When the reply message reaches the source node, the
relaxation pass is initiated by sending a relaxation message
downstream to all destinations. When sent by a node 
to a
successor 
, this message contains the cumulative delay
after relaxation 
on all nodes on the path from the source
to . During the relaxation pan, each node reduces the
priorities assigned to each outgoing link, and thus increases the
local delay on each link. The amount by which the priorities can be
reduced on a node depends on the reduce for 
and
the feasible delays on the successor nodes.
When a node receives a relaxation message, it calculates a
target value, 
, for the local delay after relaxation for
each outgoing link. This value is a fraction of the slack 
available for transmission in the subtree starting at Node
after relaxation on upstream nodes. For each successor node
, the value for the slack on the corresponding outgoing
link is defined as
The target value for the local delay on that link is then determined by the next formula:
For each successor node , the lowest priority level on the
outgoing link of is determined for which the local delay does not
exceed . Let 
be the resulting delay.
Node first finalizes the priority assignment and then forwards the
relaxation message to each successor node with
the updated value for the cumulative delay up to
after relaxation, where
The formula 4 tries to distribute the available slack equally
ones the nodes of the critical path of the subtree starting at node
. In Chapter 4, we will investigate what the
effects of varying this basic allocation scheme are. Specifically, we
will generalize the scheme from using an equal distribution to using
geometrical distribution, by introducing a relaxation factor
. By choosing appropriate , the relaxed amount of
delay is distributed as follows:
The formula in 4, therefore becomes
We note that for 
, the allocations are identical to the one
defined in formula 4.