EXTENDED FIBER BUNDLE MODEL FOR TRAFFIC JAMS ON SCALE-FREE NETWORKS

2008 ◽  
Vol 19 (11) ◽  
pp. 1727-1735 ◽  
Author(s):  
JIAN-FENG ZHENG ◽  
ZI-YOU GAO ◽  
XIAO-MEI ZHAO ◽  
BAI-BAI FU
Keyword(s):  
Failure Rate ◽  
Fiber Bundle ◽  
Load Distribution ◽  
Network Size ◽  
Traffic Load ◽  
Scaling Exponents ◽  
Scale Free ◽  
Traffic Jams ◽  
Fiber Bundle Model ◽  
Scale Free Networks

In this paper, we extend a fiber bundle model to study the propagation of traffic jams on scale-free networks. For the special distributions of traffic handling capacities of the links and traffic load on the nodes, the critical behavior of the jamming transition on scale-free networks is studied analytically. It is found that the links connecting to the nodes with larger degrees are more prone to suffering from traffic jams. This feature is associated with a propagation that follows a precise hierarchical dynamics. Finally, the average failure rate of the networks, which is defined as the fraction of total broken links of the network, is investigated analytically and by simulations in scale-free networks. We mainly find that, when β > γ (β and γ are the scaling exponents of the load distribution and degree distribution, respectively), there is a scaling between the average failure rate of the scale-free networks 1 - G and the network size N, 1 - G ~ N-1, independent of γ.

scholarly journals Diagonal Degree Correlations vs. Epidemic Threshold in Scale-Free Networks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
M. L. Bertotti ◽  
G. Modanese
Keyword(s):  
Correlation Matrix ◽  
Large Scale ◽  
Network Size ◽  
Epidemic Threshold ◽  
Correlation Matrices ◽  
Scale Free ◽  
Degree Correlation ◽  
Scale Free Networks ◽  
Degree Correlations

We prove that the presence of a diagonal assortative degree correlation, even if small, has the effect of dramatically lowering the epidemic threshold of large scale-free networks. The correlation matrix considered is P h | k = 1 − r P h k U + r δ h k , where P U is uncorrelated and r (the Newman assortativity coefficient) can be very small. The effect is uniform in the scale exponent γ if the network size is measured by the largest degree n . We also prove that it is possible to construct, via the Porto–Weber method, correlation matrices which have the same k n n as the P h | k above, but very different elements and spectra, and thus lead to different epidemic diffusion and threshold. Moreover, we study a subset of the admissible transformations of the form P h | k ⟶ P h | k + Φ h , k with Φ h , k depending on a parameter which leaves k n n invariant. Such transformations affect in general the epidemic threshold. We find, however, that this does not happen when they act between networks with constant k n n , i.e., networks in which the average neighbor degree is independent from the degree itself (a wider class than that of strictly uncorrelated networks).

ANALYSIS OF TRAFFIC FLOW ON COMPLEX NETWORKS

2011 ◽  
Vol 25 (10) ◽  
pp. 1419-1428 ◽  
Author(s):  
KUN LI ◽  
XIAOFENG GONG ◽  
SHUGUANG GUAN ◽  
C.-H. LAI
Keyword(s):  
Complex Networks ◽  
Network Capacity ◽  
Traffic Load ◽  
Packet Routing ◽  
Traffic Dynamics ◽  
Scale Free ◽  
Routing Strategy ◽  
Scale Free Networks ◽  
New Strategy ◽  
Mixed Networks

We propose a new routing strategy for controlling packet routing on complex networks. The delivery capability of each node is adopted as a piece of local information to be integrated with the load traffic dynamics to weight the next route. The efficiency of transport on complex network is measured by the network capacity, which is enhanced by distributing the traffic load over the whole network while nodes with high handling ability bear relative heavier traffic burden. By avoiding the packets through hubs and selecting next routes optimally, most travel times become shorter. The simulation results show that the new strategy is not only effective for scale-free networks but also for mixed networks in realistic networks.

LOAD DISTRIBUTION IN CONGESTED SCALE-FREE NETWORKS

2009 ◽  
Vol 20 (02) ◽  
pp. 197-207 ◽  
Author(s):  
JIAN-FENG ZHENG ◽  
ZI-YOU GAO ◽  
BAI-BAI FU
Keyword(s):  
Power Law ◽  
Load Distribution ◽  
Cost Functions ◽  
Scale Free ◽  
Load Distributions ◽  
Scale Free Networks ◽  
Practical Capacity ◽  
Congestion Effect ◽  
Link Cost ◽  
Uniform Case

In this work, we study the effects of scale-free topology and congestion on load distribution. Congestion effect can be described by link cost functions, which map link flows into travel times. Two different kinds of link's practical capacity (it is similar to link's capacity for transport) which is a parameter in link cost functions, i.e., uniform case and nonuniform case, are investigated. After introducing the effect of congestion, load distribution is typically discussed in Barábasi–Albert and Goh scale-free networks. In the uniform case, for Barábasi–Albert scale-free networks, we recover a power-law behavior for load distribution with a larger exponent, as compared with the distribution of betweenness centrality; for Goh scale-free networks, we also recover a power-law behavior and its exponent approaches to the exponent of degree distribution. While in the nonuniform case, the power-law behavior for load distribution may not always be conserved in both Barábasi–Albert and Goh scale-free networks. That is to say, different kinds of load distributions are obtained under different conditions. It may shed some light to study traffic dynamics on scale-free networks.

