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| Νόμος του Little (L = λW)× | Μοντέλο Ουράς M/M/c: Μοντέλο Ουράς Πολλαπλών Εξυπηρετητών× | |
|---|---|---|
| Πεδίο | Επιχειρησιακή Έρευνα | Επιχειρησιακή Έρευνα |
| Οικογένεια | Regression model | Regression model |
| Έτος προέλευσης≠ | 1961 | 1998 |
| Δημιουργός≠ | John D. C. Little | Queueing-theory tradition; Gross & Harris |
| Τύπος≠ | Exact queueing identity | Multi-server Markovian queueing model |
| Θεμελιώδης πηγή≠ | 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 |
| Εναλλακτικές ονομασίες | 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 |
| Συναφείς | 3 | 3 |
| Σύνοψη≠ | 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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