Self-similarity in a deterministic model of data transfer

There has been interest recently in the statistical property known as self-similarity, which has been observed experimentally in for instance LAN traffic. We define here a simple deterministic model of data transfer between remote sites and examine some of its properties. We show that waveforms that describe the network behaviour are aperiodic, despite the deterministic nature of our system, and also self-similar, with a Hurst parameter approaching unity, over a wide range of operating conditions.