We model the CPU time to communicate a message of length n by the
sum of a fixed time 
and a time dependent on the message length
n:
The factor 
is the per-byte CPU time. Notice that 
. Knowing the CPU time to communicate a message, 
,
and the communication latency, 
, the following equation
expresses the CPU load 
:
The value 
, which equals 
,
expresses the CPU load for sending a 0-byte message. Furthermore, we
can derive the following for the asymptotic CPU load 
:
In Section 8.3, we have already used
this equation. The asymptotic CPU load, , calculated
there, using 
for the per-byte CPU time for 4096 byte packets,
matches the measured CPU load for long messages.
The results presented in this paper allow us to derive the
parameters of the model that match the Comms2 communication using a
packet size of 1024, i.e., the typical packet size required for
ATLAS, and threads to perform the computation results. From
Figure 7, we can
determine that 
, the asymptotic bandwidth, equals
16.6 Mbytes/s. Furthermore, this figure allows us to determine
that 
. Since 
, we know
that 
. Knowing from Table 3
that 
, allows us to determine that
, using 
. We cannot derive from
the measurements, therefore we assume the CPU load is
100 % during 0-byte message communication, so 
. These parameters have been used to reconstruct the performance
graphs of the current system, see graph A in
Figure 12.