We study the congestion phenomenon in a mathematical model of the data packets traffic in transmission networks as a function of the topology and of the load of the network. Two types of traffic are considered: homogeneous and heterogeneous traffic. The congestion phenomenon is studied in stationary conditions through the behaviour of two quantities: the mean travel time of a packet and the mean number of packets that have not reached their destination and are traveling in the network. We define a transformation that maps a network having the small world property (Inet 3037 in our numerical experiments) into a (modified) lattice network that has the same number of nodes. This map changes the capacity of the branches of the graphs representing the networks and can be regarded as an “interpolation” between the two classes of networks. Using this transformation we compare the behaviour of Inet 3037 to the behaviour of a modified rectangular lattice and we study the behaviour of the interpolating networks. This study suggests how to change the network topology and the branch capacities in order to alleviate the congestion phenomenon. In the website: http://www.ceri.uniroma1.it/ceri/zirilli/w6 some auxiliary material including animations and stereo¬graphic scenes that helps the understanding of this paper is shown.
Homogeneous and heterogeneous traffic of data packets on complex networks: the traffic congestion phenomenon
MARIANI, FRANCESCA;
2012-01-01
Abstract
We study the congestion phenomenon in a mathematical model of the data packets traffic in transmission networks as a function of the topology and of the load of the network. Two types of traffic are considered: homogeneous and heterogeneous traffic. The congestion phenomenon is studied in stationary conditions through the behaviour of two quantities: the mean travel time of a packet and the mean number of packets that have not reached their destination and are traveling in the network. We define a transformation that maps a network having the small world property (Inet 3037 in our numerical experiments) into a (modified) lattice network that has the same number of nodes. This map changes the capacity of the branches of the graphs representing the networks and can be regarded as an “interpolation” between the two classes of networks. Using this transformation we compare the behaviour of Inet 3037 to the behaviour of a modified rectangular lattice and we study the behaviour of the interpolating networks. This study suggests how to change the network topology and the branch capacities in order to alleviate the congestion phenomenon. In the website: http://www.ceri.uniroma1.it/ceri/zirilli/w6 some auxiliary material including animations and stereo¬graphic scenes that helps the understanding of this paper is shown.
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