TFT Webinars: Wenlong Jin -- Thu Apr 30 @ 11am EST
Jorge
Generalized bathtub model of network trip flows
Speaker: Wenlong Jin, UC Irvine
Date: 4/30/2020, 11:00 EST
Link: https://gatech.bluejeans.com/2831735251 NOTE: you don't need to install the bluejeans app, just click join with browser.
Abstract: (Vickrey, 1991, 2020) proposed a bathtub model for the evolution of trip flows served by privately operated vehicles inside a road network based on three premises: (i) treatment of the road network as a single bathtub; (ii) the speed-density relation at the network level, also known as the network fundamental diagram of vehicular traffic, and (iii) the time-independent negative exponential distribution of trip distances. However, the distributions of trip distances are generally time-dependent in the real world, and Vickrey’s model leads to unreasonable results for other types of trip distance distributions. Thus there is a need to develop a bathtub model with more general trip distance distribution patterns.
In this talk, I will present a unified framework for modeling network trip flows with general distributions of trip distances, including negative exponential, constant, and regularly sorting trip distances studied in the literature. In addition to tracking the number of active trips as in Vickrey's model, this model also tracks the evolution of the distribution of active trips' remaining distances. I will derive four equivalent differential formulations based on three conservation law. Then I discuss the properties of stationary and gridlock states, the integral form of the bathtub model with the characteristic method, and two numerical methods. I further present equivalent formulations and solutions for two special types of distributions of trip distances: time-independent negative exponential or deterministic. I will conclude with potential extensions and applications, as well as the relationship to the classical model of epidemic dynamics.
Short bio: Dr. Wenlong Jin (BS in Automatic Control, University of Science and Technology of China, 1998; PhD in Applied Mathematics, UC Davis, 2003) is an Associate Professor of Civil and Environmental Engineering at UC Irvine. He’s interested in transportation modeling and control based on behavioral principles, mathematical analysis, and control theory. Dr. Wenlong Jin has made systematic contributions to network kinematic wave theory, capacity drop and lane-changing models, connected vehicle systems theory, and green driving strategies. He is an editorial board editor of Transportation Research Part B and an Associate Editor of IEEE Transactions on Intelligent Transportation Systems and Transportmetrica B.