Information Technology Reference
In-Depth Information
4.2 Probabilistic Message State Model
The message state model describes the possible message states (such as sched-
uled, expected, arrived) and the likelihood for transitions between those states
during the process. We track only messages that are defined in the process model,
each in a separate state model instance that is valid only for that particular pro-
cess type and message type.
The state model is defined as a directed graph
G
State
(
V, E
) where states are
represented by vertices (
v ∈ V
) and labeled edges (
e ∈ E
) represent transitions.
A labeled transition between neighboring states describes the probability that
this transition will occur (
w
(
v
i
,v
j
)=[0
,
1]). The sum of outgoing transition
probabilities is always 1. The state model can be interpreted as a Markov chain
that describes the probability of reaching a particular state when a transition
occurs. We neglect self-transitions as the duration a message type remains in a
certain state is irrelevant for our purpose. We are only interested in the proba-
bilities of reaching each of the subsequent states.
State transitions from
Start
to
Scheduled
,
Expected
,
M issing
,and
NotExpected
are driven by the process progress. Transitions to any
Received
state and to
Repeated
are message driven. The process termination finally trig-
gers the transition to
Occurred
and
NotOccurred
. The initial transition prob-
abilities (depicted in Figure 4) are optimistic: we assume a message to occur
exactly once when its
Expected
or
Missing
,andwhen
Not Expected
to remain
absent.
Scheduled.
Initially every message is scheduled to take place at some time
during the process lifetime.
Expected.
A message becomes expected once it is needed to activate an activity
or an activity is activated and is expected to produce the message as output.
Missing.
Whenever an activity is completed without the required input, we
mark its input message as missing. Likewise, we also mark any expected
output message of an active preceding activity as missing.
Not Expected.
When a user explicitly skips an activity, or an alternative XOR
branch is completed — thereby skipping the involved activities — any mes-
sage type to or from such activity is no longer expected.
Received Early.
A message arriving while in state
Scheduled
indicates a po-
tential change in the process model or just a one-time deviation.
Received On Time.
A message arrives on time according to the process model.
Received Late.
The arrival of a missing message indicates a potential change
in the process model or just a one-time deviation.
Received Unexpected.
Indicates that a skipped activity needed to be carried
out anyway or a parallel branch is incorrectly specified as XOR.
Repeated.
A message is received multiple times.
Occurred.
The message has been sent or received at process end.
Never Occurred.
The message did not occur for whatever reasons.
