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| M/M/1队列：单服务器排队模型× | M/M/c 队列：多服务器排队模型× | |
|---|---|---|
| 领域 | 运筹学 | 运筹学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1953 | 1998 |
| 提出者≠ | A. K. Erlang; David Kendall (notation) | Queueing-theory tradition; Gross & Harris |
| 类型≠ | Stochastic queueing model | Multi-server Markovian 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 ↗ | Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9 |
| 别名 | Single-Server Markovian Queue, Birth-Death Queue, Poisson Queue, M/M/1 Kuyruk Modeli | Multi-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu |
| 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 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. |
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