Scaling of Fluctuations in Traffic on Complex Networks

Duch, Jordi; Arenas, Àlex

doi:10.1103/physrevlett.96.218702

Cited by 100 publications

(121 citation statements)

References 19 publications

(27 reference statements)

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“…This is because a randomly chosen node has degree k, while a neighbor would have degree k with probability kP (k). Another striking example closely related to the problem here addressed in which the degree of the nodes determines the dynamical properties is the scaling law characterizing flow fluctuations in complex networks [16][17][18][19]. Admittedly, the mean traffic f and its standard deviation σ can be related through the simple scaling form σ ∼ f α [16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Exploring complex networks by means of adaptive walkers

2012

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Finding efficient algorithms to explore large networks with the aim of recovering information about their structure is an open problem. Here, we investigate this challenge by proposing a model in which random walkers with previously assigned home nodes navigate through the network during a fixed amount of time. We consider that the exploration is successful if the walker gets the information gathered back home, otherwise no data are retrieved. Consequently, at each time step, the walkers, with some probability, have the choice to either go backward approaching their home or go farther away. We show that there is an optimal solution to this problem in terms of the average information retrieved and the degree of the home nodes and design an adaptive strategy based on the behavior of the random walker. Finally, we compare different strategies that emerge from the model in the context of network reconstruction. Our results could be useful for the discovery of unknown connections in large-scale networks.

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Section: Introductionmentioning

confidence: 99%

Exploring complex networks by means of adaptive walkers

2012

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“…The study of transport processes on networks of varying types has attracted much recent interest [1,2], and is important from the point of view of applications. Earlier studies of transport processes on networks has been carried out for important classes like scale free and random networks [3,4,5].…”

Section: Introductionmentioning

confidence: 99%

Transmission of Packets on a Hierarchical Network: Avalanches, Statistics and Explosive Percolation

Gupte

Kachhvah

2013

Understanding Complex Systems

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We discuss transport on load bearing branching hierarchical networks which can model diverse systems which can serve as models of river networks, computer networks, respiratory networks and granular media. We study avalanche transmissions and directed percolation on these networks, and on the V lattice, i.e., the strongest realization of the lattice. We find that typical realizations of the lattice show multimodal distributions for the avalanche transmissions, and a second order transition for directed percolation. On the other hand, the V lattice shows powerlaw behavior for avalanche transmissions, and a first order (explosive) transition to percolation. The V lattice is thus the critical case of hierarchical networks. We note that small perturbations to the V lattice destroy the power-law behavior of the distributions, and the first order nature of the percolation. We discuss the implications of our results.

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“…Neverthless, so far there are few analysis on the fluctuation behavior of other specific networks rather than the networks which have been investigated in Ref. [6,7]. In this work, we will investigate the network evolution and fluctuation based on our previous study of the download network.…”

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confidence: 99%

“…However, a recent study on scaling of fluctuation in internet traffic shows that the fluctuation is different from 1/2 which was claimed in the above papers. They developed a model where the arrival and departure of "packets" follow exponential distribution, and the processing capability of nodes is either unlimited or finite was proposed by Duch and Arenas [7]. This model presents a wide variety of exponents between 1/2 and 1, revealing their dependence on the few parameters considered, and questioning the existence of universality classes.…”

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confidence: 99%

“…However, the above scenario which assumes any external driving force is not unique to interpret the observed crossover fluctuation exponents between 1/2 and 1. A simple traffic model in complex networks that suggests congestion as the origin of the increase of α and captures the essential parameters governing the dynamical process [7] is also possible to explain the download network fluctuation. In that model, traffic process in a complex network of N nodes as N queue systems, and a random walk simulation for the movement of packets on the network.…”

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confidence: 99%

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Fluctuation of the Download Network

Han

Liu

2008

Chinese Phys. Lett.

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The scaling behavior of fluctuation for a download network which we have investigated a few years ago based upon Zhang's Encophysics web page has been presented. A power law scaling, namely σ ∼ f α exists between the dispersion σ and average flux f of the download rates. The fluctuation exponent α is neither 1/2 nor 1 which was claimed as two universal fluctuation classes in previous publication, instead it varies from 1/2 to 1 with the time window in which the download data were accumulated. The crossover behavior of fluctuation exponents can be qualitatively understood by the external driving fluctuation model for a small-size system or a network traffic model which suggests congestion as the origin.PACS numbers: 89.75. Hc, 89.75.Da, 89.40.Dd Many phenomenological and statistical analysis have been made for the complex networks [1,2]. In those researches, most studies focused on the long-time behavior of a certain complex network. In this sense, the feature of the network corresponds to its static characteristic. However, time evolution of the network topology is also very important. During its evolution, the network nodes experience different traffic flux time by time and the fluctuation is unavoidable. Actually, fluctuation is a universal phenomenon which exists in many different fields, such as nuclear fragmentation or hadron production [3,4,5], which can also be related to the critical behavior or selforganized criticality. For instance, the dispersion (σ) of an order parameter, such as the charge of the largest fragments in nuclear fragmentation, shows a transition from σ ∝ f 1/2 (the ordered phase) to σ ∝ f (the disordered phase) when the multifragmentation phase transition takes place in hot nuclear system [3,4] (here f is the average of the order parameter). For network dynamics, recently, Menezes and Barabási investigated the fluctuation in a number of real world networks, which includes internet, river network, microchip, WWW and highway network dynamics and presented a model to understand the origin of fluctuation in traffic process [6]. They found that the fluctuation is dominantly driven by either internal or external dynamics of the complex system [6]. In their studies, they found there is a power-law scaling for the dispersion and the average flux, namely σ ∝ f α , and there are two classes of universality for real systems. In the Internet and the computer chip there is robust internal dynamics which leads to the fluctuation exponent α = 1/2, while highway and Web traffic are driven by external demand which leads to the fluctuation exponent α = 1. Authors use a stylized model of random walkers throughout network, they thought what is probably one of the most important factors in the traffic dynamics on networks is the limited capacity of nodes to handle packets simultaneously, which leads to packpack interaction and induce large fluctuations or even network congestion. However, a recent study on scaling of fluctuation in internet traffic shows that the fluctuation is different from 1/2 which ...

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Scaling of Fluctuations in Traffic on Complex Networks

Cited by 100 publications

References 19 publications

Exploring complex networks by means of adaptive walkers

Exploring complex networks by means of adaptive walkers

Transmission of Packets on a Hierarchical Network: Avalanches, Statistics and Explosive Percolation

Fluctuation of the Download Network

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