Khinchin–Pollaczek formula
E378997
The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
All labels observed (2)
| Label | Occurrences |
|---|---|
| Khinchin–Pollaczek formula canonical | 1 |
| Pollaczek–Khinchine formula | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T3677826 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Khinchin–Pollaczek formula Context triple: [Aleksandr Khinchin, notableWork, Khinchin–Pollaczek formula]
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Clark–Ocone formula
The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
-
C.
Chapman–Kolmogorov equation
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
-
D.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
E.
Isserlis’ theorem in probability theory
Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Khinchin–Pollaczek formula Target entity description: The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
-
A.
Feynman–Kac formula
The Feynman–Kac formula is a fundamental result connecting solutions of certain partial differential equations with expectations over stochastic processes, forming a bridge between quantum mechanics, probability theory, and mathematical finance.
-
B.
Clark–Ocone formula
The Clark–Ocone formula is a key result in stochastic calculus and Malliavin calculus that provides an explicit integral representation of square-integrable random variables with respect to Brownian motion.
-
C.
Chapman–Kolmogorov equation
The Chapman–Kolmogorov equation is a fundamental relation in the theory of stochastic processes that expresses how transition probabilities of a Markov process over longer time intervals can be obtained by integrating over intermediate states.
-
D.
Berry–Esseen theorem
The Berry–Esseen theorem is a quantitative refinement of the central limit theorem that provides explicit bounds on the rate of convergence of normalized sums of independent random variables to the normal distribution.
-
E.
Isserlis’ theorem in probability theory
Isserlis’ theorem in probability theory is a result that expresses higher-order moments of jointly Gaussian random variables in terms of sums of products of their pairwise covariances.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical formula
ⓘ
result in probability theory ⓘ result in queueing theory ⓘ |
| appliesTo |
GI/G/1 queue
ⓘ
M/G/1 queue ⓘ single-server queues ⓘ |
| appliesUnder |
independent interarrival and service processes
ⓘ
independent service times ⓘ stationary arrival process ⓘ |
| assumes |
first-come first-served discipline
ⓘ
single server ⓘ stability condition for the queue ⓘ |
| characterizes |
distribution of customer waiting time
ⓘ
distribution of virtual waiting time ⓘ |
| concerns |
steady-state behavior of queues
ⓘ
waiting time of customers in a queue ⓘ |
| domain |
operations research
ⓘ
stochastic processes ⓘ |
| field |
applied probability
ⓘ
probability theory ⓘ queueing theory ⓘ |
| focusesOn |
equilibrium distribution of waiting time
ⓘ
steady-state waiting time ⓘ |
| gives |
Laplace–Stieltjes transform of the waiting-time distribution
ⓘ
explicit expression for the waiting-time distribution ⓘ stationary waiting-time distribution ⓘ |
| historicalPeriod | 20th century mathematics ⓘ |
| isPartOf | classical queueing theory results ⓘ |
| mathematicalTool |
Laplace–Stieltjes transforms
ⓘ
complex analysis ⓘ generating functions ⓘ |
| namedAfter |
Aleksandr Khinchin
ⓘ
Felix Pollaczek ⓘ |
| relatedTo |
Laplace transform methods
ⓘ
Lindley equation ⓘ Khinchin–Pollaczek formula self-linksurface differs ⓘ
surface form:
Pollaczek–Khinchine formula
renewal theory ⓘ |
| requires |
finite mean service time
ⓘ
load less than one ⓘ |
| typeOf | transform-domain representation of distributions ⓘ |
| usedFor |
computing higher moments of waiting time
ⓘ
computing mean waiting time ⓘ computing waiting-time distributions ⓘ performance analysis of queues ⓘ |
| usedIn |
computer system performance analysis
ⓘ
telecommunications modeling ⓘ traffic engineering ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Khinchin–Pollaczek formula Description of subject: The Khinchin–Pollaczek formula is a result in probability theory and queueing theory that provides an explicit expression for the stationary waiting-time distribution in certain single-server queues.
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Pollaczek–Khinchine formula