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Ensemble calculations are essential for systems with uncertain data but require substantial increase in computational resources. This increase severely limits ensemble size. To reach beyond current limits, we present a first-order…
This paper proposes an iterative methodology to integrate large-scale behavioral activity-based models with dynamic traffic assignment models. The main novelty of the proposed approach is the decoupling of the two parts, allowing the…
In this paper, we first propose a filter-based continuous Ensemble Eddy Viscosity (EEV) model for stochastic turbulent flow problems. We then propose a generic algorithm for a family of fully discrete, grad-div regularized, efficient…
Vickrey's classic single-bottleneck departure time choice equilibrium model exhibits instability under many plausible day-to-day learning dynamics. Such instability is not observed in reality -- does this difference stem from the day-to-day…
Integro-difference equation (IDE) models describe the conditional dependence between the spatial process at a future time point and the process at the present time point through an integral operator. Nonlinearity or temporal dependence in…
This paper proposes a framework to assess the stability of an ordinary differential equation which is coupled to a 1D-partial differential equation (PDE). The stability theorem is based on a new result on Integral Quadratic Constraints…
In this series of works, we develop a discrete-velocity-direction model (DVDM) with collisions of BGK-type for simulating rarefied flows. Unlike the conventional kinetic models (both BGK and discrete-velocity models), the new model…
Ubiquitous mobile computing have enabled ride-hailing services to collect vast amounts of behavioral data of riders and drivers and optimize supply and demand matching in real time. While these mobility service providers have some degree of…
In this paper, we consider a dynamic equilibrium transportation problem. There is a fixed number of cars moving from origin to destination areas. Preferences for arrival times are expressed as a cost of arriving before or after the…
This paper continues the study of equilibria for flows over time in the fluid queueing model recently considered by Koch and Skutella [10]. We provide a constructive proof for the existence and uniqueness of equilibria in the case of a…
A major challenge in multi-agent systems is that the system complexity grows dramatically with the number of agents as well as the size of their action spaces, which is typical in real world scenarios such as autonomous vehicles, robotic…
Fractional differential equations (FDEs) are an extension of the theory of fractional calculus. However, due to the difficulty in finding analytical solutions, there have not been extensive applications of FDEs until recent decades. With…
We study a variant of Vickrey's classic bottleneck model. In our model there are $n$ agents and each agent strategically chooses when to join a first-come-first-served observable queue. Agents dislike standing in line and they take actions…
We present polynomial-time algorithms as well as hardness results for equilibrium computation in atomic splittable routing games, for the case of general convex cost functions. These games model traffic in freight transportation, market…
Dynamic tolls present an opportunity for municipalities to eliminate congestion and fund infrastructure. Imposing tolls that regulate travel along a public highway through monetary fees raise worries of inequity. In this article, we…
We present a simulation scheme for discrete-velocity gases based on {\em local thermodynamic equilibrium}. Exploiting the kinetic nature of discrete-velocity gases, in that context, results in a natural splitting of fluxes, and the…
This article proposes a numerical scheme for computing the evolution of vehicular traffic on a road network over a finite time horizon. The traffic dynamics on each link is modeled by the Hamilton-Jacobi (HJ) partial differential equation…
We study the optimal provision of information for two natural performance measures of queuing systems: throughput and makespan. A set of parallel links is equipped with deterministic capacities and stochastic travel times where the latter…
Generating trajectories that ensure both vehicle safety and improve traffic efficiency remains a challenging task at intersections. Many existing works utilize Nash equilibrium (NE) for the trajectory planning at intersections. However,…
In this research a continuous model for resource allocations in a queuing system is considered and a local prediction on the system behavior is developed. As a result we obtain a set of possible cases, some of which lead to quite clear…