Equilibrium Manifolds in 2D Fluid Traffic Models

Complementarity Models for Traffic Equilibrium with Ridesharing

It is estimated that 76% of commuters are driving to work alone while each of them experiences a 38-hour delay annually due to traffic congestion. Ridesharing is an efficient way to utilize the unused capacity and help with congestion reduction, and it has recently become more and more popular due to new communication technologies. Understanding the complex relations between ridesharing and tra...

Invariant Manifolds for Stochastic Models in Fluid Dynamics

This paper is a survey of recent results on the dynamics of Stochastic Burgers equation (SBE) and two-dimensional Stochastic Navier–Stokes Equations (SNSE) driven by affine linear noise. Both classes of stochastic partial differential equations are commonly used in modeling fluid dynamics phenomena. For both the SBE and the SNSE, we establish the local stable manifold theorem for hyperbolic sta...

Manifolds in Fluid Dynamics

In studying fluid dynamics it is useful to employ two different perspectives of a fluid flowing through a domain D. The Eulerian point of view is to consider a fixed point x ∈ D, and observe the fluid flowing past. The Lagrangian point of view is to consider a fixed but arbitrary volume of fluid, called a parcel of fluid, and follow the parcel as it travels with the flow. One would think that o...

Dynamic Traffic Equilibrium with Discrete/Continuous Econometric Models

A procedure is developed to simulate the spatial and temporal distribution of traffic flows on a simplified highway network for home-to-work commuter trips. The procedure is based on a discrete/ continuous econometric frq,mework in which travelers' choices of route and departure time are modeled. Equilibrium traffic flows are determined using the estimated econometric models in a classic supply...

Computation of Equilibrium Distributions of Markov Traffic-Assignment Models