BPMN and Beyond Business process modelling notation, workflow ...

ComplMultInstExit has to keep track of whether the initially empty set of those activity
instances, which have AlreadyCompleted and have passed their continuation tokens to the outgoing
arc, has reached the prescribed number tokenNo(complexMiFlowCond) of elements. If yes, the
remaining instances upon their completion are prevented from passing further tokens outside the
multiple instance activity. If not, each time an instance appears to be in NewCompleted we once
more Produce a token on the outgoing arc out—if the TokenTime(complexMiFlowCond) condition
allows us to do so, in which case we also insert the instance into the set AlreadyCompleted.
Since the context apparently is distributed and since the standard document contains no constraint
on TokenTime(complexMiFlowCond), at each moment more than one instance may show up in
NewCompleted. 32 Therefore we use a selection function select NewCompleted to choose an element
from the set NewCompleted 33 of multiple instances that have Completed but not yet produced
their continuation token. 34 In the following definition n is supposed to be a multiple instance activity
node with parallel miOrdering. The standard document leaves it open whether output (if
any) is produced either after each instance has completed or only at the end of the entire multiple
instance activity, so that in our definition we write the corresponding updates in square brackets
to indicate that they may be optional.
ComplMultInstExit(n, t) = // for miOrdering(n) = Parallel
AlreadyCompleted := ∅ // initially no instance is completed
seq
while AlreadyCompleted ≠ {i | i ≤ miNumber(n)} do
if NewCompleted(n, t) ≠ ∅ then
if | AlreadyCompleted |< tokenNo(complexMiFlowCond)
then
if TokenTime(complexMiFlowCond) then
let i 0 = select NewCompleted in
Produce(miExitToken(t, i 0 ), out)
Insert(i 0 , AlreadyCompleted)
[ProduceOutput(outputSets(n), currInput(n))]
else forall i ∈ NewCompleted(n, t) Insert(i, AlreadyCompleted)
where
NewCompleted(n, t) =
{i ≤ miNumber(n) | Completed(iterBody(n, miToken(t, i)[. . .])) and i ∉ AlreadyCompleted}
The EveryMultInstExit machine is an instance of ComplMultInstExit where tokenNo
is the number (read: cardinality of the set) of all to-be-considered activity instances and the
TokenTime is any time.
EveryMultInstExit(n, t) = ComplMultInstExit(n, t)
where
tokenNo(complexMiFlowCond) =| {i | i ≤ miNumber(n)} |
TokenTime(complexMiFlowCond) = true
32 The description of the case miFlowCond = One in the standard document is ambiguous: the wording
after only one of the activity instances has completed seems to implicitly assume that at each moment
at most one activity instance can complete its action. It is unclear whether this is really meant and if
yes, how it can be achieved in a general distributed context.
33 In ASM terminology this is a derived set, since its definition is fixed and given in terms of other dynamic
locations, here Completed and AlreadyCompleted.
34 If one prefers not to describe any selection mechanism here, one could instead use the forall construct
as done in the else branch. This creates however the problem that it would not be impossible for
more than tokenNo(complexMiFlowCond) many process instances to complete simultaneously so that a
more sophisticated mechanism must be provided to limit the number of those ones that are allowed to
Produce a token on the outgoing arc.
28