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| M/M/c-Warteschlange: Mehrserver-Warteschlangenmodell× | Little's Gesetz (L = λW)× | |
|---|---|---|
| Fachgebiet | Operations Research | Operations Research |
| Familie | Regression model | Regression model |
| Entstehungsjahr≠ | 1998 | 1961 |
| Urheber≠ | Queueing-theory tradition; Gross & Harris | John D. C. Little |
| Typ≠ | Multi-server Markovian queueing model | Exact queueing identity |
| Wegweisende Quelle≠ | Gross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9 | Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387. DOI ↗ |
| Aliasnamen | Multi-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu | L = λW Theorem, Little's Theorem, Little's Result, Little Yasası |
| Verwandt | 3 | 3 |
| Zusammenfassung≠ | 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. | 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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