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Modelul Erlang C×Legea lui Little (L = λW)×M/M/c Coadă: Model de Coadă cu Mai Mulți Deservitori×
DomeniuCercetare operaționalăCercetare operaționalăCercetare operațională
FamilieRegression modelRegression modelRegression model
Anul apariției198119611998
Autorul originalAgner Krarup Erlang; CooperJohn D. C. LittleQueueing-theory tradition; Gross & Harris
TipSteady-state queueing modelExact queueing identityMulti-server Markovian queueing model
Sursa seminalăCooper, R. B. (1981). Introduction to Queueing Theory (2nd ed.). North-Holland. ISBN: 978-0-444-00379-7Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387. DOI ↗Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9
Denumiri alternativeM/M/c Queue, Multi-Server Queueing Model, Erlang Delay Formula, Erlang-C Bekleme ModeliL = λW Theorem, Little's Theorem, Little's Result, Little YasasıMulti-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu
Înrudite333
RezumatThe 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.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/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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ScholarGateCompară metode: Erlang C Model · Little's Law · M/M/c Queue. Preluat la 2026-06-18 de pe https://scholargate.app/ro/compare