In the early 1990s there was interest in experimentally observed self-similar, or long range dependent, behaviour in local area network (LAN) traffic [Leland 1994] and VBR video traffic [Garrett 1994].
The cause of self-similarity in traffic statistics in real networks is sometimes ascribed to the behaviour of the service demand. Here we ask, are traffic flow control protocols capable of generating chaotic [Ott 1993] behaviour, (which is known to be self-similar)? Experiments were conducted on simple models of communications networks and found [Deane 1994] chaos. This present report finds, in addition, self-similarity in the traffic flow.
The simple model consists of a two-dimensional network of routing cells for data transfer, governed by deterministic rules, whose dynamics are nonetheless very complex [Deane 1994], [Deane 1993]. The network is in principle a feasible means for transferring data and the dynamics of the system display self-similarity. We show that the Hurst parameter H [Hurst 1951], which is a measure of self-similarity, when calculated for the the average packet age time series, is close to unity. The maximum possible degree of self-similarity happens for a Hurst parameter 1.
One advantage of extracting complex dynamics from computer experiments on simple models of idealised networks is that the network designer may be made aware of the likely behaviour of the system under both regular and irregular traffic demand. Simulations conducted on actual protocols may give the same qualitative results but the causes of the complex dynamics will be hidden from the designer by the complexities of the real system.
In addition, the irregular flows observed in real computer networks may also be a consequence of the dynamics of the protocols as well as of the irregularities in the service demand. This means that even for deterministic multiple access mechanisms, the system is capable of displaying irregular traffic dynamics under certain conditions.
The rest of the paper is organised as follows: we describe in detail the network we have studied and then summarise a variety of possible state variables whose time evolution describes the network behaviour. We then illustrate typical network behaviour before defining and discussing the statistical calculations that show the system to be self-similar. The implications of self-similarity are then discussed.