Сравнение на методи
Прегледайте избраните методи един до друг; редовете с разлики са откроени.
| Закон на Литъл (L = λW)× | M/M/1 опашка: Основният модел на опашка с един обслужващ канал× | Опашка M/M/c: Модел на опашка с множество сървъри× | |
|---|---|---|---|
| Област | Изследване на операциите | Изследване на операциите | Изследване на операциите |
| Семейство | Regression model | Regression model | Regression model |
| Година на възникване≠ | 1961 | 1953 | 1998 |
| Създател≠ | John D. C. Little | A. K. Erlang; David Kendall (notation) | Queueing-theory tradition; Gross & Harris |
| Тип≠ | Exact queueing identity | Stochastic queueing model | Multi-server Markovian queueing model |
| Основополагащ източник≠ | Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387. DOI ↗ | 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 |
| Други названия | L = λW Theorem, Little's Theorem, Little's Result, Little Yasası | 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 |
| Свързани | 3 | 3 | 3 |
| Резюме≠ | 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/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. |
| ScholarGateНабор от данни ↗ |
|
|
|