Distributions

Every random quantity in a model — interarrival times on a source, service times on a resource — is drawn from a distribution. YourSimulation ships eight, defined in distributions.ts. Each is written as a small JSON object with a dist tag plus its parameters.

Picking the right shape matters: exponential interarrivals are the textbook default for "random independent arrivals", but real service times are usually not exponential, and using the wrong distribution skews waits and utilization.

Service and interarrival times cannot be negative. normal draws are clamped at 0; the others are non-negative by construction.

const

Fixed value — no randomness. Useful for deterministic timings or as a sanity baseline.

• Params: value
• JSON: { "dist": "const", "value": 5 }

exp — exponential

The memoryless distribution: the chance of the next event in the coming instant doesn't depend on how long you've already waited. This is the canonical model for random, independent arrivals (a Poisson process) and the "M" in M/M/1.

• Use it for: arrival processes; the baseline for theory comparisons.
• Params: mean
• JSON: { "dist": "exp", "mean": 2 }

uniform

Equally likely anywhere between min and max. A simple "I only know the range" choice.

• Use it for: rough bounds with no central tendency.
• Params: min, max
• JSON: { "dist": "uniform", "min": 1, "max": 4 }

triangular

A peaked distribution defined by three numbers: the smallest plausible value, the most likely, and the largest. It encodes an expert's min / likely / max estimate without needing data.

• Use it for: service times when you have a stakeholder estimate but no measurements.
• Params: min, mode, max
• JSON: { "dist": "triangular", "min": 1, "mode": 3, "max": 6 }

normal

The bell curve, symmetric around mean with spread sd. Draws are clamped at 0 so times stay non-negative.

• Use it for: quantities that cluster tightly around an average with symmetric variation.
• Params: mean, sd
• JSON: { "dist": "normal", "mean": 5, "sd": 1 }

lognormal

A right-skewed distribution: most values near a typical level, with an occasional long tail of large values. It's the realistic default for service durations, where most jobs are quick but a few drag on.

• Use it for: right-skewed service times. Note the params are the mean (mu) and sd (sigma) of the underlying normal, not of the lognormal itself.
• Params: mu, sigma
• JSON: { "dist": "lognormal", "mu": 1, "sigma": 0.5 }

erlang

The sum of k independent exponential stages, each averaging mean / k. It models a process made of several sequential exponential steps and is less variable than a single exponential of the same mean.

• Use it for: multi-stage service (e.g. form, then check, then stamp); a "smoother than exponential" service time.
• Params: k (integer ≥ 1), mean
• JSON: { "dist": "erlang", "k": 3, "mean": 6 }

empirical

Samples directly from a list of observed values, optionally weighted. The closest you get to "just replay my measured data".

• Use it for: measured/historical data — no distributional assumption needed.
• Params: values (array), optional weights (array; defaults to equal weights)
• JSON: { "dist": "empirical", "values": [2, 3, 5, 8], "weights": [4, 3, 2, 1] }

Choosing quickly

Situation	Distribution
Random independent arrivals	exp
Expert min/likely/max guess	triangular
Realistic, right-skewed service	lognormal
Several sequential service steps	erlang
You have measured data	empirical
Fixed timing / baseline	const

See the glossary for related terms, and queueing theory for how the choice of distribution moves the math out of closed-form and into simulation.