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Overview

A field that varies run-to-run can be drawn from a probability distribution instead of a fixed number. Distributions let a model reflect real-world variability: cycle times that vary, demand that clusters and lulls, processing durations with realistic long tails. In the Modeler, the distribution picker appears on:
  • Processing Time on a Process
  • Arrival Logic on a Source — note this is an inter-arrival time (time between arrivals), not a rate
  • The Distribution assignment strategy for Number attributes on Source, Combiner, Separator, and Transformer outputs
Resource requirements on a Process take a whole-number quantity, and a Resource’s changeover times take a fixed duration. If you need either to vary, ask Dexter to set it up.
The Quantity to release on a release action takes a literal number or a DSL expression, not a distribution.
Open the distribution picker and choose from ten options: Fixed, Normal, Exponential, Uniform, Lognormal, Weibull, Triangular, Erlang, Beta, Gamma. Each choice reveals its own set of parameter fields below the picker, pre-filled with starting values. Every parameter field is a duration picker (days, hours, minutes, seconds) by default. Click the </> toggle (Switch to expression) next to a parameter to type a DSL expression instead: that’s how you make variability depend on simulation state, constants, or entity attributes. The distribution choice is static configuration. Individual parameter values can be literals or expressions, mixed freely.
The duration picker holds whole seconds, even for dimensionless parameters like Beta’s shape parameters, Weibull’s shape, or Lognormal’s Sigma. To enter a fractional value such as a Sigma of 0.294 or an Alpha of 2.5, switch the parameter to expression mode and type the number. The field keeps the exact value, but when you leave it, it switches back to the duration picker, which shows the value rounded to a whole second. Editing it in the picker replaces it with a whole number.

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Supported Distributions

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Fixed

A deterministic value. Technically not a distribution, but included for consistency so every distribution field uses the same picker. Parameters
  • Value: the constant the field always resolves to.
A new Process or Source starts at Fixed, 1 second. Until you change it, the Process takes one second per entity and the Source releases an entity every second. Set the value before you run.
Use for: predictable, non-random values. Useful when you want the field to be wired the same way as variable fields but the value should not vary.
Fixed + expression mode is how you feed a computed value into a distribution slot. There’s no way to call a distribution from the DSL, but the reverse composition works: pick Fixed, switch its Value to expression mode, and write LOOKUP(CYCLE_TIMES, ENTITY_TYPE, default:=60) or any other expression.

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Normal

The classic bell curve: symmetric around a mean, spread controlled by standard deviation. Parameters
  • Mean: center of the distribution.
  • Standard Deviation: spread around the mean.
Use for: processing times that cluster tightly around a central value with symmetric variability. Machine cycle times, measurement errors, and anything subject to many small independent sources of variation. Watch out: normal distributions extend to negative infinity, so a Normal can draw negative values. Processing and arrival times are clamped to zero, so those draws become zero-duration steps or simultaneous arrivals, and the average shifts above the Mean you set. For strictly positive quantities (times, weights), prefer Lognormal or Gamma.

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Exponential

Time between memoryless events. Higher concentration near zero, long tail. Parameters
  • Beta: the mean (equivalently, 1 over the rate). Despite the name, it’s the expected value of a sample.
Use for: inter-arrival times in Poisson processes (random arrivals), time until a random failure, time until a random event with constant hazard rate.

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Uniform

Every value between the bounds is equally likely. Flat distribution. Parameters
  • Lower Bound: minimum sample value.
  • Upper Bound: maximum sample value. Must be greater than the Lower Bound.
Use for: cases where you only know the bounds and have no reason to favor any specific value within them. Often a starting assumption before better data is available.

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Lognormal

A log-transform of a normal distribution: right-skewed, strictly positive, with a long right tail. Parameters
  • Mu: mean of the underlying normal distribution (before the log transform), not of the lognormal itself.
  • Sigma: standard deviation of the underlying normal distribution.
Mu and Sigma are log-space parameters, not the mean and standard deviation of your data. Entering a real-world mean of 60 as Mu is the #1 lognormal mistake — it produces samples around e⁶⁰. Convert first (below). Extremely large Mu (above roughly 700) overflows the exponential entirely.
Converting from a real-world mean and CV. Process-engineering numbers usually arrive as a mean duration and a coefficient of variation (CV = standard deviation ÷ mean), not as log-space parameters. Convert them with:
For example, mean 60 with CV 0.3: sigma² = ln(1.09) ≈ 0.086 → Sigma ≈ 0.294, Mu = ln(60) − 0.043 ≈ 4.05. Both are fractional, so enter them in expression mode. You can also give Dexter the mean and CV and ask it to set up the lognormal for you. Use for: service times, task durations, and any quantity that’s positive, has a clear typical value, and occasionally has long outliers. Many real-world “how long does this take?” distributions are well-modeled by lognormal.

