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Introduction

To date, the three most prominent references to the possibility of chaotic behaviour occurring in traffic flows across communication networks are [1] -- [3].

There is no doubt that communication networks in general can be viewed as large-scale, nonlinear dynamical systems, characterised by the fact that they are

  1. described almost entirely by discrete variables (with the sole exception of time, t)
  2. generally complicated and not well modelled by differential equations or mappings
  3. subject to random rather than deterministic effects

In the light of (3), it is their statistics rather than their dynamics that have generally been studied hitherto, and there is a vast literature on this subject.

We address item (1) above. Whilst classically chaotic systems are described by continuous variables, which are required to bring out the full fractal structure of the attractors, in practice real systems which display chaos are adequately described by continuous variables having dynamic range from noise floor to overload, which in an electronic context comprises a range of only about 10 orders of magnitude. Small perturbations and noise in a computer representation of such practical systems can be described by setting all the bits beyond the 33rd bit arbitrarily. In the system to be described below, there are ten to the power of several hundreds of possible states --- that is, very many more than are available in a one-dimensional practical system subject to noise.

In this paper, we describe in some detail a simple two-dimensional coupled array of processors, known as routing or switching cells, whose purpose is to transfer data packets between pairs of remote sites in the array. Despite the fact that this system is discrete and deterministic, its dynamics are very complex. We describe how state vectors for the system have been defined and discuss other dynamical variables of interest. Finally, we look at the possibility of the dynamics of such a system being in any sense chaotic.



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Jonathan Deane, and David Jefferies
Wed Jun 12 10:19:26 BST 1996