Related papers: Designing optimal networks for multi-commodity tra…
Wardrop equilibria in nonatomic congestion games are in general inefficient as they do not induce an optimal flow that minimizes the total travel time. Network tolls are a prominent and popular way to induce an optimum flow in equilibrium.…
In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of…
We consider multicommodity flow and cut problems in {\em polymatroidal} networks where there are submodular capacity constraints on the edges incident to a node. Polymatroidal networks were introduced by Lawler and Martel and Hassin in the…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
We give a short overview of advantages and drawbacks of the classical formulation of minimum cost network flow problems and solution techniques, to motivate a reformulation of classical static minimum cost network flow problems as optimal…
Vascular networks are used across the kingdoms of life to transport fluids, nutrients and cellular material. A popular unifying idea for understanding the diversity and constraints of these networks is that the conduits making up the…
A Mathematical Program with Equilibrium Constraints (MPEC) is formulated to capture the relationships between multiple Mobility Service Providers (MSPs) and the users of a multi-modal transport network. The network supply structure is…
We have developed a steady state theory of complex transport networks used to model the flow of commodity, information, viruses, opinions, or traffic. Our approach is based on the use of the Markov chains defined on the graph…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…
Resilience has become a key aspect in the design of contemporary infrastructure networks. This comes as a result of ever-increasing loads, limited physical capacity, and fast-growing levels of interconnectedness and complexity due to the…
We provide $m^{1+o(1)}k\epsilon^{-1}$-time algorithms for computing multiplicative $(1 - \epsilon)$-approximate solutions to multi-commodity flow problems with $k$-commodities on $m$-edge directed graphs, including concurrent…
In this paper, we introduce a hierarchical decision-making framework for emerging mobility systems. Despite numerous studies focusing on optimizing vehicle flow, practical feasibility has often been overlooked. To address this gap, we…
This paper presents a mathematical model for the routing of multicommodity freight in an intermodal network under disruptions. A stochastic mixed-integer program was formulated to minimize not only operational costs of various modes and…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
Advanced integration of logistics systems has been promoted for the sake of competitiveness and sustainability. Such efforts will enable more globally optimal and flexible operations by efficiently utilizing transportation capacity. At the…
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum $s$-$t$ flow and maximum concurrent…
Replacing positivity constraints by an entropy barrier is popular to approximate solutions of linear programs. In the special case of the optimal transport problem, this technique dates back to the early work of Schr\"odinger. This approach…
Optimal transport (OT) theory provides a principled framework for modeling mass movement in applications such as mobility, logistics, and economics. Classical formulations, however, generally ignore capacity limits that are intrinsic in…
This study addresses a large-scale multimodal transit network design problem, with Shared Autonomous Mobility Services (SAMS) as both transit feeders and an origin-to-destination mode. The framework captures spatial demand and modal…