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| Erlang C 模型× | L = λW× | |
|---|---|---|
| 领域 | 运筹学 | 运筹学 |
| 方法族 | Regression model | Regression model |
| 起源年份≠ | 1981 | 1961 |
| 提出者≠ | Agner Krarup Erlang; Cooper | John D. C. Little |
| 类型≠ | Steady-state queueing model | Exact queueing identity |
| 开创性文献≠ | 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. DOI ↗ |
| 别名 | 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 |
| 相关 | 3 | 3 |
| 摘要≠ | 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. |
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