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1.2 Limitations of Modeling 5

Fig. 1.2 The same process modeled in terms of BPMN

currence of examine casually will disable examine thoroughly. In other words, there
is a choice between these two activities. Transition examine thoroughly is executed
for requests that are suspicious or complex. Straightforward requests only need a
casual examination. Firing check ticket does not disable any other transition, i.e.,
it can occur concurrently with examine thoroughly or examine casually. Transition
decide is only enabled if both input places contain a token. The ticket needs to be
checked (token in place c4) and the casual or thorough examination of the request
has been conducted (token in place c3). Hence, the process synchronizes before
making a decision. Transition decide consumes two tokens and produces one token
for c5. Three transitions share c5 as an input place, thus modeling the three pos-
sible outcomes of the decision. The requested compensation is paid (transition pay
compensation fires), the request is declined (transition reject request fires), or fur-
ther processing is needed (transition reinitiate request fires). In the latter case, the
process returns to the state marking places c1 and c2: transition reinitiate request
consumes a token from c5 and produces a token for each of its output places. This
was the marking directly following the occurrence of register request. In principle,
several iterations are possible. The process ends after paying the compensation or
rejecting the request.
Figure 1.1 models the process as a Petri net. There exist many different notations
for process models. Figure 1.2 models the same process in terms of a so-called
BPMN diagram [72, 127]. The Business Process Modeling Notation (BPMN) uses
explicit gateways rather than places to model the control-flow logic. The diamonds
with a “×” sign denote XOR split/join gateways, whereas diamonds with a “+”sign
denote AND split/join gateways. The diamond directly following activity register
request is an XOR-join gateway. This gateway is used to be able to “jump back”
after making the decision to reinitiate the request. After this XOR-join gateway,
there is an AND-split gateway to model that the checking of the ticket can be done
in parallel with the selected examination type (thorough or casual). The remainder
of the BPMN diagram is self explanatory as the behavior is identical to the Petri net
described before.
Figures 1.1 and 1.2 show only the control-flow, i.e., the ordering of activities
for the process described earlier. This is a rather limited view on business processes.
Therefore, most modeling languages offer notations for modeling other perspectives
such as the organizational or resource perspective (“The decision needs to be made
by a manager”), the data perspective (“After four iteration always a decision is made