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| M/M/1队列：单服务器排队模型× | Erlang C 模型× | |
|---|---|---|
| 领域 | 运筹学 | 运筹学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1953 | 1981 |
| 提出者≠ | A. K. Erlang; David Kendall (notation) | Agner Krarup Erlang; Cooper |
| 类型≠ | Stochastic queueing model | Steady-state queueing model |
| 开创性文献≠ | 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. DOI ↗ | Cooper, R. B. (1981). Introduction to Queueing Theory (2nd ed.). North-Holland. ISBN: 978-0-444-00379-7 |
| 别名 | Single-Server Markovian Queue, Birth-Death Queue, Poisson Queue, M/M/1 Kuyruk Modeli | M/M/c Queue, Multi-Server Queueing Model, Erlang Delay Formula, Erlang-C Bekleme Modeli |
| 相关 | 3 | 3 |
| 摘要≠ | 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. | 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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