Duration Probabilities

Specifying Duration Probability Distributions

The activity duration in the Simulation Feature utilizes a statistical distribution to vary the amount of processing time each activity instance requires. Since it is very unusual even for the same person to always complete the same task in the same amount of time or a service to take exactly the same execution time for each invocation, the statistical distribution provides a way to vary the processing time within a range of values.

Gaussian Distribution

The Gaussian distribution, also called Normal distribution, statistical distribution is commonly used in various fields. For the purposes of business process simulation, the Gaussian distribution provides values from a predictable range of independent values. So for example, Gaussian might be used to represent the average duration to handle a call in a call center activity with a consistent range of service times. Each call is independent of another since the duration of one call is not affected by the length of another and their duration tends to occur in a very predictable (uniform) range. Some service calls might be relatively short, others relatively long, but given enough independent calls fitting the range, an average (with leading and following tails) will be formed since the length of calls is predictable (e.g. 5 to 25 minutes). The overall shape of the curve will vary according to the amount of variance possible (e.g. shortest compared to longest time) and the frequency of those extremes. Because Gaussian tends to be associated with more stable (predictable) elements of a process, it can sometimes be confirmed with historical data from other sources. In these cases, existing reports can inform you to use Gaussian distributions at certain points in the process being simulated.

The Gaussian Distribution requires two properties, the

The expected value describes the value for the average duration, the standard deviation describes how the duration varies between different executions of this activity.

You can specify these properties on the Simulation > Duration property page in the property dialog for activities:

Duration Distribution - Gaussian

All changes of the two properties will be reflected in the curve immediately.

Additionally, you may specify the Unit for the time axis (t).

Poisson Distribution

The Poisson, or exponential distribution is popular in process simulation situations where there is a wide range of variance in values. In various fields, it is commonly used for predicting error rates or exceptions, which may occur in clusters, or rarely if at all. In business process simulation, the Poisson distribution is useful when the range of values for an element of process is not easy to predict (not uniform) but whose value or occurrence is independent of other events (i.e. not directly affected by previous or successive work). In an activity duration, Poisson may be appropriate when the nature of the work itself can have a large impact on the processing time for the activity. This situation might occur in activities where a human worker is cross-trained to carry out many variations of the same task (perhaps a knowledge worker), but each variation may greatly impact the amount of time required. For example, a knowledge worker activity to author or review a technical document might vary greatly in duration based on the nature of the document. A similar, but perhaps less common, example for system activities could occur when the system invoked for the activity is flexible enough to take many different paths based upon the nature of work, or has unusual technical dependencies (such as access to other systems not always available).

Note that the Poisson distribution is a discrete distribution which only returns integer, not fractal values for the time unit selected.

Note also, that although the Poisson distribution may take negative values, only positive values are considered for simulation runs.

The Poisson distribution requires a single properties, the

The Lambda value describes the value of most of the durations.

You can specify this property on the Simulation > Duration property page in the property dialog for activities:

Duration Distribution - Lambda

All changes of this property will be reflected in the curve immediately.

Additionally, you may specify the Unit for the time axis (t).

Uniform Distribution

The Uniform distribution establishes one resulting value for the distribution. In process simulation, this may be useful if a process element is highly predictable over a period of time. For example, if the activity duration for an outsourced activity (e.g. to print and send some information out via postal mail) is always exactly two-days, then the uniform distribution might be useful to represent the non-variant behavior.

The Uniform distribution requires two properties, the

Both properties demarcate the interval of durations in which durations might occur with the same probability.

You can specify these properties on the Simulation > Duration property page in the property dialog for activities:

Duration Distribution

All changes of these properties will be reflected in the curve immediately.

Additionally, you may specify the Unit for the time axis (t).

Custom Distribution

Custom distributions may be created when the time needed for an activity duration is largely predictable and relatively simple, but not represented well by the Uniform distribution. For example, an activity in a data processing center might alternate between 20, 30 and 45 minutes. Where each successive request will be serviced within one of these three time periods. This situation (and some more complex examples), can be graphed using the custom distribution.

Duration Distribution

For details on how to modify the curve of a custom distribution, see Working With Curves.

When you change the curve of the custom distribution, the percentage of values varying between the left and right boundary of a "bar" in the curve is displayed in the bars of the curve.

Retrieving Duration Distributions From Audit Trail Data

Instead of specifying properties or distribution curves explicitly, you may retrieve these from audit trail data of already executed process instances. This way you may obtain a "real world behavior" of your simulation.

In case of the Gaussian, Poisson and Uniform distribution, only the distribution properties (e.g. the Lambda value of a Poisson distribution) are retrieved from Audit Trail Data. In case of the custom distribution, the entire distribution is retrieved.

To specify, that a distribution or its properties are retrieved from audit trail data, select the check box Derived From Audit Trail Data in the property pages listed above.