where residual T denotes the residual time that is seen by
node i until the network is idle, and { } k E T is the expected time
of the k th collision. { } k E T depends on the number of
backlogged and unbacklogged nodes as well as message arrival
rate at each node. For the 12th collision, the node discards this
message and reports an error message to the higher level
processing units[8]. It can be seen that block T is not
deterministic and may be unbounded due to the discarding of
messages.
In ControlNet, if a node wants to send a message, it must
wait to receive the token from the logically previous node.
Therefore, the blocking time, block T , can be expressed by the
transmission time and token rotation time of previous nodes.
The general formula for block T can be described by the
following equation: