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| قانون لیتل (L = λW)× | صف مدل M/M/c: مدل صف چند-خدمتدهندهای× | |
|---|---|---|
| حوزه | پژوهش عملیات | پژوهش عملیات |
| خانواده | Regression model | Regression model |
| سال پیدایش≠ | 1961 | 1998 |
| پدیدآور≠ | John D. C. Little | Queueing-theory tradition; Gross & Harris |
| نوع≠ | Exact queueing identity | Multi-server Markovian queueing model |
| منبع بنیادین≠ | Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387. DOI ↗ | Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9 |
| نامهای دیگر | L = λW Theorem, Little's Theorem, Little's Result, Little Yasası | Multi-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu |
| مرتبط | 3 | 3 |
| خلاصه≠ | 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. | 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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