A new algorithm for packet routing problems using chaotic neurodynamics and its surrogate analysis

Abstract

We propose a new algorithm for routing packets which effectively avoids packet congestion in computer networks. The algorithm involves chaotic neurodynamics. To realize effective packet routing, we first composed a basic method by a neural network, which routes packets with shortest path information between two nodes in the computer network. When the computer network has an irregular topology, the basic routing method does not work well, because most of packets cannot be transmitted to their destinations due to packet congestion in the computer network. To avoid such an undesirable problem, we employed chaotic neurodynamics to extend the basic method. Numerical experiments show that our proposed method exhibits good performance for scale-free networks. We also analyze why the proposed routing method is effective, comparing the proposed method with several stochastic methods. We introduced the method of surrogate data, a statistical hypothesis testing which is often used in the field of nonlinear time-series analysis. Analysis of the proposed method by the method of surrogate data reveals that the chaotic neurodynamics is most effective to decentralize the packet congestion in the computer network.

An improved routing algorithm using chaotic neurodynamics for packet routing problems

“…We first describe the method to implement the conventional chaotic method [5][6][7][8][9]. Moreover, we explain how the conventional chaotic method fails to decentralize the packets if packet flow increases.…”

“…In the chaotic routing model [5][6][7][8][9], the ith node has a chaotic neural network with N i chaotic neurons, and the ijth neuron represents connections between the ith and the jth nodes. Furthermore, if the ijth neuron fires, a packet is transmitted from the ith to the jth adjacent nodes.…”

“…Typical examples of static combinatorial optimization problems are the traveling salesman problem [1,2], the quadratic assignment problem [3] and the vehicle routing problem [4], whereas examples of dynamic combinatorial optimization problems are the packet routing problem [5][6][7][8][9][10][11][12][13][14][15][16][17] and the traffic flow control problem [18]. In static combinatorial optimization problems, the search space of the solution does not change.…”

“…To remove the congestion in the networks, the routing method that autonomously distributes packet transmissions using chaotic neurodynamics has been proposed [5][6][7][8][9]. By using a refractory effect that successfully memorizes packet routing history, the routing method [5][6][7][8][9] is more successful at avoiding the loss of packets better than the sp-hop method.…”

“…By using a refractory effect that successfully memorizes packet routing history, the routing method [5][6][7][8][9] is more successful at avoiding the loss of packets better than the sp-hop method. However, we have noted that the chaotic method [5][6][7][8][9] fails to remove congestion at hub nodes if the number of packets continues to increase in the network.…”