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The power flow equations are fundamental to power system planning, analysis, and control. However, the inherent non-linearity and non-convexity of these equations present formidable obstacles in problem-solving processes. To mitigate these…
Despite technological advancements, the significance of interdisciplinary subjects like complex networks has grown. Exploring communication within these networks is crucial, with traffic becoming a key concern due to the expanding…
Real world networks are often subject to severe uncertainties which need to be addressed by any reliable prescriptive model. In the context of the maximum flow problem subject to arc failure, robust models have gained particular attention.…
In previous work, we developed a topological framework for solving Riemann initial-value problems for a system of conservation laws. Its core is a differentiable manifold, called the wave manifold, with points representing shock and…
Recently different formulations of the first-order Lighthill-Whitham-Richards (LWR) model have been identified in different coordinates and state variables. However, there exists no systematic method to convert higher-order continuum models…
We present a new limiter method for solving the advection equation using a high-order, finite-volume discretization. The limiter is based on the flux-corrected transport algorithm. We modify the classical algorithm by introducing a new…
Many real life queueing networks have finite buffers with overflows. To understand the behavior of such networks, we consider traffic equations that generalize the traffic equations of classic open queueing networks where some nodes are…
In this paper we present a new kind of model for traffic flow which couples a first-order macroscopic approach with a second-order microscopic approach, avoiding any interface or boundary conditions between them. The Euler-Godunov scheme…
Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…
Understanding network flows such as commuter traffic in large transportation networks is an ongoing challenge due to the complex nature of the transportation infrastructure and of human mobility. Here we show a first-principles based method…
We propose a model to implement and simulate different traffic-flow conditions in terms of quantum graphs hosting an ($N$+1)-level dot at each site, which allows us to keep track of the type and of the destination of each vehicle. By…
Here we study the abstract nonlinear differential equation of second order that in special case is the equation of the type of equation of traffic flow. We prove the solvability theorem for the posed problem under the appropriate conditions…
This paper investigates structure-preserving $H_2$-optimal model order reduction (MOR) for linear systems with quadratic outputs. Within a Petrov-Galerkin projection framework, the $H_2$-optimal MOR problem is first formulated as an…
In this paper, we address the problem of modeling the traffic flow of a heritage city whose streets are represented by a network. We consider a mean field approach where the standard forward backward system of equations is also intertwined…
This work is concerned with constructing a second-order, invariant-domain preserving approximation of the compressible multi-species Euler equations where each species is modeled by an ideal gas equation of state. We give the full solution…
We present a robust optimisation framework for computing invariant solutions of wall-bounded flows by recasting the Navier-Stokes equations as a variational problem as established in Ashtari and Schneider, JFM (2023). The approach minimises…
In analogy to gas-dynamical detonation waves, which consist of a shock with an attached exothermic reaction zone, we consider herein nonlinear traveling wave solutions, termed "jamitons," to the hyperbolic ("inviscid") continuum traffic…
We present two accurate and efficient algorithms for solving the incompressible, irrotational Euler equations with a free surface in two dimensions with background flow over a periodic, multiply-connected fluid domain that includes…
The deployment of Autonomous Vehicles (AVs) poses considerable challenges and unique opportunities for the design and management of future urban road infrastructure. In light of this disruptive transformation, the Right-Of-Way (ROW)…
Recovering missing flows on the edges of a network, while exactly respecting local conservation laws, is a fundamental inverse problem that arises in many systems such as transportation, energy, and mobility. We introduce FlowSymm, a novel…