The number of possible states of the network is equal to the number of
ways in which P distinct objects (packets) can be arranged in 
slots (routing cells), one per slot.
Even for modestly sized networks the total number of states 
can be very large; for a 
grid with 100 packets, 
is about 
The system operates deterministically, so its behaviour will always be periodic, The period is so large that it would take more than the lifetime of the Universe to carry out a calculation in which even one complete maximum period is executed, and so we can regard the number of states as `effectively infinite' and the behaviour as `effectively aperiodic'. We also assume that the period of any cycles that do occur is so long that it does not affect any of our computer experiments.
We have looked at a variety of state variables that could be used to define the state of the network as a function of discrete time (the number of token passes).
One of these is the average age of all packets on completion of the i-th token pass. This is convenient to calculate and is also a simple measure of the efficiency of the system --- the higher the average age, the longer the packets are taking to reach their destinations.