting. A new method, which we call the iterative approach, is developed to find subgame perfect Nash equilibria. When the discount function…
We study the transport properties of nonautonomous chaotic dynamical systems over a finite time duration. We are particularly interested in those regions that remain coherent and relatively non-dispersive over finite periods of time,…
In routing games, agents pick their routes through a network to minimize their own delay. A primary concern for the network designer in routing games is the average agent delay at equilibrium. A number of methods to control this average…
We have developed a numerical approach to compute real-time path integral expressions for quantum transport problems out of equilibrium. The scheme is based on a deterministic iterative summation of the path integral (ISPI) for the…