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)

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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 ⓘ
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

Referenced by (5)

Full triples — surface form annotated when it differs from this entity's canonical label.

Aleksandr Khinchin → notableWork → Khinchin–Pollaczek formula ⓘ
Khinchin–Pollaczek formula → relatedTo → Pollaczek–Khinchine formula ⓘ
linked to: Khinchin–Pollaczek formula
Felix Pollaczek → notableWork → Pollaczek–Khinchine formula ⓘ
linked to: Khinchin–Pollaczek formula
Felix Pollaczek → knownFor → Pollaczek–Khinchine formula ⓘ
linked to: Khinchin–Pollaczek formula
Felix Pollaczek → notableConcept → Pollaczek–Khinchine formula ⓘ
linked to: Khinchin–Pollaczek formula