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| 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× | |
|---|---|---|
| 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 |
| 系統 | Regression model | Regression model |
| 提唱年≠ | 1998 | 1981 |
| 提唱者≠ | Queueing-theory tradition; Gross & Harris | Agner Krarup Erlang; Cooper |
| 種類≠ | Multi-server Markovian queueing model | Steady-state queueing model |
| 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 |
| 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 |
| 関連 | 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. |
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