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File d'attente M/M/c : Modèle de file d'attente multi-serveurs×La loi de Little (L = λW)×
DomaineRecherche opérationnelleRecherche opérationnelle
FamilleRegression modelRegression model
Année d'origine19981961
Auteur d'origineQueueing-theory tradition; Gross & HarrisJohn D. C. Little
TypeMulti-server Markovian queueing modelExact queueing identity
Source fondatriceGross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387. DOI ↗
AliasMulti-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c KuyruğuL = λW Theorem, Little's Theorem, Little's Result, Little Yasası
Apparentées33
RésuméThe M/M/c queue is a multi-server stochastic model in which customers arrive according to a Poisson process at rate λ, are served by c identical servers each with exponentially distributed service times at rate μ, and wait in a single common queue when all servers are busy. Systematized within classical queueing theory and thoroughly treated by Gross and Harris (1998), it extends the simpler M/M/1 model to settings with parallel servers, making it the foundational tool for capacity planning in service systems.Little's Law is a fundamental theorem in queueing theory that relates the long-run average number of items in a stable system (L) to the long-run average arrival rate (λ) and the long-run average time an item spends in the system (W), expressed as L = λW. Introduced and rigorously proved by John D. C. Little in 1961, the law holds for virtually any stable stochastic system, requiring no assumptions about arrival distributions, service distributions, or queue disciplines.
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ScholarGateComparer des méthodes: M/M/c Queue · Little's Law. Consulté le 2026-06-17 sur https://scholargate.app/fr/compare