Struct KingmanFormula 

pub struct KingmanFormula { /* private fields */ }

Kingman’s VUT Formula for queue wait times.

The expected wait time in queue is approximated by: W_q ≈ (ρ / (1-ρ)) × ((c_a² + c_s²) / 2) × t_s

where:

• ρ: Utilization (arrival rate / service rate)
• c_a: Coefficient of variation of inter-arrival times
• c_s: Coefficient of variation of service times
• t_s: Mean service time

This formula reveals the “hockey stick” effect: wait times grow exponentially as utilization approaches 100%.

Implementations

impl KingmanFormula

pub fn new() -> Self

Create a new Kingman’s Formula equation.

pub fn expected_wait_time(&self, rho: f64, c_a: f64, c_s: f64, t_s: f64) -> f64

Calculate expected wait time in queue.

Arguments

• rho: Utilization (0 < ρ < 1)
• c_a: Coefficient of variation of arrivals
• c_s: Coefficient of variation of service
• t_s: Mean service time

Returns

Expected wait time in queue.

pub fn utilization_factor(&self, rho: f64) -> f64

Get the utilization factor ρ/(1-ρ).

pub fn variability_factor(&self, c_a: f64, c_s: f64) -> f64

Get the variability factor (c_a² + c_s²)/2.

Trait Implementations

impl Clone for KingmanFormula

fn clone(&self) -> KingmanFormula

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for KingmanFormula

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.

impl Default for KingmanFormula

fn default() -> Self

Returns the “default value” for a type.

impl GoverningEquation for KingmanFormula

fn latex(&self) -> &str

Get the LaTeX representation of the equation.

fn class(&self) -> EquationClass

Get the equation’s classification.

fn citation(&self) -> Citation

Get the primary citation for this equation.

fn variables(&self) -> Vec<EquationVariable>

Get all variables in this equation.

fn description(&self) -> &str

Get a human-readable description.

fn name(&self) -> &'static str

Get the equation name.

fn validate_consistency( &self, values: &[(&str, f64)], tolerance: f64, ) -> Result<(), String>

Validate that a set of values satisfies the equation within tolerance.