We study network traffic dynamics in a two-dimensional communication network with regular nodes and hubs. If the network experiences heavy message traffic, congestion occurs due to the finite capacity of the nodes. We discuss strategies to manipulate hub capacity and hub connections to relieve congestion and define a coefficient of betweenness centrality (CBC), a direct measure of network traffic, which is useful for identifying hubs that are most likely to cause congestion. The addition of assortative connections to hubs of high CBC relieves congestion very efficiently. © 2005 The American Physical Society.

Neelima Gupte

Department Of Physics

Brajendra K. Singh

Telecommunication links

Telecommunication networks

Telecommunication traffic

COEFFICIENT OF BETWEENNESS CENTRALITY (CBC)

HUBS

Nodes

Congestion control (communication)

Fulltext

IIT Madras is a public technical and research university located in Chennai, Tamil Nadu. Founded in 1959, it is recognised as an Institute of National Importance.

IIT Madras has been ranked as the top engineering institute in India for four years in a row by the National Institutional Ranking Framework of the MHRD

It currently offers undergraduate, postgraduate and research degrees across 16 disciplines in Engineering, Sciences, Humanities and Management. About 596 faculty belonging to science and engineering departments and centres of the Institute are engaged in teaching, research and industrial consultancy.

IIT Madras

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

We analyze an idealized model for the transmission or flow of particles, or discrete packets of information, in a weight bearing branching hierarchical two dimensional network and its variants. The capacities add hierarchically down the clusters. Each node can accommodate a limited number of packets, depending on its capacity, and the packets hop from node to node, following the links between the nodes. The statistical properties of this system are given by the Maxwell-Boltzmann distribution. We obtain analytical expressions for the mean occupation numbers as functions of capacity, for different network topologies. The analytical results are shown to be in agreement with the numerical simulations. The traffic flow in these models can be represented by the site percolation problem. It is seen that the percolation transitions in the 2D model and in its variant lattices are continuous transitions, whereas the transition is found to be explosive (discontinuous) for the V lattice, the critical case of the 2D lattice. The scaling behavior of the second-order percolation case is studied in detail. We discuss the implications of our analysis. © 2012 American Physical Society.

Transmission of packets on a hierarchical network: Statistics and explosive percolation

We identify the statistical characterizers of congestion and decongestion for message transport in model communication lattices. These turn out to be the travel time distributions, which are Gaussian in the congested phase, and logarithmic normal in the decongested phase. Our results are demonstrated for two-dimensional lattices, such the Waxman graph, and for lattices with local clustering and geographic separations, gradient connections, as well as for a one-dimensional ring lattice with random assortative connections. The behavior of the distribution identifies the congested and decongested phase correctly for these distinct network topologies and decongestion strategies. The waiting time distributions of the systems also show identical signatures of the congested and decongested phases. The distributions are explained using a stochastic differential equation to model the transport. © 2010 The American Physical Society.

Statistical characterizers of transport in communication networks

We study the synchronization in the context of network traffic on a 2-d communication network with local clustering and geographic separations. The network consists of nodes and randomly distributed hubs where the top five hubs ranked according to their coefficient of betweenness centrality (CBC) are connected by random assortative and gradient mechanisms. For multiple message traffic, messages can trap at the high CBC hubs, and congestion can build up on the network with long queues at the congested hubs. The queue lengths are seen to synchronize in the congested phase. Both complete and phase synchronization are seen, between pairs of hubs. In the decongested phase, the pairs start clearing and synchronization is lost. A cascading master-slave relation is seen between the hubs, with the slower hubs (which are slow to decongest) driving the faster ones. These are usually the hubs of high CBC. Similar results are seen for traffic of constant density. Total synchronization between the hubs of high CBC is also seen in the congested regime. Similar behavior is seen for traffic on a network constructed using the Waxman random topology generator. We also demonstrate the existence of phase synchronization in real internet traffic data. © 2009 The American Physical Society.

Queue-length synchronization in communication networks

We study the efficiency of the gradient mechanism of message transfer in a two-dimensional communication network of regular nodes and randomly distributed hubs. Each hub on the network is assigned some randomly chosen capacity and hubs with lower capacities are connected to the hubs with maximum capacity. The average travel times of single messages traveling on the lattice decrease rapidly as the number of hubs increase. The functional dependence of the average travel times on the hub density shows q -exponential behavior with a power-law tail. We also study the relaxation behavior of the network when a large number of messages are created simultaneously at random locations and travel on the network toward their designated destinations. For this situation, in the absence of the gradient mechanism, the network can show congestion effects due to the formation of transport traps. We show that if hubs of high betweenness centrality are connected by the gradient mechanism, efficient decongestion can be achieved. The gradient mechanism is less prone to the formation of traps than other decongestion schemes. We also study the spatial configurations of transport traps and propose minimal strategies for their elimination. © 2008 The American Physical Society.

Gradient mechanism in a communication network

We study network traffic dynamics in a two dimensional communication network with regular nodes and hubs. If the network experiences heavy message traffic, congestion occurs due to finite capacity of the nodes. We discuss strategies to manipulate hub capacity and hub connections to relieve congestion and define a coefficient of betweenness centrality (CBC), a direct measure of network traffic, which is useful for identifying hubs which are most likely to cause congestion. The addition of assortative connections to hubs of high CBC relieves congestion very efficiently.

European Physical Journal B

Role of connectivity in congestion and decongestion in a communication network

We address the problem of message transfer in a communication network. The network consists of nodes and links, with the nodes lying on a two-dimensional lattice. Each node has connections with its nearest neighbors, whereas some special nodes, which are designated as hubs, have connections to all the sites within a certain area of influence. The degree distribution for this network is bimodal in nature and has finite variance. The distribution of travel times between two sites situated at a fixed distance on this lattice shows fat-fractal behavior as a function of hub density. If extra assortative connections are now introduced between the hubs so that each hub is connected to two or three other hubs, the distribution crosses over to power-law behavior. Crossover behavior is also seen if end-to-end short cuts are introduced between hubs whose areas of influence overlap, but this is much milder in nature. In yet another information transmission process, namely, the spread of infection on the network with assortative connections, we again observed crossover behavior of another type, viz., from one power law to another for the threshold values of disease transmission probability. Our results are relevant for the understanding of the role of network topology in information spread processes. © 2003 The American Physical Society.

Journal	Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
ISSN	15393755
Open Access	No