Distributions¶

~name(args…)

Sample a number each time the expression is evaluated. Arguments are required numeric expressions. A wrong argument count is a link error. A draw is allowed only at moments that permit sampling: const expressions and hold headers cannot draw. See evaluation moments.

Distribution index¶

Distribution	Parameters	Mean	Description
`~exp(mean)`	`mean: expr`	`mean`	Exponential.
`~det(x)`	`x: expr`	`x`	Constant value.
`~uniform(lo, hi)`	`lo, hi: expr`	`(lo + hi) / 2`	Continuous uniform.
`~erlang(k, mean)`	`k, mean: expr`	`mean`	Sum of exponential phases.
`~h2(mean, cv2)`	`mean, cv2: expr`	`mean`	Balanced two-phase hyperexponential.
`~bernoulli(p)`	`p: expr`	`p`	0 or 1.

`exp`¶

~exp(mean: expr) -> number

Parameters: mean is the mean duration in the consumer's unit. Use a positive finite mean for an exponential duration.

Returns: an exponential draw of mean mean and squared coefficient of variation (CV²) 1. The parameter is a mean, not a rate.

`det`¶

~det(x: expr) -> number

Parameters: x is the value to return.

Returns: exactly x. It is still a draw expression for validation, so it cannot be used where draws are forbidden.

`uniform`¶

~uniform(lo: expr, hi: expr) -> number

Parameters: lower and upper bounds lo and hi. Use finite ordered bounds for a bounded duration.

Returns: lo + (hi - lo) * U, where U is uniform in [0, 1). Equal bounds return that value; floating-point rounding applies at the endpoints. Mean: (lo + hi) / 2.

`erlang`¶

~erlang(k: expr, mean: expr) -> number

Parameters: k is the phase count, rounded down and taken to be at least 1. mean is the total mean, not the mean of each phase; use a positive finite value for a duration.

Returns: the sum of k independent exponential draws, each with mean mean / k. Its CV² is 1 / k after the phase-count conversion.

`h2`¶

~h2(mean: expr, cv2: expr) -> number

Parameters: mean is the total mean; use a positive finite value for a duration. cv2 is the squared coefficient of variation, taken to be at least 1. For cv2 = 1, the law is exponential.

Returns: a draw from the balanced two-phase hyperexponential law. For v = max(cv2, 1) and p = (1 + sqrt((v - 1) / (v + 1))) / 2, choose an exponential of mean mean / (2*p) with probability p, otherwise one of mean mean / (2*(1-p)).

`bernoulli`¶

~bernoulli(p: expr) -> number

Parameters: p is a probability in [0, 1].

Returns: 1 with probability p, otherwise 0. The form branch with (p) uses this draw; see branch.

Validation and reproducibility¶

The domains above describe the intended distributions, not a guarantee that every invalid parameter is rejected at link time. The consuming construct validates its own requirements: for example, a renewal gap must be positive and finite when drawn or the run fails.

The run's seed initializes separate streams for arrivals, workload draws, session statements and eviction keys. Workload draws are keyed by session and turn: unchanged draw expressions with the same inputs reproduce the same values across scheduling policies. See workloads.

Examples¶

A complete program with bursty arrivals and Erlang service times:

fn main() {
  stage svc : fifo;
  workload {
    arrive renewal(~h2(2, 4));
  }
  server {
    set t0 = now;
    run svc (cost(svc, ~erlang(4, 1)));
    observe response = now - t0;
  }
}

Save as model.sq, then run:

serq run model.sq --horizon 1000 --seed 10

Distributions¶

Distribution index¶

exp¶

det¶

uniform¶

erlang¶

h2¶

bernoulli¶