手法を比較

	M/M/1待ち行列：単一サーバ待ち行列モデル	Little's Law	M/M/c待ち行列: マルチサーバー待ち行列モデル
分野	オペレーションズ・リサーチ	オペレーションズ・リサーチ	オペレーションズ・リサーチ
系統	Regression model	Regression model	Regression model
提唱年	1953	1961	1998
提唱者	A. K. Erlang; David Kendall (notation)	John D. C. Little	Queueing-theory tradition; Gross & Harris
種類	Stochastic queueing model	Exact queueing identity	Multi-server Markovian queueing model
原典	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.	Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387.	Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9
別名	Single-Server Markovian Queue, Birth-Death Queue, Poisson Queue, M/M/1 Kuyruk Modeli	L = λW Theorem, Little's Theorem, Little's Result, Little Yasası	Multi-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu
関連	3	3	3
概要	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.	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.