In this section, we concentrate on a selection of
results from computer experiments on a 
network.
Figures 2 and 3 illustrate throughput-load characteristics for the system. Figure 2 shows the overall average packet age over a run of 20,000 token passes versus percentage load, for both the multiple and single packet transfer cases. Figure 3 shows the average number of packets arriving at their destination, per token pass, as the load is varied.
Figure 2: Overall average packet age against percentage load for a
network with M = 16.
Figure 3: Average number of packets delivered per token pass
(throughput), against percentage load for an M = 16 network.
We now look at the behaviour of 
as a function of discrete time n. Only in
exceptional circumstances does 
display periodic behaviour with a
short period --- typically when the load is very low (one or two packets) or
very high (
). In the former case, the packet density is so low
that they do not interact with each other; in the latter case, the behaviour is
only approximately periodic (see later).
For intermediate values of load, apparently aperiodic behaviour is always
observed. Several average age waveforms are illustrated in
figure 4, for different values of load. The initial
transient is not shown. Despite the fact that the system is
deterministic, these waveforms have a surprisingly noise-like appearance.
Figure 4: Average age of all packets as a function of discrete time, for
20, 40, 60 and 80% load on a 
network. This illustrates
( a) the prevalence of aperiodic behaviour and ( b) the fact that the
average age increases as the load increases.
It is not our intention to present here a thorough investigation of this network as a communications system. We should point out, though, the fact that it has several desirable properties from that point of view, such as
,
implying that there is at least one cell that does not contain a
packet, our computer experiments indicate that all packets will
eventually reach their destination. If 
, which might be regarded
as a worst case, each packet will systematically visit every cell in turn
and hence is guaranteed to arrive at its destination in a finite time.
In other cases, we have not proved that the network does not suffer from
dead- or livelock, but all our experiments indicate this.
There is evidence that chaotic behaviour is displayed by the network. This is presented in [Deane 1994], and is based on a numerical computation of Lyapunov exponents [Ott 1993]. These are a measure of exponential divergence of initially close state vectors, as defined above, and a positive Lyapunov exponent is a strong indicator of the presence of chaotic behaviour.