Related papers: On Variants of Network Flow Stability
The paper investigates the throughput behavior of single-commodity dynamical flow networks governed by monotone distributed routing policies. The networks are modeled as systems of ODEs based on mass conversation laws on directed graphs…
We consider nonlinear scalar conservation laws posed on a network. We establish $L^1$ stability, and thus uniqueness, for weak solutions satisfying the entropy condition. We apply standard finite volume methods and show stability and…
Increasing concerns on the security and quality of water distribution systems (WDS), call for computational tools with performance guarantees. To this end, this work revisits the physical laws governing water flow and provides a hierarchy…
Transmission Control Protocol (TCP) continues to be the dominant transport protocol on the Internet. The stability of fluid models has been a key consideration in the design of TCP and the performance evaluation of TCP algorithms. Based on…
We study a robust control problem for dynamical flow networks. In the considered dynamical models, traffic flows along the links of a transportation network --modeled as a capacited multigraph-- and queues up at the nodes, whereby control…
Simple analytical criteria are derived to determine whether axisymmetric base flows in annuli and pipes are stable or unstable. Both axisymmetric and non-axisymmetric inviscid disturbances are considered. Our sufficient condition for…
Join the shortest queue (JSQ) refers to networks whose incoming jobs are assigned to the shortest queue from among a randomly chosen subset of the queues in the system. After completion of service at the queue, a job leaves the network. We…
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…
We study the following fundamental network optimization problem known as Maximum Robust Flow (MRF): A planner determines a flow on $s$-$t$-paths in a given capacitated network. Then, an adversary removes $k$ arcs from the network,…
We consider a class of learning problems that involve a structured sparsity-inducing norm defined as the sum of $\ell_\infty$-norms over groups of variables. Whereas a lot of effort has been put in developing fast optimization methods when…
The solution of potential-driven steady-state flow in large networks is a task which manifests in various engineering applications, such as transport of natural gas or water through pipeline networks. The resultant system of nonlinear…
Generative Flow Networks (GFlowNets) learn to sample states proportional to an unnormalized reward. Despite their theoretical promise, practical training is often unstable, exhibiting severe loss spikes and mode collapse. To tackle this, we…
We consider general, steady, balanced flows of a commodity over a network where an instance of the network flow is characterized by edge flows and nodal potentials. Edge flows in and out of a node are assumed to be conserved, thus…
Conservation laws and balance equations for physical network systems typically can be described with the aid of the incidence matrix of a directed graph, and an associated symmetric Laplacian matrix. Some basic examples are discussed, and…
Clar number and Fries number are two thoroughly investigated parameters of plane graphs emerging from mathematical chemistry to measure stability of organic molecules. We consider first a common generalization of these two concepts for…
This paper analyzes stochastic networks consisting of a set of finite capacity sites where different classes of individuals move according to some routing policy. The associated Markov jump processes are analyzed under a thermodynamic limit…
In this article, we consider nonlocal Hamilton-Jacobi Equations on networks with Kirchhoff type conditions for the interior vertices and Dirichlet boundary conditions for the boundary ones: our aim is to provide general existence and…
We probe the stability of Watts-Strogatz DC microgrids, in which droop-controlled producers and constant power load consumers are homogeneously distributed and obey Kirchhoff's circuit laws. The concept of survivability is employed to…
This work addresses the question of the stability of stratified, spatially periodic shear flows at low P\'eclet number but high Reynolds number. This little-studied limit is motivated by astrophysical systems, where the Prandtl number is…
The goal of traffic management is efficiently utilizing network resources via adapting of source sending rates and routes selection. Traditionally, this problem is formulated into a utilization maximization problem. The single-path routing…