Граф состояний одноканальной системы массового обслуживания с отказом

2c:null 2d:["$","title",null,{"children":"Бизнес-аналитика. Контрольная работа №1 | Philippe Rigovanov | Observable"}] 32:Tb24,htl.svg``33:T10a0,htl.svg``34:[{"id":"051d2606730154a36218d68a02fcf19ff8071d4e1d083dda4d91c1c8ebc5021b93451b7717968dd6dbfba1978077ea3fad7a41ef822bf409b20c764f2e2985b9","href":"https://static.observableusercontent.com/files/051d2606730154a36218d68a02fcf19ff8071d4e1d083dda4d91c1c8ebc5021b93451b7717968dd6dbfba1978077ea3fad7a41ef822bf409b20c764f2e2985b9","name":"freq.csv","type":"text/csv","lastModified":1624473960347.259,"size":259}] 30:{"id":"b1973b8d7f7f7afc","slug":"ba-01","title":"Бизнес-аналитика. 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Контрольная работа №1","cells":[{"id":0,"value":"# Бизнес-аналитика. Контрольная работа №1","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":5,"value":"## 1) Определить интенсивность потока заявок за час работы","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":9,"value":"requestFlow = [\n [5, 2, 1, 7, 6, 5, 3, 4, 5, 1],\n [6, 3, 7, 5, 8, 6, 1, 7, 6, 8],\n [8, 4, 5, 3, 3, 3, 4, 5, 7, 4],\n [9, 6, 8, 8, 1, 5, 6, 5, 8, 6],\n [3, 7, 3, 5, 1, 1, 7, 3, 2, 4],\n [2, 3, 2, 4, 3, 2, 8, 2, 4, 3],\n [6, 6, 4, 4, 5, 3, 2, 1, 5, 2],\n [6, 8, 6, 3, 7, 6, 4, 1, 6, 5],\n [1, 9, 7, 2, 8, 7, 6, 1, 2, 7]\n]","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":11,"value":"days = requestFlow[0].length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":12,"value":"hoursPerDay = requestFlow.length","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":14,"value":"sum = requestFlow.flat().reduce((a, b) => a + b, 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":16,"value":"Всего ${sum} заявок за ${days} дней (по ${hoursPerDay} часов в день).","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":20,"value":"requestFlowIntensity = sum / (days * hoursPerDay)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":21,"value":"Интенсивность потока заявок λ ≈ ${requestFlowIntensity.toFixed(2)}","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":24,"value":"## 2) Определить интенсивность обслуживания","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":30,"value":"frequency = FileAttachment(\"freq.csv\").csv({ typed: true })","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":33,"value":"frequencies = frequency.map((f) => {\n const a = f[\"Интервал времени обслуживания (min)\"];\n const b = f[\"Интервал времени обслуживания (max)\"];\n const middle = (b + a) / 2;\n f[\"Интервал\"] = `${a} — ${b}`;\n return {\n \"Номер интервала\": \"\" + f[\"Номер интервала\"],\n Интервал: f[\"Интервал\"],\n \"Середина интервала\": middle,\n Частота: f[\"Частота\"],\n \"Середина интервала × Частота\": middle * f[\"Частота\"]\n };\n})","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":35,"value":"Inputs.table(frequencies)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":37,"value":"productsSum = frequencies.reduce(\n (a, b) => a + b[\"Середина интервала × Частота\"],\n 0\n)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":39,"value":"Сумма произведений середин интервалов на их частоты: ${productsSum}","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":41,"value":"frequenciesSum = frequencies.reduce((a, b) => a + b[\"Частота\"], 0)","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":46,"value":"Сумма частот: ${frequenciesSum}","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":49,"value":"serviceMeantime = productsSum / frequenciesSum","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":51,"value":"Среднее время облуживания t ≈ ${serviceMeantime.toFixed(1)}","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":54,"value":"serviceIntensity = 1 / serviceMeantime","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":56,"value":"Интенсивность облуживания μ ≈ ${serviceIntensity.toFixed(3)}","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":60,"value":"## 3) Составить графы состояний систем массового обслуживания (СМО)","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":142,"value":"### 1\\. Одноканальная СМО с отказом","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":154,"value":"$32","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":98,"value":"- S₀ – система свободна (простаивает)\n- S₁ – система занята обслуживанием\n- S₂ – система занята обслуживанием, образуется очередь","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":147,"value":"### 2\\. Многоканальная СМО с отказом","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":262,"value":"$33","pinned":false,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":101,"value":"- S₀ – система свободна (простаивает)\n- S₁ – занят один канал обслуживания\n- S₂ – занято `2` канала обслуживания\n- Sₖ – занято `k` каналов обслуживания\n- Sₙ – все каналы системы заняты обслуживанием, образуется очередь\n","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":77,"value":"## 4) Дополнительно","pinned":false,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":59,"value":"loadIntensity = requestFlowIntensity / serviceIntensity","pinned":true,"hidden":false,"mode":"ojs","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"},{"id":68,"value":"Интенсивность нагрузки ρ ≈ ${loadIntensity.toFixed(2)}","pinned":true,"hidden":false,"mode":"md","author":"$undefined","summary":"$undefined","output":"$undefined","database":"$undefined"}],"files":"$W34","stdlib":"1","titling":"auto"}} 31:"$30:body"