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Model Erlang C×Fronta M/M/1: Model fronty s jedným obslužným miestom×Model viac-servisového obslužného systému M/M/c×
OdborOperačný výskumOperačný výskumOperačný výskum
RodinaRegression modelRegression modelRegression model
Rok vzniku198119531998
TvorcaAgner Krarup Erlang; CooperA. K. Erlang; David Kendall (notation)Queueing-theory tradition; Gross & Harris
TypSteady-state queueing modelStochastic queueing modelMulti-server Markovian queueing model
Pôvodný zdrojCooper, R. B. (1981). Introduction to Queueing Theory (2nd ed.). North-Holland. ISBN: 978-0-444-00379-7Kendall, 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 ↗Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9
Ďalšie názvyM/M/c Queue, Multi-Server Queueing Model, Erlang Delay Formula, Erlang-C Bekleme ModeliSingle-Server Markovian Queue, Birth-Death Queue, Poisson Queue, M/M/1 Kuyruk ModeliMulti-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu
Príbuzné333
ZhrnutieThe Erlang C model is a steady-state queueing formula that determines the probability a customer must wait before being served in a system with c parallel servers, Poisson arrivals at rate lambda, and exponentially distributed service times. Originally developed by Danish engineer Agner Krarup Erlang in the early twentieth century for telephone exchange design, and formalized in the queueing theory literature by Cooper (1981), it remains the canonical staffing model for call centers and service operations worldwide.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.The 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.
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ScholarGatePorovnať metódy: Erlang C Model · M/M/1 Queue · M/M/c Queue. Získané 2026-06-18 z https://scholargate.app/sk/compare