Distributions

Every distribution family desflow can draw from, generated from the registry of distributions in the code. Arrivals and Services explains how a draw works, and how each family is seeded and changed live.

Each family lists its parameters, the rules they must follow, and the registry path of each parameter that can change during a run. The mean, variance and value with no random generator are computed by the family's own functions for the example given. In a blueprint, a time-valued parameter (mean, std, low, mode, high, scale, value, values, edges) also takes a duration such as 5 min.

Family	Parameters	Live paths
exponential	rate	.rate
normal	mean, std	.mean, .std
lognormal	mean, std	.mean, .std
truncated_normal	mean, std, low	.mean, .std, .low
constant	value	.value
uniform	low, high	.low, .high
triangular	low, mode, high	.low, .mode, .high
gamma	shape, scale	.shape, .scale
weibull	shape, scale	.shape, .scale
empirical	values, weights, edges, counts	none

exponential

Gaps between independent arrivals; the memoryless distribution.

dist	exponential
Parameters	rate
Defaults	none
Rules	rate > 0, in events per second
Registry paths	<sim_id>.service.<name>.rate (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: exponential, rate: 0.5}: mean 2, variance 4, and with no random generator every draw is 2.

normal

Symmetric times around a mean. Draws below 0.00001 s (min_delay) are raised to it, which raises the mean; truncated_normal avoids that.

dist	normal
Parameters	mean, std
Defaults	std 0
Rules	std >= 0; a std of 0 gives the mean every time
Registry paths	<sim_id>.service.<name>.mean, <sim_id>.service.<name>.std (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: normal, mean: 3.0, std: 0.5}: mean 3, variance 0.25, and with no random generator every draw is 3.

lognormal

Positive times with a long right tail, given by their mean and std.

dist	lognormal
Parameters	mean, std
Defaults	std 0
Rules	mean > 0, std >= 0
Registry paths	<sim_id>.service.<name>.mean, <sim_id>.service.<name>.std (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: lognormal, mean: 4.0, std: 3.0}: mean 4, variance 9, and with no random generator every draw is 4.

truncated_normal

A normal that draws again below low instead of clamping.

dist	truncated_normal
Parameters	mean, std, low
Defaults	std 0, low 0
Rules	std >= 0; low is 0 when not given; with std 0, mean >= low
Registry paths	<sim_id>.service.<name>.mean, <sim_id>.service.<name>.std, <sim_id>.service.<name>.low (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: truncated_normal, mean: 1.0, std: 1.0, low: 0.0}: mean 1.288, variance 0.6297, and with no random generator every draw is 1.

constant

The same time every draw, such as a conveyor or a set-up.

dist	constant
Parameters	value
Defaults	none
Rules	value >= 0
Registry paths	<sim_id>.service.<name>.value (and .arrival. for an arrival)
Uses a random number	no

For the example {dist: constant, value: 1.5}: mean 1.5, variance 0, and with no random generator every draw is 1.5.

uniform

Every time between low and high equally likely.

dist	uniform
Parameters	low, high
Defaults	none
Rules	low < high
Registry paths	<sim_id>.service.<name>.low, <sim_id>.service.<name>.high (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: uniform, low: 1.0, high: 2.0}: mean 1.5, variance 0.08333, and with no random generator every draw is 1.5.

triangular

An expert's estimate: the shortest, the most likely and the longest time.

dist	triangular
Parameters	low, mode, high
Defaults	none
Rules	low <= mode <= high, low < high
Registry paths	<sim_id>.service.<name>.low, <sim_id>.service.<name>.mode, <sim_id>.service.<name>.high (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: triangular, low: 1.0, mode: 1.25, high: 2.25}: mean 1.5, variance 0.07292, and with no random generator every draw is 1.5.

gamma

Times less variable than exponential. A whole-number shape is the Erlang distribution: that many exponential steps in a row.

dist	gamma
Parameters	shape, scale
Defaults	none
Rules	shape > 0, scale > 0; mean = shape * scale
Registry paths	<sim_id>.service.<name>.shape, <sim_id>.service.<name>.scale (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: gamma, shape: 9.0, scale: 0.1667}: mean 1.5, variance 0.2501, and with no random generator every draw is 1.5.

weibull

Time to failure: a shape below 1 fails early, above 1 wears out.

dist	weibull
Parameters	shape, scale
Defaults	none
Rules	shape > 0, scale > 0
Registry paths	<sim_id>.service.<name>.shape, <sim_id>.service.<name>.scale (and .arrival. for an arrival)
Uses a random number	yes

For the example {dist: weibull, shape: 1.5, scale: 3600.0}: mean 3250, variance 4.869e+06, and with no random generator every draw is 3250.

empirical

Times taken from real data: listed values with optional weights, or a histogram of edges and counts. Taken at load; they do not change live.

dist	empirical
Parameters	values, weights, edges, counts
Defaults	none
Rules	values, or edges and counts; one weight per value and one count per bin, each 0 or more and adding up to more than 0; edges increasing
Registry paths	none: the lists are taken at load
Uses a random number	yes

For the example {dist: empirical, values: [1.2, 1.5, 1.5, 2.1, 3.0]}: mean 1.86, variance 0.4104, and with no random generator every draw is 1.86.