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9.4 Predict 253

Fig. 9.9 Statistics collected while replaying the first two cases: t is the time the state is visited,
e is the elapsed time since the start when visiting the state, r is the remaining flow time, and s is
the sojourn time

the next event occurred 7 time units later. State [p1,p2] is tagged with annotation
(t = 19,e = 7,r = 35,s = 6) because a completed at time t = 19. e = 19 − 12 = 7
because a completed 7 time units after the case started. r = 54 − 19 = 35 because
the case ended at time 54. s = 25 − 19 = 6 because the next event occurred 6 time
units later. Figure 9.9 shows all annotations related to the first two cases. For exam-
ple, state [p3,p4] was visited once by each of the two cases resulting in annotations
(t = 33,e = 21,r = 21,s = 2) and (t = 38,e = 21,r = 35,s = 12). The initial state
[start] has no annotations since no events have occurred when visiting this state. The
final state [p5] has no sojourn time because there is no next event when visiting this
state.
Table 9.1 shows only a fragment of the whole event log. However, it is ob-
vious that the other cases in the log can be replayed in a similar fashion to
gather more annotations. For example, the third case visited state [p3,p4] twice:
after event d 40 and after event d 67 . The first visit resulted in annota-
complete complete
tion (t = 40,e = 15,r = 58,s = 5) and the second visit resulted in annotation
(t = 67,e = 42,r = 31,s = 13). Assuming a large event log, there may be hundreds
or even thousands of annotations per state. For each state, x it is possible to create
remaining
a multi-set Q x of remaining flow times based on these annotations. For state
remaining
[p3,p4] this multi-set is Q =[21,35,58,31,...]: the first case visited state
[p3,p4]
[p3,p4] once (21 time units before completion), the second case visited [p3,p4]
once (35 time units before completion), the third case visited [p3,p4] twice (58
and 31 time units before completion), etc. Similar multi-sets exist for elapsed times