WT(i)\mathit{WT}(i)
Dimension:
Time
Granularity:
Activity instance

Description

Elapsed time between the start event of an activity instance and the complete event of the activity instance that precedes it.

Potential use

Event log in which the time spent between every activity instance is of relevance.

Assumptions

Minimizing waiting time is desirable.

Desired Value:

MINIMIZE

Required attributes

actinst
case
time
type

Equations

Formula for practitioners

{stime(i)ctime(x)for any xprev(i)0if prev(i)=\begin{cases} \mathit{stime}(i) - \mathit{ctime}(x) & \mathit{for~any \ } x \in \mathit{prev}(i) \\ 0 & \mathit{if \ } \mathit{prev}(i) = \emptyset \end{cases}

stime(i)\mathit{stime}(i) returns the start timestamp of activity instance ii.
ctime(x)\mathit{ctime}(x) returns the completion timestamp of activity instance xx.
prev(i)\mathit{prev}(i) returns the set of preceding activity instances to instance ii.

Formal Definition

{stime(i)ctime(x)for any xprev(i)0if prev(i)=\begin{cases} \mathit{stime}(i) - \mathit{ctime}(x) & \mathit{for~any \ } x \in \mathit{prev}(i) \\ 0 & \mathit{if \ } \mathit{prev}(i) = \emptyset \end{cases}

Tags

actinst
case
time
type

Python implementation

This indicator is implemented in the process_performance_indicators Python library.

process_performance_indicators.indicators.time.instances.waiting_time