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M/M/1 Queue

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.

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M/M/1 Single-Server Queue

Taksonomski zapis metode · regression-model / operations-research

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 10.1214/aoms/1177728975

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Taxonomic bucketErlang C Modelmachine-suggested · Relational suggestion, not evidence.Taxonomic bucketLittle's Lawmachine-suggested · Relational suggestion, not evidence.Taxonomic bucketM/M/c Queuemachine-suggested · Relational suggestion, not evidence.