Related papers: The dynamic system of the traffic assignment probl…
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…
A significant mathematical error is identified and corrected in a recent highly-cited paper on oscillatory flows of second-grade fluids [Fetecau & Fetecau (2005). Int. J. Eng. Sci., 43, 781--789]. The corrected solutions are shown to agree…
Numerical algorithms for the integration of stochastic differential equations in the presence of white noise are introduced and compared. Algorithms for the integration of stochastic correlated forces are also briefly reviewed. Finally, a…
This document is an exposition of an assortment of open problems arising from the exact enumeration of (perfect) matchings of finite graphs. Roughly half have been solved at the time of this writing; see the document "Twenty Open Problems…
This paper considers the problem of routing and rebalancing a shared fleet of autonomous (i.e., self-driving) vehicles providing on-demand mobility within a capacitated transportation network, where congestion might disrupt throughput. We…
A new coupling argument is introduced to establish Driver's integration by parts formula and shift Harnack inequality. Unlike known coupling methods where two marginal processes with different starting points are constructed to move…
This paper has been withdrawn. With the advancement of statistical theory and computing power, data sets are providing a greater amount of insight into the problems of today. Statisticians have an ever increasing number of tools to attack…
This paper describes TARDIS (Traffic Assignment and Retiming Dynamics with Inherent Stability) which is an algorithmic procedure designed to reallocate traffic within Internet Service Provider (ISP) networks. Recent work has investigated…
Connected automated driving has the potential to significantly improve urban traffic efficiency, e.g., by alleviating issues due to occlusion. Cooperative behavior planning can be employed to jointly optimize the motion of multiple…
The traffic assignment problem (TAP) aims to predict how traffic flows distribute themselves across a road network, traditionally requiring computationally expensive iterative simulations to reach a user equilibrium (UE) where no driver can…
Various operational optimization problems arise in cross-dock synchronization. The combination of the truck scheduling with other decision problems in cross-docking has been targeted by researchers in the recent years. In most of the truck…
The content of this paper is incorporated into hep-th/9805093
Routing and scheduling problems are fundamental problems in combinatorial optimization, and also have many applications. Most variations of these problems are NP-Hard, so we need to use heuristics to solve these problems on large instances,…
Concepts and techniques from statistical physics inspired a new method for traffic prediction. This method is particularly suitable in settings where the only information available is floating car data. We propose a system, based on the…
Some optimization or equilibrium problems involving somehow the concept of optimal transport are presented in these notes, mainly devoted to applications to economic and game theory settings. A variant model of transport, taking into…
The paper presents complexity results and performance guaranties for a family of approximation algorithms for an optimisation problem arising in software testing and manufacturing. The problem is formulated as a partitioning of a set where…
This work addresses the problem of autonomous traffic management at an isolated intersection for connected and automated vehicles. We decompose the trajectory of each vehicle into two phases: the provisional phase and the coordinated phase.…
In this survey, we address mixing from the point of view of partial differential equations, motivated by applications that arise in fluid dynamics. We give an account of optimal mixing, loss of regularity for transport equations, enhanced…
This article surveys the burgeoning area at the intersection of dynamical systems theory and algorithms for NP-hard problems. Traditionally, computational complexity and the analysis of non-deterministic polynomial-time (NP)-hard problems…
This is a paper in Analytic Topology.