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8.4 Time and Probabilities 231

Table 8.7 Compact representation of the event log highlighting timestamps; artificial timestamps
are used to simplify the presentation of the time-based replay approach
Case id Trace

12
33
1 a start ,a 19 ,b 25 ,d 26 ,b 32 ,d complete ,e 35 ,e 40 ,h 50 ,h 54
complete
start
start
complete
start
complete
complete
start
28
17
2 a start ,a 23 ,d start ,c 30 ,d 32 ,c 38 ,e 50 ,e 59 ,g 70 ,g 73
start
complete
start
complete
complete
complete
start
complete
25
50
40
55
32
3 a start ,a 30 ,c start ,c 35 ,d 35 ,d complete ,e 45 ,e 50 ,f start ,f complete ,b 60 ,
start
start
start
complete
complete
complete
87
62
80
98
d start ,b 65 ,d 67 ,e start ,e complete ,g 90 ,g complete
start
complete
complete
... ...
Fig. 8.11 Timed replay of the first three cases in the event log: Case 1 starts at time 12 and ends
at time 54, Case 2 starts at time 17 and ends at time 73, Case 3 starts at time 25 and ends at time 98

running from time 25 until time 30. At time 30, c and d became enabled. However,
as shown, c started at time 32 and d started at time 35. This implies that there was
a waiting time of 2 before c started and a waiting time of 5 before d started. After
completing c and d, i.e., at time 40, the first instance of e became enabled. Since
the first instance of activity e ran from time 45 until 50, the waiting time for this
instance of e was 45 − 40 = 5 time units. Note that from time 35 until time 45 there
wasatokeninplace p3 (because c completed at time 35 and e started at time 45).
However, only half of this period should be considered as waiting time for e, because
e only got enabled at time 40 when d completed. As discussed in Sect. 7.4.3, such