We have observed the statistical property of self-similarity in a deterministic model of data transfer. We believe this to be an important step because it shows that it is the underlying rules (protocols) that govern the dynamics of data traffic flow despite the random fluctuations engendered by service demand.
We suggest that the existence of self-similarity is to do with the fact that behaviour in our model can occur on any timescale. This is to be contrasted with ageing systems, in which packets are deleted when their age exceeds a predetermined value.
Three independent calculations support the thesis that for intermediate loading of our net, the traffic flow is self-similar. Recalling that we are only dealing with flow on a small network, this result may be taken as indicative of the state of affairs on much larger real networks. Elsewhere [4] we have presented evidence for chaotic behaviour in this network (in the sense that the trajectories diverge initially with at least one positive Lyapunov exponent). With some confidence, we put forward the observation that the flow on our network is both chaotic and self-similar.
There is some purpose, for the protocols designer, in studying the dynamics of simple protocol models, and attempting to obtain experimentally boundaries for certain behaviours ( periodic, aperiodic, self-similar) which may be altered by simple protocol changes, under the control of the designer. We suggest that this experimental approach is a useful addition to the tools available to the designer.
Self-similarity has been observed in LANs based upon carrier sense multiple access with collision detection (CSMA/CD) [1], in which access is probabilistic in nature. We, on the other hand, have observed self-similar behaviour in a deterministic network.