Self-Organized Network Flows

Abstract

Abstract.A model for traffic flow in street networks or material flows in supply networks is presented, that takes into account the conservation of cars or materials and other significant features of traffic flows such as jam formation, spillovers, and load-dependent transportation times. Furthermore, conflicts or coordination problems of intersecting or merging flows are considered as well. Making assumptions regarding the permeability of the intersection as a function of the conflicting flows and the queue lengths, we find self-organized oscillations in the flows similar to the operation of traffic lights.

Sensitivity analysis of permeability parameters for flows on Barcelona networks

“…Here we consider permeability as a function γ (t) ∈ [0, 1]. In [11] some solutions are proposed for connecting, merging, diverging or intersection points of the homogeneous road sections. The latter are based on two rules introduced in [4,7]:…”

“…To overcome the difficulties encountered by complex fluid dynamic models, in this work we make use of a simplified two-phase model for flows on roads, proposed by last author and collaborators (descriptions of such model and similar ones can be found in [9][10][11]). The road network is decomposed into road sections (links) of homogeneous capacity and nodes for their connections.…”

“…In [11], these parameters are assumed to be always zero or one (to model a traffic light, with permeability equal to one corresponding to green light). Here we consider permeability as a function γ (t) ∈ [0, 1].…”

“…In particular, we describe the effects of variation of permeability parameters, that indicate the amount of flow allowed to enter a junction from incoming roads. On each road, a model suggested by Helbing et al (2007) [11] is considered: free and congested regimes are distinguished, characterized by an arrival flow and a departure flow, the latter depending on a permeability parameter. Moreover we provide a rigorous derivation of the model from fluid dynamic ones, using recent results of Bretti et al (2006) [3].…”

Centralized versus decentralized control—A solvable stylized model in transportation

“…[9], a fluid-dynamic model is proposed to unveil that self-control of traffic lights and vehicle flows might lead to efficient traffic processes. As intersecting flows of vehicular traffic are often managed by an external control that might lead to oscillatory behaviors, decentralized control strategies become thus interesting and fruitful alternatives, [10,11]. Also somehow related to the present study, a model of commuters having the choice between alternative roads and basing their routing decisions on their neighbors' most recent waiting experience and on their own complete waiting history (i.e.…”