手法を比較

	M/M/c待ち行列: マルチサーバー待ち行列モデル	Erlang C モデル	Little's Law
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	1998	1981	1961
提唱者	Queueing-theory tradition; Gross & Harris	Agner Krarup Erlang; Cooper	John D. C. Little
種類	Multi-server Markovian queueing model	Steady-state queueing model	Exact queueing identity
原典	Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9	Cooper, R. B. (1981). Introduction to Queueing Theory (2nd ed.). North-Holland. ISBN: 978-0-444-00379-7	Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387.
別名	Multi-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu	M/M/c Queue, Multi-Server Queueing Model, Erlang Delay Formula, Erlang-C Bekleme Modeli	L = λW Theorem, Little's Theorem, Little's Result, Little Yasası
関連	3	3	3
概要	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.	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.