Distribution Pattern Dialog

The Distribution Pattern Dialog enables values and times with random variation to be generated. For example the time a Multi-server takes to handle an item, or the inter-arrival time of items produced at an Entry.

Distributions are listed on the left. Fields appear depending on the distribution selected.

All distributions also include a truncation/rounding option button and a final scaling factor. Truncation/rounding is applied first, then scaling on the resulting number.

Fixed Value	Value	No variation, returns a single value.
Equally Likely	Mean Range */-	Uniformly distributed values centred on the mean.
Equally Likely (Min/Max)	Minimum Maximum	Uniformly distributed values ranging from minimum to maximum. Note that the maximum value will always be < maximum by either 1/32768 or 1/4billion, depending on the random generator selected in the model Engine options.
Triangular	Minimum Mode Maximum	Distribution shaped like a triangle with its peak at mode and probabilities decreasing to zero at Minimum and Maximum, keeping the value constrained.
Bell Curve	Mean StdDev	Normally distributed values with a distribution that looks like a bell. The standard deviation value determines the amount of variability. 95% of all values drawn will be within 3 standard deviations from the mean.
Log Normal	Mu Sigma
Random Delays	Mean
Erlang	Mean K
Weibull	Minimum Scale Shape
C.D.F. Table	Table
Point Freq. Table	Table

Bell Curve
The Normal Distribution, using an average and a deviation value. The value is taken from the bell-shaped curve with average Avg and sigma Dev. This is also known as the Normal Distribution.

Random Delays
The Poisson Distribution, using an average value only. Completely random behaviour. The value on average will be Avg but can range to very large values (with a decreasing probability). This is also known as Negative Exponential distribution.

Erlang
A Distribution that can be skewed, using a K value. The value is determined using the Erlang distribution curve, which is generated by summing K negative exponential distributions, each with an average of Avg. Large K values give an approximation to the Normal (Bell Curve) distribution.
Weibull A Distribution that is specified by Min and Scale values and a shape factor. The Weibull curve is often used for equipment breakdowns.

C.D.F Table
The Cumulative Distribution Function reads from a table, or into which you can import your own data. For use with ACTUAL HISTORICAL DATA samples, and enables an arbitrary distribution curve to be imported and used. Data is read from a file with a .CDF extension, or referenced in the attribute selection dialog as a specific Attribute Mode (CDF Dist).

Point Frequency.
The Point Frequency Distribution Function reads from a table, or into which you can import your own data. For use with ACTUAL HISTORICAL DATA samples, and enables a distribution to be described where only particular values can occur. For each value a probability value is specified. Data is read from a file with a .PMF extension, or referenced in the attribute selection dialog as a specific Attribute Mode (PDF Dist).

Setting the Parameter Values
On the right, one or more fields appear where parameter values may be entered. Small buttons to the right again of each of these fields enable references to Attributes to be entered. Deviations about the average are required for some distributions.

Scale Button
A distribution parameter and its pattern (eg. delay or Interarrival time) can be scaled by reference to (and therefore depend upon) the value of an Attribute. The distribution time gets scaled by the attribute's current value.
e.g. A Multi-server is set to a fixed parameter value of 1 hour, and also contains a reference to an Item Attribute. If the value of the Item Attribute for the item entering the server is 2, then that Item will take (1hr x 2 =) 2 hours at the server.

Truncate Button
The Truncate button enables a value truncation mode to be selected. This enables values to be restricted to whole units, either by truncation or rounding.

Truncation Options in the Distribution Pattern Dialog
Truncate Option Description
None None The default. No truncation or rounding of values occurs.
Units Units Truncates all values to the lowest whole unit, or rounds up or down to the nearest whole unit.
Seconds Seconds Seconds truncate to the lowest whole unit of seconds,or round up or down to the nearest whole unit of seconds. e.g. 1.25 truncates to 1, and 27.7 truncates to 27. With Rounding, 1.25 becomes 1, and 27.7 becomes 28.
Minutes Minutes Minutes truncate to the lowest whole unit of minutes, or round up or down to the nearest whole unit of minutes. e.g. 115 seconds truncates to to 60 seconds, and 00:05 25.00 truncates to 5 minutes or 00:05. With Rounding, 115 seconds is rounded up to 120 seconds and 00:05 25.00 is rounded down to 5 minutes or 00:05.
Hours Hours Truncates all values to the lowest whole hour Rounds all values up or down to the nearest whole hour.
Days Days Truncates all values to the lowest whole day. Rounds all values up or down to the nearest whole day.
Months Months Truncates all values to the lowest whole month. Rounds all values up or down to the nearest whole month.
Years Years Truncates all values to the lowest whole year Rounds all values up or down to the nearest whole year.

Preview Button
The Preview button enables a graphical view of the values which would be generated using the current parameters in the dialog.

This graph assists in interpreting the variation which values can undergo when random variation is used. It is not available if any distribution parameters are referencing attributes.

Random Streams
Distributions which introduce random variation draw upon a specific stream of variation and you are able to alter the stream number setting. Refer to <Random Number Streams> for more details.

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