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Kingman's Formula

In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue.

Version
v1 · 2026-09-28 · History
Domain-specific #
10253
Domain group
Formal Sciences
Origin domain
Operations Research
Subdomain
Queueing Theory → Operations Research

Core Idea

Kingman's Formula is treated here as the recurring formal models and representations identity summarized by this source-grounded definition: In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue. In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue.

Scope of Application

  • Statement of formula. \mathbb E(Wq) \approx \left( \frac{\rho}{1-\rho} \right) \left( \frac{ca2+cs2}{2}\right) \tau.

  • Statement of formula. where \mathbb E(Wq) is the mean waiting time, τ is the mean service time (i.e. μ = 1/τ is the service rate), λ is the mean arrival rate, ρ =.

  • Documented setting. In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation for the mean waiting time in a.

  • Documented setting. The formula is the product of three terms which depend on utilization (U), variability (V) and service time (T).

  • Documented setting. It was first published by John Kingman in his 1961 paper The single server queue in heavy traffic.

Clarity

A clear use of Kingman's Formula names the carrier, the operative relation, and the conditions under which the source treats the identity as present. The minimal definition is In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue.

Manages Complexity

Kingman's Formula compresses multiple formal models and representations details into a stable diagnostic relation. The source shows both the central mechanism—it was first published by John Kingman in his 1961 paper The single server queue in heavy traffic.—and the practical consequence—it is known to be generally very accurate, especially for a system operating close to saturation.

Abstract Reasoning

  1. Type the carrier. Identify the formal models and representations entities to which the claim applies.
  2. State the relation. Use the source-grounded identity: In queueing theory, a discipline within the mathematical theory of probability, Kingman's formula, also known as the VUT equation, is an approximation for the mean waiting time in a G/G/1 queue.
  3. Check operation and conditions. \mathbb E(Wq) \approx \left( \frac{\rho}{1-\rho} \right) \left( \frac{ca2+cs2}{2}\right) \tau.
  4. Demand recognition evidence.

Knowledge Transfer

Within the home domain. Knowledge about Kingman's Formula transfers literally when a new case preserves the same carrier type, relation, and recognition test. \mathbb E(Wq) \approx \left( \frac{\rho}{1-\rho} \right) \left( \frac{ca2+cs2}{2}\right) \tau. where \mathbb E(Wq) is the mean waiting time, τ is the mean service time (i.e. μ = 1/τ is the service rate), λ is the mean arrival rate, ρ = λ/μ is the utilization, c a is the coefficient of variation for arrivals (that is the standard deviation of arrival times divided by the mean arrival.

Relationships to Other Abstractions

Local relationship map for Kingman's FormulaParents appear above the current abstraction, mutual partners to the right, and children below. Node labels state whether each abstraction is prime or domain-specific; colors identify relation types.Kingman's FormulaDOMAINPrime abstraction: Approximation — is a kind ofApproximationPRIME

Current abstraction Kingman's Formula Domain-specific

Parents (1) — more general patterns this builds on

  • Kingman's Formula is a kind of Approximation Prime

    Kingman's Formula is a strict kind of Approximation: its frozen identity entails the parent's defining structure while adding domain-specific restrictions.

Hierarchy path (1) — routes to 1 parentless root

Neighborhood in Abstraction Space

Kingman's Formula sits in a moderately populated region (41st percentile for distinctiveness): it has near-neighbors but no dense thicket of look-alikes.

Family — Service-Quality Rates & Queueing Metrics (13 abstractions)

Nearest neighbors

Computed from structural-signature embeddings · 2026-10-08