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Hukum Little (L = λW)×Simulasi Kejadian Diskrit (DES)×Antrean M/M/1: Model Antrean Pelayan Tunggal×Model Antrean M/M/c: Model Antrean Multi-Pelayan×
BidangRiset OperasiSimulasiRiset OperasiRiset Operasi
KeluargaRegression modelProcess / pipelineRegression modelRegression model
Tahun asal19611960s (formalized); modern computational form from 1970s onward19531998
PencetusJohn D. C. LittleBanks, Carson, Nelson & Nicol (textbook lineage); foundational work by Tocher & Conway (1960s)A. K. Erlang; David Kendall (notation)Queueing-theory tradition; Gross & Harris
TipeExact queueing identityStochastic process simulationStochastic queueing modelMulti-server Markovian queueing model
Sumber perintisLittle, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387. DOI ↗Banks, J., Carson, J.S., Nelson, B.L. & Nicol, D.M. (2010). Discrete-Event System Simulation (5th ed.). Pearson. ISBN: 978-0136062127Kendall, 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
AliasL = λW Theorem, Little's Theorem, Little's Result, Little YasasıDES, event-driven simulation, Ayrık Olay Simülasyonu (DES)Single-Server Markovian Queue, Birth-Death Queue, Poisson Queue, M/M/1 Kuyruk ModeliMulti-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c Kuyruğu
Terkait3433
RingkasanLittle'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.Discrete-Event Simulation (DES) is a computational modeling paradigm in which the state of a system changes only at a countable sequence of points in time — the events. Between events nothing changes, so the simulation clock jumps directly from one event to the next. Formalized through the foundational textbooks of Banks, Carson, Nelson and Nicol and of Law in the 1960s–2000s, DES has become the standard tool for analyzing queuing systems, healthcare patient flows, manufacturing lines, and logistics networks where entities move through resources over time.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.
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ScholarGateBandingkan metode: Little's Law · Discrete-Event Simulation · M/M/1 Queue · M/M/c Queue. Diakses 2026-06-18 dari https://scholargate.app/id/compare