Journal ArticleDOI
A Linear Programming Model for the Single Destination System Optimum Dynamic Traffic Assignment Problem
TLDR
The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA.Abstract:
Recently, Daganzo introduced the cell transmission model--a simple approach for modeling highway traffic flow consistent with the hydrodynamic model. In this paper, we use the cell transmission model to formulate the single destination System Optimum Dynamic Traffic Assignment (SO DTA) problem as a Linear Program (LP). We demonstrate that the model can obtain insights into the DTA problem, and we address various related issues, such as the concept of marginal travel time in a dynamic network and system optimum necessary and sufficient conditions. The model is limited to one destination and, although it can account for traffic realities as they are captured by the cell transmission model, it is not presented as an operational model for actual applications. The main objective of the paper is to demonstrate that the DTA problem can be modeled as an LP, which allows the vast existing literature on LP to be used to better understand and compute DTA. A numerical example illustrates the simplicity and applicability of the proposed approach.read more
Citations
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Journal ArticleDOI
On-demand high-capacity ride-sharing via dynamic trip-vehicle assignment
TL;DR: A more general mathematical model for real-time high-capacity ride-sharing that scales to large numbers of passengers and trips and dynamically generates optimal routes with respect to online demand and vehicle locations is presented.
Journal ArticleDOI
Foundations of dynamic traffic assignment : the past, the present and the future
TL;DR: This opening paper will summarize the current understanding of DTA, review the existing literature, make the connection to the approaches presented in this special issue, and attempt to hypothesize about the future.
Journal ArticleDOI
Optimal freeway ramp metering using the asymmetric cell transmission model
Gabriel Gomes,Roberto Horowitz +1 more
TL;DR: It is shown that a near-global solution to the resulting nonlinear optimization problem can be found by solving a single linear program, whenever certain conditions are met.
Journal ArticleDOI
Robust optimization for emergency logistics planning: Risk mitigation in humanitarian relief supply chains
TL;DR: In this article, the authors proposed a methodology to generate a robust logistics plan that can mitigate demand uncertainty in humanitarian relief supply chains by applying robust optimization for dynamically assigning emergency response and evacuation traffic flow problems with time dependent demand uncertainty.
Journal ArticleDOI
Robotic load balancing for mobility-on-demand systems
TL;DR: This paper develops methods for maximizing the throughput of a mobility-on-demand urban transportation system and develops a rebalancing policy that lets every station reach an equilibrium in which there are excess vehicles and no waiting customers and that minimizes the number of robotic vehicles performing rebalanced trips.
References
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Book
Linear and nonlinear programming
David G. Luenberger,Yinyu Ye +1 more
TL;DR: Strodiot and Zentralblatt as discussed by the authors introduced the concept of unconstrained optimization, which is a generalization of linear programming, and showed that it is possible to obtain convergence properties for both standard and accelerated steepest descent methods.
Journal Article
On kinetic waves, II . A theory of traffic flow on long crowded roads
M J Lighthill,G B Whitham +1 more
TL;DR: In this paper, a functional relationship between flow and concentration for traffic on crowded arterial roads has been postulated for some time, and has experimental backing, from which a theory of the propagation of changes in traffic distribution along these roads may be deduced.
Journal ArticleDOI
On kinematic waves II. A theory of traffic flow on long crowded roads
TL;DR: The theory of kinematic waves is applied to the problem of estimating how a ‘hump’, or region of increased concentration, will move along a crowded main road, and is applicable principally to traffic behaviour over a long stretch of road.
Journal ArticleDOI
Shock Waves on the Highway
TL;DR: In this article, a simple theory of traffic flow is developed by replacing individual vehicles with a continuous fluid density and applying an empirical relation between speed and density, which is a simple graph-shearing process for following the development of traffic waves.
Journal ArticleDOI
The cell transmission model: a dynamic representation of highway traffic consistent with the hydrodynamic theory
TL;DR: In this paper, a simple representation of traffic on a highway with a single entrance and exit is presented, which can be used to predict traffic's evolution over time and space, including transient phenomena such as the building, propagation, and dissipation of queues.