Glossary

A quick reference for the terms used across this site. For the full story behind each, follow the links into the theory pages.

Arrival rate (λ)

The average number of entities arriving per unit time. If inter-arrival times average $1/\lambda$, the arrival rate is $\lambda$. A source with exponential inter-arrivals is a Poisson arrival process. See queueing theory.

Balking

An arriving entity that leaves immediately because the queue is full (at its capacity) rather than joining it. The engine reports balked counts on the queue.

Capacity

The maximum number of entities a queue can hold. Arrivals beyond capacity balk. Omit it for an unbounded queue.

Confidence interval

A range around an estimated mean that, with a stated probability, contains the true value. The engine reports each KPI as a mean ± a 95% CI half-width across replications, so you can tell signal from noise.

Cross-Entropy

The optimization method behind optimize(): it samples candidate designs from a distribution, keeps the best ("elite") few, and re-fits the distribution toward them, iterating until it converges on a cheap, feasible design. See Cross-Entropy optimization.

Discrete-event simulation

A simulation that advances time by jumping from one scheduled event to the next (arrival, service completion, …) rather than ticking at fixed steps. See discrete-event simulation.

Erlang-C

The classic formula for the probability that an arriving customer must wait in an M/M/c queue; the basis for the closed-form results the engine is validated against. See queueing theory.

Kendall notation

The shorthand A/S/c describing a queue: arrival process / service distribution / number of servers (e.g. M/M/1, M/M/c). "M" means Markovian (exponential / memoryless).

M/M/1

A single-server queue with exponential (Markovian) inter-arrival and service times. Has simple closed-form results used to validate the engine. See queueing theory.

M/M/c

Like M/M/1 but with c parallel servers sharing one queue. Waiting depends on the Erlang-C formula. See queueing theory.

Queue discipline

The rule for choosing which waiting entity is served next: FIFO (first in, first out), LIFO, or priority. Set on a queue's discipline parameter.

Replication

One independent run of the model with its own random stream. Averaging KPIs over many replications, and reporting a confidence interval, gives statistically meaningful results.

Resource

A node modeling a pool of servers; each busy server holds one entity for a sampled service time. A resource must be fed by a queue so entities always have somewhere to wait. Reports utilization.

Service rate (μ)

The average number of entities one server can complete per unit time; the inverse of the mean service time. See queueing theory.

Source

A node that creates entities, spacing arrivals by an inter-arrival distribution. Model a stream of arrivals (passengers, packets, calls) as one source with a rate — never one node per arriving entity.

Throughput

The number of entities that completed (reached a sink) over the run — the system's effective output rate.

Time in system

The total time an entity spends from arrival to exit: waiting plus service across all nodes it visits. Reported on the sink.

Utilization

The fraction of a resource's server capacity that is busy, $\rho =\lambda /(c\mu )$. The system is stable only when $\rho <1$; wait grows sharply as $\rho \to 1$. See queueing theory.

Warm-up

An initial period whose statistics are discarded so transient startup behavior (an empty system filling up) doesn't bias steady-state KPIs. Set via the warmup run setting.

Wait time

The time an entity spends waiting in a queue before a server is free (excludes the service itself). Reported as avgWait, with percentiles in detailed mode.