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.

Truncation/rounding is useful where specific values are needed, for example when using a distribution to select between options.

Scaling is useful where the distribution might not change but needs to be adapted in continuous or batch processing situations.

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	This is a distribution where the logarithm of the random values is normally distributed. It is used in cases where many random factors multiply together, including finance and communications.
Random Delays	Mean	This is the Negative Exponential or Poisson distribution and characterises the number of events that will occur over a period of time if the probability of each event is random and independent. It features a long tail of decreasing probability of occurance.
Erlang	Mean K	This characterises the time between independent events (eg: arrivals). It is actually the sum of 'K' random delays.
Weibull	Minimum Scale Shape	This distribution has a minimum and is often used to characterise equipment breakdowns.
C.D.F. Table	Table	This uses a table enabling any distribution of values to be generated. The reference must point to a "accumulating probability" column in a table where the first row cell is 0 and subsequent rows increase until the final row which must have a 1.0. PL uses a uniform (0..1) draw and locates the row where that probability lies. The value in column 1 is then returned. If the value was between rows, interpolation is used. This results in a continuous distribution of values.
Point Freq. Table	Table	This uses a table to define discrete values and their probabilities. The table reference points to a column of probabilities. The sum of all the probabilities in this column must be 1. A uniform (0..1) draw is made and the row (bin) within which that draw lies is found in the table. The corresponding value in column 1 is returned. There is no interpolation. This results in discrete values, corresponding to the values in column 1 of the table, occuring at probabilities as set in the probability column.

The Truncation / Rounding button selects either round (to closest integer) or truncate (remove fraction) operation. For times, more options appear enabling truncating/rounding a time (always in seconds) to the nearest second (1, same as unit but included for clarity), minute (60), hour (3600) or day (86400).

For example:

Round Unit 3.7 = 4
Truncate Unit 3.7 = 3
Round Hour 3500 = 3600 (would display as 1:00 00 in a time formatted view)
Truncate Hour 7100 = 3600 (1:00 00)

Preview Button
Generates a graphical view of the values which would be generated using the current parameters. In cases where non numeric references are used, a preview cannot be generated. You can code your model to log the values in a table and process them to generate a graph.

Random Streams
Distributions draw upon a specific generator of basic random numbers and you are able to alter the stream number setting. Normally all random values (including ones Planimate uses internally eg: for probability switches) draw from stream 0.

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