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Red M/M/c: Model stohastičkog čekanja s više poslužitelja×Model Erlang C×Littleov zakon (L = λW)×
PodručjeOperacijska istraživanjaOperacijska istraživanjaOperacijska istraživanja
ObiteljRegression modelRegression modelRegression model
Godina nastanka199819811961
TvoracQueueing-theory tradition; Gross & HarrisAgner Krarup Erlang; CooperJohn D. C. Little
VrstaMulti-server Markovian queueing modelSteady-state queueing modelExact queueing identity
Temeljni izvorGross, D., & Harris, C. M. (1998). Fundamentals of Queueing Theory (3rd ed.). Wiley. ISBN: 978-0-471-17083-9Cooper, R. B. (1981). Introduction to Queueing Theory (2nd ed.). North-Holland. ISBN: 978-0-444-00379-7Little, J. D. C. (1961). A proof for the queuing formula: L = λW. Operations Research, 9(3), 383–387. DOI ↗
Drugi naziviMulti-Server Erlang Queue, c-Server Markovian Queue, Erlang-C Queue, Çok Sunuculu M/M/c KuyruğuM/M/c Queue, Multi-Server Queueing Model, Erlang Delay Formula, Erlang-C Bekleme ModeliL = λW Theorem, Little's Theorem, Little's Result, Little Yasası
Srodne333
SažetakThe 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.The Erlang C model is a steady-state queueing formula that determines the probability a customer must wait before being served in a system with c parallel servers, Poisson arrivals at rate lambda, and exponentially distributed service times. Originally developed by Danish engineer Agner Krarup Erlang in the early twentieth century for telephone exchange design, and formalized in the queueing theory literature by Cooper (1981), it remains the canonical staffing model for call centers and service operations worldwide.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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