In this section we describe the behaviour of a 
network. We use the
average age of all P packets as our measure of behaviour in this section. The age of an
individual packet is set to zero when it reaches its destination and is increased by one every token pass.
Since packets are travelling between opposite sides of the network (though not necessarily along
vertical or horizontal paths) the average age would under ideal
conditions be 
for an 
network. This is because packets can move
diagonally as well as horizontally and vertically and so the minimum distance travelled between
transmission and reception is N cells.
Hence, the age of a packet varies linearly between 0 (just transmitted) and N (just received),
with an average of 
.
For a load of 11% (28 packets), there is a transient of about 900 token passes, and thereafter the behaviour is periodic, with a period of 16 passes. The transient time depends on the initial state.
Figure 2: Typical behaviour of average age as a function of time for different numbers of
packets (11 -- 80% loading). The network comprises 
cells.
Increasing the load to 25% (64 packets), the average age as a function of time becomes aperiodic, although the overall average is close to the ideal value of 8. At a load of 42% (107 packets) bistability occurs: the average age is more or less constant at about 10, but suddenly rises to much larger values for a short period before settling back to around 10. The reason for this is that the packets tend to bunch together in one area of the network, causing a temporary blockage. The value of 42% is critical --- the phenomenon is not seen for a load of 41% or 43%.
At 80% load, the average age is seen to be an aperiodic function of time, and much greater (typically 500) than the ideal. At high levels of loading the network becomes inefficient at transferring packets.
It is seen from the above that
The percentages referred to above depend on the size of the network.
Aperiodic behaviour arises from the interaction of the packets among themselves, which in turn is a result of the fact that the presence of one packet at a site blocks the transfer of another packet to the same site. Nonlinearity in the system arises solely from this fact.