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Hàng đợi M/M/1: Mô hình Hàng đợi Đơn Máy phục vụ×Mô hình Erlang C×Định luật Little (L = λW)×
Lĩnh vựcVận trù họcVận trù họcVận trù học
HọRegression modelRegression modelRegression model
Năm ra đời195319811961
Người khởi xướngA. K. Erlang; David Kendall (notation)Agner Krarup Erlang; CooperJohn D. C. Little
LoạiStochastic queueing modelSteady-state queueing modelExact queueing identity
Công trình gốcKendall, 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 ↗Cooper, 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 ↗
Tên gọi khácSingle-Server Markovian Queue, Birth-Death Queue, Poisson Queue, M/M/1 Kuyruk ModeliM/M/c Queue, Multi-Server Queueing Model, Erlang Delay Formula, Erlang-C Bekleme ModeliL = λW Theorem, Little's Theorem, Little's Result, Little Yasası
Liên quan333
Tóm tắtThe 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 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.
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ScholarGateSo sánh phương pháp: M/M/1 Queue · Erlang C Model · Little's Law. Truy cập ngày 2026-06-18 từ https://scholargate.app/vi/compare