Queueing_theory - Wikiparency

# Queueing theory  ## Microsims — three.js ### Queueing theory (three.js) <div class="microsim-player"> <iframe src="https://wikitube-3d-microsims.netlify.app/Queueing_theory.html" width="100%" height="620" frameborder="0" loading="lazy" sandbox="allow-scripts allow-same-origin" title="Queueing theory — three.js microsim"></iframe> </div> **Open it full-screen:** [Queueing_theory.html](https://wikitube-3d-microsims.netlify.app/Queueing_theory.html) · library `threejs` · route `microsim/threejs/` ### Related microsims Live sims on neighbouring articles: - [[Failure_mode_and_effects_analysis]] - [[Mathematical_optimization]] - [[Reliability_engineering]] - [[Stanford_torus]] - [[Structural_engineering]] - [[Tribology]] *Sim hosted off-article; the article owns the reference, not the runtime (WIKI_RULES §10.4). Placed by `g08_place_microsims.py`.*  ## MicroSim spec ### Parameters (tunable controls) - `Arrival rate lambda` · 0–2 · mean customers arriving per unit time - `Service rate mu` · 0–2 · mean customers served per unit time - `Servers c` · 1–5 · number of parallel service channels ### What animates Customers arrive, wait in a line, and depart from servers; the queue grows and shrinks live. ### Learning objective Relate arrival and service rates to queue length and waiting time. ## Links (Wikipedia order)  `ARPANET` · `Agner_Krarup_Erlang` · `Aleksandr_Khinchin` · `Average` · `Balance_equation` · `Birth–death_process` · [[Black_box]] · `Bulk_queue` · `Buzen's_algorithm` · `Computing` · `Continuous-time_Markov_chain` · `Data_buffer` · `David_George_Kendall` · `Diffusion_process` · `Empirical_measure` · `Epidemiology` · `Erlang_(unit)` · `Erlang_distribution` · `FIFO_(computing_and_electronics)` · `Flow_control_(data)` · `Flow_network` · `Fluid_queue` · `Frank_Kelly_(mathematician)` · `G-network` · `Geometric_distribution` · `Gordon–Newell_theorem` · [[Industrial_engineering]] · [[Information_system]] · `Integral_equation` · `John_Kingman` · `Journal_of_the_ACM` · `K._Mani_Chandy` · `Layered_queueing_network` · `Leonard_Kleinrock` · `Line_management` · `M/G/1_queue` · `M/M/1_queue` · `M/M/c_queue` · [[Management_science]] · `Markovian_arrival_process` · `Massachusetts_Institute_of_Technology` · `Mathematical_Proceedings_of_the_Cambridge_Philosophical_Society` · `Mean-field_theory` · `Mean_sojourn_time` · `Message_queue` · `Message_switching` · `Mor_Harchol-Balter` · `Network_congestion` · `Network_scheduler` · `Network_simulation` · `Normalizing_constant` · `Operations_Research_(journal)` · [[Operations_research]] · `Ornstein–Uhlenbeck_process` · `Orthant` · `Packet_switching` · `Peter_Whittle_(mathematician)` · `Phase-type_distribution` · `Pipeline_(software)` · `Poisson_point_process` · `Probability_distribution` · [[Project_management]] · `Project_production_management` · `Quality_of_service` · `Queue_area` · `Reflected_Brownian_motion` · `Renewal_theory` · `Round-robin_scheduling` · `Scheduling_(computing)` · `Shortest_job_next` · `Shortest_remaining_time` · `Steady_state` · `Stochastic_scheduling` · `Survival_analysis` · [[Telecommunications]] · `Teletraffic_engineering` · [[Traffic_engineering_(transportation)]] · `Transient_state` ## From the Real GENERATIVE library ![Queueing theory](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2b/ServidorParalelo.jpg/220px-ServidorParalelo.jpg) *Queueing theory — placed from the Real G.E.N.E.R.A.T.I.V.E. course library (Engineering room). Source: Wikimedia Commons (via Wikipedia article media). [Details & license](https://commons.wikimedia.org/wiki/File:ServidorParalelo.jpg).* > Queueing theory is the mathematical study of waiting lines, or queues.[1] A queueing model is constructed so that queue lengths and waiting time can be predicted.[1] Queueing theory is generally considered a branch of operations research because the results are often used when making business decisions about the resources needed to provide a service. ([Wikipedia](https://en.wikipedia.org/wiki/Queueing_theory))  > p5.js MicroSim stub · part of Systems Engineering · [Wikipedia source](https://en.wikipedia.org/wiki/Queueing_theory) ## Concept summary Queueing theory is the mathematical study of waiting lines, or queues. A queueing model is constructed so that queue lengths and waiting time can be predicted. ## Build checklist - [ ] Claim it: set `status: in-progress` + `lease` + `leased_at` - [ ] Write the child page explaining the concept (tie it back to Systems Engineering) - [ ] Finalize parameter ranges and defaults - [ ] Implement the p5.js sketch (drawing + control regions) - [ ] Add caption + the learning objective on the page - [ ] Set `status: done` ## p5.js sketch ```javascript // MicroSim: Queueing theory const ARTICLE = "Queueing_theory"; let p1, p2, p3; function setup() { createCanvas(720, 520); pixelDensity(2); // queue-sim sim — create the three sliders described above: // Arrival rate lambda (0–2), Service rate mu (0–2), Servers c (1–5). // TODO: build labelled sliders in the control region (below the drawing region). } function draw() { background(248); // TODO: read p1/p2/p3; render the queue-sim in the drawing region and respond live. // TODO: HUD — title + en.wikitube.io/wiki/Queueing_theory + control hints + live readouts. } ``` --- Back to Systems Engineering ---  ## Semiotic profile > *The semiotic universals this article invokes, machine-derived from the crossref — **unverified** (born so). Populated 2026-07-06 for the Systems room.* **Universals (1):** 🟡 system (4) **Enter by sign:** Systems Semiotic Gateway · Alphabetum · Icon Registry · ← Systems Portal   ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Queueing_theory) : [Wikitube](https://en.wikitube.io/wiki/Queueing_theory) ## Previous hub tags Tree parents: [[Operations_research]] · [[Systems_engineering]]. Legacy hubs: none. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*