Date post: | 18-Dec-2015 |
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A service landscape
How to combine logs?
Merge using time stamps!
Are timestamps synchronized in landscape?
Semantics of timestamps?• Time when the event occurred?• Time when it started / completed?• Time when the event is recorded?• Time when the event is stored?• ...
Time stamps
• Time scale of data?• Dense (time stamps)• Coarse (hour, minute, day)
• Reliability of the data?• User entered?• System generated?
Events & intervals: “old theory”
• Structure of concurrency:− Observe whether an event preceded another event− Observe whether events occurred simultaneously
• Implies an order• Interval order!
• Position of intervals on the axis!
Interval orders
• Define relation > by a > b iff “a occurs wholly after b”• Interval order if:
• [ a > b and c > d ] imply [ a > d or c > b ]
• Generalization of transitivity• Simultaneousness: ⌐ ( a > b) /\ ⌐ ( b > a)
b a
cd
b
a
b
a
But only works on level of events!
Process mining & intervals
1. Derive interval for each event• Singleton set (single time stamp)• Accurracy interval ( t ± )• Time scale (week, day, hour, minute, ...)
2. Relate events and intervals to activity
3. Discover process model
Activities & intervals
• Activities relate to a set of intervals• Many different mappings possible!• Granularity (Density of intervals)
− Fine: many small intervals− Coarse: few large intervals
• Finest interval function:• Only intervals of single points
• Coarsest interval function• Each activity maps to a single interval
Process mining & intervals
1. Derive interval for each event• Singleton set (single time stamp)• Accurracy interval ( t ± )• Time scale (week, day, hour, minute, ...)
2. Relate events and intervals to activity• Many different approaches!
3. Discover process model
Relations on interval sets (1)
• Simultaneousness• Weak: there is somewhere some overlap
• Dependent: always if A occurs, then B occurs as well
• Strong: if A occurs, then B occurs and vice versa
Relations on interval sets (2)
• Causality• Wholly: all intervals of A before B
• Succeeded: each interval of B followed by one of C
• Preceeded: each interval of B occurs after one of A
Declarative language
• Interval relations are highly declarative:• Granularity influences degree of concurrency
• Activities occur simultaneously, unless prohibited
Succeeds!
Preceeds!
Discover declarative model
1. Derive interval sets
2. Calculate relations on interval sets
3. Generate declarative model− Problems:
− Simultaneousness relations overlapping− Causality: always finds the transitive closure!
• Transitive reduction: S S* = R* R
• Minimal edge problem:• Only use “existing” edges for transitive reduction• What are existing arcs in process mining?
Causality & transitive closure
Polynomial
NP-hard
Next to and betweenness relation
• Next to• Weak: there is an interval of A directly followed by A• Strong: all intervals of A are directly followed by B
• Betweenness: • interval of B is between two intervals of A• Weak or strong?
ba
c
aa
c
b
d? ?