We now describe how the above simulation model is executed using the parallel simulation protocol described in the previous chapter. LPs have two attributes associated with them at all times:
A blocked LP in non-deterministic mode uses a combination of the conditional event and the null message protocols to determine which messages in its message queues are safe. Safe messages are are matched with the LP's request list in exactly the same way as with deterministic LPs, until the request the LP is waiting on gets satisfied.
In order to explain in detail the computations performed by the null message and conditional event protocols, we define the following terms:
: A lower bound on the send timestamp of the
next message LP P will send on communicator C.
: A lower bound on the send timestamp of the
next acknowledgement LP P will send on communicator C.
: In round r of the conditional
event protocol, a lower bound on the send timestamp of the next
message or acknowledgement that LP P will
send, provided it does not get any additional messages or
acknowledgements (see Chapter 4.5.2.2).
: The minimum of 
and the send
timestamp of the earliest message sent by P in round r.
: A lower bound on the send timestamp
of the next message LP P will get on communicator C, as calculated
by the null message protocol.
: A lower bound on the send timestamp
of the next acknowledgement LP P will get on communicator C,
as calculated by the null message protocol.
: A lower bound on the send timestamp of the
next message or acknowledgement LP P will get, as calculated
by the conditional event protocol.
: Defined as 
.
: Defined as 
.
is calculated as
i.e. the minimum of the
message EOTs of all LPs in communicator C. The acknowledgement EIT,
is computed in a similar way.
The conditional event protocol cannot use the communication topology
so it computes a single EIT for all communicators.
Consequently, for LP P,
is calculated as 
i.e.
the minimum of the ECOTs of all LPs in the simulation, where
r is the latest round for which P has received all effective ECOTs.
At LP P,
a message on communicator C is deemed safe if its send timestamp
is less than 
. In other words, the better of the EIT estimates
of the null and conditional event protocols is used in deciding
if a message is safe to process.
As described in the previous chapter,
we use a demand driven implementation
of the null message and conditional event protocols, and hence
both protocols
get automatically switched off when all LPs are in deterministic mode.
We now describe how an LP computes its message and acknowledgement
EOTs (i.e. 
and 
respectively) and
its ECOT (i.e. 
).
An LP must be able to compute these
values irrespective of its execution or simulation status.
In all the calculations presented subsequently,
let the current simulation time of LP P be 
.
We assume the simulation time is updated whenever EITs
change, in order to ensure that the following inequalities always hold:
(a) If P is blocked waiting for an acknowledgement
on communicator C, 
, and
(b) If P is blocked waiting for a message on communicator
C, 
. L is the minimum message
latency of the target machine and consequently the receive timestamp
of any message or acknowledgment must be at least L more than
its send timestamp.
Additionally, we assume that if
P has terminated, 
is 
.