We have seen self-similarity in a the traffic flow patterns in a deterministic model of data transfer.
This shows that the underlying rules (protocols) govern the dynamics of data traffic flow despite the random fluctuations engendered by service demand. Of course, such fluctuations may also be self-similar.
Perhaps the existence of such strong 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. This value would set an upper limit to a timescale for traffic fluctuations which are a consequence of the dynamics rather than of the demand. In a real system in which both processes are operating, it may be that the longer timescales associated with traffic demand result in self-similarity even though the protocol is an ageing system, and only responsible for approximate self-similarity at the shorter timescales.
As the study of flicker noise in electronic systems shows, the combination of a number of different processes each with their own region of self-similarity only serves to make the overall behaviour more self-similar, over a wider range of timescales.
We have presented above three independent calculations all of which support
the thesis that for intermediate loading of our `tennis' net, the traffic flow
is self-similar. Recalling that we are only dealing with flow on a small
(
) network, having at most 
transmit/receive
stations, this result may be taken as indicative of the state of affairs on
much larger real networks. Elsewhere [Deane 1994] 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.
The observations [Leland 1994] of self-similar behaviour in traffic flow on real LAN computer networks may indicate that there is an underlying protocol whose dynamic contributes to the observed traffic fluctuations. In many chaotic systems, the time series statistics are sometimes (if conditions are right) robust in the presence of added noise. If the chaotic nature of the flow gives rise to the observed self-similar behaviour, we speculate that the observed statistics on real networks may be both due to the protocols used as well as a consequence of the irregular traffic service demands, to which these networks are clearly subject.
Therefore 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 ( e.g. 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) [Leland 1994], in which access is probabilistic in nature. We, on the other hand, have observed self-similar behaviour in a deterministic network. This behaviour is not entirely determined by the multiple access mechanism, but can also result from the overall structure of the communications profile.