Related Experiment Video
Updated: May 14, 2026
05:30
Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit
Published on: September 8, 2023
Effect of network structure on phase transitions in queuing networks
Norbert Barankai1, Attila Fekete, Gábor Vattay
1Department of the Physics of Complex Systems, Eötvös University, Pázmány Péter Sétány 1/A, H-1117 Budapest, Hungary.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|February 2, 2013
Summary
This study investigates traffic congestion phase transitions in random networks. We link network structure with critical traffic load, finding quenched and annealed formulas match in dense networks but diverge in sparse ones due to local structure.
Area of Science:
- Statistical mechanics
- Network science
- Transportation phenomena
Background:
- De Martino et al. introduced a framework for transportation on annealed random networks.
- Their work clarified phase transitions in traffic load on uncorrelated networks.
Purpose of the Study:
- To investigate phase transitions in transportation networks.
- To connect uncorrelated random graph structure with quenched disorder to critical traffic load.
Main Methods:
- Utilized a discrete time random walk model.
- Analyzed transportation phenomena on random networks with quenched disorder.
Main Results:
- Established a direct connection between network structure and critical traffic load.
- Demonstrated that quenched and annealed formulas for critical loading probability coincide in dense networks.
- Identified higher-order corrections related to local network structure in sparse graphs.
Conclusions:
- The local structure of sparse networks significantly influences critical traffic load.
- The findings extend the understanding of phase transitions in disordered transportation networks.
Related Concept Videos
02:31Phase Transitions
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
01:21Phase Transitions
A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
01:28Phase Diagrams of Ternary Systems
Consider a ternary system, which is composed of three components: water (W), ethanoic acid (E), and trichloromethane (T). Here, Ethanoic acid (E) is fully miscible with both water (W) and trichloromethane (T), meaning it can mix entirely with either of them. However, water and trichloromethane have partial miscibility, meaning they can only mix to a certain extent, beyond which two separate phases will form.The phase diagram of a ternary system is represented as an equilateral triangle, where...
01:25Network Function of a Circuit
Frequency response analysis in electrical circuits provides vital insights into a circuit's behavior as the frequency of the input signal changes. The transfer function, a mathematical tool, is instrumental in understanding this behavior. It defines the relationship between phasor output and input and comes in four types: voltage gain, current gain, transfer impedance, and transfer admittance. The critical components of the transfer function are the poles and zeros.
01:20The Phase Rule
The phase rule describes the relationship between the variance (degrees of freedom), the number of components, and the number of phases in a system at equilibrium.Variance is a concept that denotes the number of independent intensive properties (properties are those that do not depend on the amount of material in the system), such as temperature, pressure, and composition, that can be altered without impacting the number of phases in equilibrium.In a single-component system, such as pure water,...
02:39Phase Transitions: Melting and Freezing
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...