scholarly journals SURVIVING OPINIONS IN SZNAJD MODELS ON COMPLEX NETWORKS

2005 ◽  
Vol 16 (11) ◽  
pp. 1785-1792 ◽  
Author(s):  
F. A. RODRIGUES ◽  
L. DA F. COSTA
Keyword(s):  
Complex Networks ◽  
Scaling Law ◽  
Network Size ◽  
Random Networks ◽  
Scale Free ◽  
Scale Free Networks ◽  
Network Topologies

The Sznajd model has been largely applied to simulate many sociophysical phenomena. In this paper, we applied the Sznajd model with more than two opinions on three different network topologies and observed the evolution of surviving opinions after many interactions among the nodes. As result, we obtained a scaling law which depends of the network size and the number of possible opinions. We also observed that this scaling law is not the same for all network topologies, being quite similar between scale-free networks and Sznajd networks but different for random networks.

scholarly journals EFFICIENT ROUTING ON SCALE-FREE NETWORKS

2007 ◽  
Vol 21 (23n24) ◽  
pp. 4071-4075 ◽  
Author(s):  
TAO ZHOU
Keyword(s):  
Traffic Congestion ◽  
Traffic Load ◽  
Fluctuation Analysis ◽  
Scale Free ◽  
Routing Strategy ◽  
Rate Fluctuation ◽  
Scale Free Networks ◽  
Traffic Rate ◽  
And Control ◽  
Detrended Fluctuation

The nodes with the largest degree are very susceptible to traffic congestion, thus an effective way to improve traffic and control congestion can be redistributing traffic load in hub nodes to others. We proposed an efficient routing strategy, which can remarkably enhance the network throughput. In addition, by using detrended fluctuation analysis, we found that the traffic rate fluctuation near the critical point exhibits the 1/f scaling in the power spectrum, which is in accordance with the empirical data.

scholarly journals Characterizing the intrinsic correlations of scale-free networks

2016 ◽  
Vol 27 (03) ◽  
pp. 1650024 ◽  
Author(s):  
J. B. de Brito ◽  
C. I. N. Sampaio Filho ◽  
A. A. Moreira ◽  
J. S. Andrade
Keyword(s):  
Extreme Values ◽  
Network Models ◽  
Network Size ◽  
Scale Free Network ◽  
Scale Free ◽  
Scale Free Networks ◽  
Free Network ◽  
Degree Correlations ◽  
Multiple Edges ◽  
Random Scale

When studying topological or dynamical properties of random scale-free networks, it is tacitly assumed that degree–degree correlations are not present. However, simple constraints, such as the absence of multiple edges and self-loops, can give rise to intrinsic correlations in these structures. In the same way that Fermionic correlations in thermodynamic systems are relevant only in the limit of low temperature, the intrinsic correlations in scale-free networks are relevant only when the extreme values for the degrees grow faster than the square root of the network size. In this situation, these correlations can significantly affect the dependence of the average degree of the nearest neighbors of a given vertex on this vertices degree. Here, we introduce an analytical approach that is capable to predict the functional form of this property. Moreover, our results indicate that random scale-free network models are not self-averaging, that is, the second moment of their degree distribution may vary orders of magnitude among different realizations. Finally, we argue that the intrinsic correlations investigated here may have profound impact on the critical properties of random scale-free networks.

AN EFFICIENT BANDWIDTH ALLOCATION STRATEGY FOR SCALE-FREE NETWORKS

2012 ◽  
Vol 23 (10) ◽  
pp. 1250065 ◽  
Author(s):  
ZHONG-YUAN JIANG ◽  
MAN-GUI LIANG ◽  
SHUAI ZHANG ◽  
SHU-JUAN WANG ◽  
DONG-CHAO GUO
Keyword(s):  
Bandwidth Allocation ◽  
Service Providers ◽  
Network Size ◽  
Urban Transport ◽  
Allocation Strategy ◽  
Transport Networks ◽  
Scale Free ◽  
Traffic Capacity ◽  
Optimal Value ◽  
Scale Free Networks

Traffic capacity is critical for various networks and strongly depends on the distribution of link's bandwidth resources. In this paper, we propose a betweenness-based bandwidth allocation strategy in which the bandwidth of each link lij is allocated proportionally to the product (1 + Bi)α(1 + Bj)α, where α is a tunable parameter, and Bi and Bj are the betweenness of node i and node j, respectively. The optimal value of α is achieved by extensive simulations and slightly increases with the network size. Our new bandwidth allocation strategy achieves the highest traffic capacity when compared with the average bandwidth allocation strategy and the previously proposed degree-based bandwidth allocation strategy. Our work will be beneficial for network service providers to improve the traffic capacity by efficiently allocating or reallocating the overall finite link's bandwidth resources of networks such as the Internet, urban transport networks and airway networks.

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