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254 9 Operational Support

Fig. 9.10 Each state has a multi-set of remaining flow times (one element for each visit). This
is the basis for predicting the remaining flow time of future cases. For a case with partial trace
526
512
a start ,a 518 ,d 525 ,d complete ,b 532 ,b 533 , the predicted remaining flow time is 42.56. This
start
start
complete
complete
is the mean remaining flow time of cases in state [p3,p4]
elapsed sojourn
(Q =[21,21,15,42,...]) and sojourn times (Q =[2,12,5,13,...]).
[p3,p4] [p3,p4]
Based on these multi-sets all kinds of statistics can be computed. For example, the
mean remaining flow time in state [p3,p4] is Q(q)×q with Q = Q remaining .
q∈Q |Q| [p3,p4]
Like in Sect. 8.4, it is possible to compute other standard statistics such as stan-
dard deviation, minimum, and maximum. One can also fit a distribution on the
sample data using standard statistical software. For example, based on the sam-
remaining
ples Q =[21,35,58,31,...] one could find that these remaining flow
[p3,p4]
times are best described by a Gamma distribution with parameters r = 8.0502 and
λ = 0.18915. This distribution has a mean of 42.56 and a standard deviation of 15.0.
As shown in Chap. 8, such insights can be used to extend models with the time in-
formation. Moreover, the annotated transition system can also be used actively, and
predict the remaining time for a running case.
Figure 9.10 shows the transition system with annotations for state [p3,p4].
Moreover, the path of a partial trace of a case that is still running is highlighted
525
518
512
526
in the figure. The partial trace of this case is: a start ,a complete ,d start ,d complete ,b 532 ,
start
b 533 . At time 533, we are interested in the remaining flow time of this case.
complete
An obvious predictor for the remaining flow time of the running case is the mean
remaining flow time of all earlier cases in the same state, i.e., 42.56. Hence, the case
is expected to complete around time 575.56. This illustrates that for any running
case, at any point in time, one can predict the remaining flow time.
The annotated transition system can be used to make more refined statements
about the predicted remaining flow time. For example, it is clear that the size
remaining
of multi-set Q and the standard deviation of the historic samples in this
[p3,p4]