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Weibull

Flexible distribution that can model increasing, constant, or decreasing hazard rates depending on its shape parameter. Parameters
  • Shape: controls how the hazard rate evolves with elapsed time. Shape < 1 models infant mortality (failure rate decreasing over time), Shape = 1 reduces to Exponential (constant rate), Shape > 1 models wear-out (failure rate increasing over time).
  • Scale: characteristic magnitude of the samples.
Both parameters must be greater than zero. Use for: time-to-failure modeling (reliability engineering), fatigue life, and any process where the rate of occurrence changes with elapsed time.

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Triangular

A simple three-point distribution. Parameters
  • Lower Bound: minimum possible value.
  • Upper Bound: maximum possible value.
  • Mode: most likely value. Must satisfy Lower Bound ≤ Mode ≤ Upper Bound.
The mean of a Triangular sample is (lower + upper + mode) / 3 — handy for sanity-checking results against the numbers you were given. Use for: expert-elicited estimates (“fastest it ever takes is 2 min, typically 5 min, worst case 10 min”). A reasonable default when you have three-point estimates but no empirical distribution to fit.

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Erlang

Sum of Shape independent exponential random variables, where Shape must be a positive integer. Parameters
  • Shape: number of exponential stages summed (a positive integer; a fractional value is truncated to a whole number when the model runs).
  • Scale: mean of each underlying exponential stage.
Use for: multi-stage processes where each stage is exponentially distributed, or when you need positive distributions with more shape control than exponential and less complexity than gamma. If you want a non-integer shape, use Gamma — it’s the continuous generalization of Erlang.

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Beta

Distribution on the interval [0, 1], flexibly shaped by two parameters. Parameters
  • Alpha: first shape parameter.
  • Beta Parameter: second shape parameter. (The label is spelled out to avoid confusion with the Beta distribution name itself.)
Both shape parameters must be greater than zero. Use for: proportions, yields, and probabilities that vary run-to-run. Shape parameters let you express everything from uniform (Alpha = 1, Beta Parameter = 1) through bell-like shapes to heavily skewed.

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Gamma

General-purpose continuous distribution for positive quantities, controlled by two parameters. Parameters
  • Alpha: shape parameter.
  • Beta: scale parameter, so the mean is Alpha × Beta.
Both parameters must be greater than zero. Gamma reduces to Exponential at Alpha = 1 and to Erlang at integer Alpha. Use for: positive quantities with a more flexible shape than exponential or lognormal. Service times, waiting times, and queueing phenomena.

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Choosing a Distribution

If you have real data, fit a distribution to it. If you don’t: For processing times where you have “average” and “worst case” numbers from the floor, Triangular is a pragmatic default; if you have a mean and a spread, Lognormal is usually better. For arrival patterns, Exponential is the standard start. Avoid Normal for durations — its negative draws are clamped to zero. For distribution-sensitive work (queue analysis, reliability), fit to real data.

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Parameterizing with DSL Expressions

Each parameter field has a </> toggle next to its label. Click it and the duration picker is replaced by a single-line text input where you type a DSL expression: references to constants, state variables, entity attributes (where the context allows), or composed expressions. Click the timer icon (Switch to duration) to go back to the duration picker. A parameter in expression mode might hold:
  • base_time * complexity_factor: scale a Normal distribution’s Mean by entity attributes while leaving Standard Deviation as a literal.
  • LOOKUP(MEAN_INTERARRIVAL_BY_SHIFT, CURRENT_SHIFT): drive an Exponential distribution’s Beta from a shift-indexed lookup table and a state variable.
  • LOOKUP(LOG_MEAN_WEIGHT_BY_PRODUCT, ENTITY_TYPE): pick a Lognormal Mu per product type while keeping Sigma fixed.
Expression-mode and duration-picker parameters can be mixed freely on the same distribution: switch only the parameters that need to vary. This composability is what lets a single model represent rich, data-driven variability without hardcoding numbers across dozens of fields.

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Tips

  • Draw from the distribution at use time, not at entity creation time. For processing times especially, sample the distribution when the Process runs, not as an entity attribute set at the Source. This keeps the sample close to the state it should depend on.
  • Normal isn’t always the answer. It’s familiar but it can draw negative values. For strictly positive quantities, prefer Lognormal or Gamma.
  • Check parameter labels carefully. Different distributions reuse names even when the mathematical concept is similar: Exponential’s Beta is a mean, Gamma’s Beta is a scale (mean = Alpha × Beta), and Beta’s Beta Parameter is a shape. The picker’s labels are the source of truth.
  • Respect parameter constraints. Uniform needs upper > lower; Triangular needs lower ≤ mode ≤ upper; Erlang’s shape must be a positive integer; Weibull, Gamma, Beta, and Exponential parameters must all be positive. The play button doesn’t check these. When a run meets an invalid parameter, it corrects the value (swapping reversed bounds, clamping the mode or a non-positive parameter) and reports a runtime advisory on the run. A fractional Erlang shape is truncated without an advisory. If a run finishes with advisories, check them before trusting the results.
  • Match distribution to data when possible. A fitted distribution on real MES cycle times will give much more realistic results than an assumed parametric one.
  • Use Fixed to simplify initial modeling. Start with fixed values to verify the structure, then swap in distributions once the model is correct.