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

AndJoinGateTransition(node) = WorkflowTransition(node)
where
CtlCond(node) = forall in ∈ inArc(node) Enabled(in)
CtlOp(node) =
let [in 1 , . . . , in n ] = inArc(node)
let [t 1 , . . . , t n ] = firingToken(inArc(node))
ConsumeAll({(t j , in j )) | 1 ≤ j ≤ n})
Produce(andJoinToken({t 1 , . . . , t n }), out)
DataOp(node) = forall i ∈ assignments(out) Assign(to i , from i )
4.3 OR-Split Gateway Nodes
An OR-split node is structurally similar to an AND-split node in the sense that by the normal form
assumption it has one incoming and finitely many outgoing arcs, but semantically it is different
since instead of producing tokens on every outgoing arc, this may happen only on a subset of them.
The chosen alternative depends on certain conditions OrSplitCond(o) to be satisfied that are
associated to outgoing arcs o. In BPMN the choice among these alternatives is based either upon
process-data-involving GateConditions that evaluate to true (data-based case) or upon GateEvents
that are Triggered (event-based case). Further variants considered in BPMN depend upon whether
at each moment exactly one alternative is chosen (the exclusive case) or whether more than one of
the alternative paths can be taken (so-called inclusive case).
We formulate the choice among the alternatives by an abstract function select Produce (node),
which is constrained to select at each invocation a non-empty subset of arcs outgoing node that
satisfy the OrSplitCondition. If there is no such set, the rule cannot be fired.
Constraints for select Produce
select Produce (node) ≠ ∅
select Produce (node) ⊆ {out ∈ outArc(node) | OrSplitCond(out)} 15
This leads to the following instantiation of the WorkflowTransition(node) scheme for orsplit
gateway nodes. The involvement of process data or gate events for the decision upon the
alternatives is formalized by letting DataCond and EventCond in the rule guard and their related
operations in the rule body depend on the parameter O for the chosen set of alternatives. As done
for AND-split nodes, we use an abstract function orSplitToken to describe the tokens Produced
on the outgoing arc; in general their values depend on the incoming tokens.
OrSplitGateTransition(node) =
let O = select Produce (node) in WorkflowTransition(node, O)
where
CtlCond(node) = Enabled(in)
CtlOp(node, O) =
let t = firingToken(in)
Consume(t, in)
ProduceAll({(orSplitToken(t, o), o) | o ∈ O})
DataOp(node, O) = forall o ∈ O forall i ∈ assignments(o) Assign(to i , from i )
From OrSplitGateTransition also AndSplitGateTransition can be defined by requiring
the selection function to select the full set of all outgoing arcs.
15 Instead of requiring this constraint once and for all for each such selection function, one could
include the condition as part of DataCond(node, O) resp. EventCond(node, O) in the guard of
OrSplitGateTransition.
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