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Опашка M/M/c: Модел на опашка с множество сървъри×Закон на Литъл (L = λW)×M/M/1 опашка: Основният модел на опашка с един обслужващ канал×
ОбластИзследване на операциитеИзследване на операциитеИзследване на операциите
СемействоRegression modelRegression modelRegression model
Година на възникване199819611953
СъздателQueueing-theory tradition; Gross & HarrisJohn D. C. LittleA. K. Erlang; David Kendall (notation)
ТипMulti-server Markovian queueing modelExact queueing identityStochastic queueing model
Основополагащ източникGross, 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 ↗Kendall, D. G. (1953). Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain. The Annals of Mathematical Statistics, 24(3), 338–354. DOI ↗
Други названияMulti-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 YasasıSingle-Server Markovian Queue, Birth-Death Queue, Poisson Queue, M/M/1 Kuyruk Modeli
Свързани333
РезюмеThe 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.The M/M/1 queue is the foundational single-server queueing model in which customers arrive according to a Poisson process with rate λ, are served one at a time by a single server with exponentially distributed service times at rate μ, and wait in an infinite-capacity first-come-first-served queue. Formalized within the Kendall notation framework by David Kendall in 1953, building on A. K. Erlang's early twentieth-century telephone traffic work, it yields closed-form steady-state performance measures when the traffic intensity ρ = λ/μ is less than one.
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ScholarGateСравнение на методи: M/M/c Queue · Little's Law · M/M/1 Queue. Извлечено на 2026-06-18 от https://scholargate.app/bg/compare