ࡾ୐༔հ / Pepabo R&D Institute, GMO Pepabo, Inc. 2019.09.28 Web System Architecture ݚڀձ (WSAݚ) #5 Kaburaya AutoScaler: ଟ؀ڥͰͷ ӡ༻ੑΛߟྀͨࣗ͠཯దԠܕ ΦʔτεέʔϦϯά੍ޚܥ

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1. ͸͡Ίʹ 2. ΦʔτεέʔϦϯάͷಋೖɾӡ༻ʹؔΘΔ՝୊ 3. ଟ؀ڥͰͷӡ༻ੑΛߟྀͨࣗ͠཯దԠܕΦʔτεέʔϦ ϯά੍ޚܥ 4. ධՁ 5. ·ͱΊ 3 ໨࣍

1. ͸͡Ίʹ

• ΦʔτεέʔϦϯάػೳΛɼଟ༷͔ͭมԽ͢Δ؀ڥʹରͯ͠खؒͳ͘ಋೖɾӡ ༻͢Δ͜ͱ͸Մೳ͔ʁ 5 ຊݚڀͷʮ໰͍ʯ

6 ͳΊΒ͔ͳγεςϜͷੈք؍ ৘ใγεςϜͷ͜ͱΛ͍͏ͷΈͳΒͣɼޓ͍ʹӨڹΛٴ΅͠߹͏ܧଓతͳؔ܎ʹ ͋Δར༻ऀʢϢʔβ͓Αͼ։ൃӡ༻ऀʣͱ৘ใγεςϜͱ͔ΒͳΔ૯ମͱͯ͠ͷ γεςϜ ग़ॴ܀ྛ݈ଠ࿠ ࡾ୐༔հ দຊ྄հ ͳΊΒ͔ͳγεςϜΛ໨ࢦͯ͠ ϚϧνϝσΟΞɺ෼ࢄɺڠௐͱϞόΠϧʢ%*$0.0ʣγϯϙδ΢Ϝ # +VM

7 ͳΊΒ͔ͳγεςϜͱΦʔτεέʔϦϯά Ϣʔβ͔ΒͷϦΫΤετ਺ͷ૿ݮʹԠͯ͡࠷దͳαʔό୆਺Λௐ੔͢Δɽ݁Ռ ͱͯ͠ར༻ऀͷշద͞ͱ৘ใγεςϜͷӡӦίετΛཱ྆͢Δ΋ͷ ɹɹɹϢʔβ⁶৘ใγεςϜؒͷͳΊΒ͔͞

8 ͳΊΒ͔ͳγεςϜͱΦʔτεέʔϦϯά ҰํͰɼΦʔτεέʔϦϯάΛಋೖ͠ɼܧଓతʹ҆ఆͨ͠ӡ༻͢ΔͨΊʹ͸։ ൃӡ༻ऀͷӡ༻౒ྗ͕ඞཁɽӡ༻͢Δ؀ڥͷ૿ՃʹΑͬͯർฐ͢Δɽ ɹɹɹ৘ใγεςϜ⁶ϢʔβؒͷͳΊΒ͔͞Λ໨ࢦ͢

2. ΦʔτεέʔϦϯάͷಋೖɾӡ༻ʹ ؔΘΔ՝୊

• εέʔϦϯάܖػͱͳΔ৚݅ͱ࣮ࢪྔΛܾఆ͢ΔͨΊʹ͸ݸผͷΞϓϦέʔγϣ ϯಛੑͷ೺Ѳ͕ඞཁ • ࣌ࠁϕʔεͰ͋Ε͹ΞΫηεස౓ͷ࣌ܥྻత܏޲ • ϦιʔεมಈϕʔεͰ͋Ε͹ϘτϧωοΫͱͳΔϝτϦΫε • ͜ΕΒͷ৚݅ʹର͢Δඞཁ୆਺ͷܾఆ 10 ՝୊1: ΞϓϦέʔγϣϯಛੑͷ೺Ѳ

• ಛੑ೺ѲͷࣗಈԽ • ༧ଌతΞϓϩʔν: ΞΫηεස౓ͷ༧ଌϞσϧΛߏங[1] • ୳ࡧతΞϓϩʔν: ύϥϝλΛมߋͨ͠ෛՙࢼݧͷࣗಈԽ[2] • ࣗಈԽʹΑΓɼมԽ͢Δ؀ڥʹର͢Δ௥ैੑ͸޲্ • ҰํͰɼࣄલతͳΞϓϩʔνͰ͋ΔͨΊɼ༧ଌͷޡࠩɼ୳ࡧΛߦͬͨ؀ڥ ͱຊ൪؀ڥͷޡࠩʹରॲͰ͖ͳ͍ 11 ରࡦ: ΞϓϦέʔγϣϯಛੑͷ೺Ѳ <>ࡾ୐༔հ দຊ྄հ ྗ෢݈࣍ ܀ྛ݈ଠ࿠ ΞΫηεස౓༧ଌʹجͮ͘Ծ૝αʔόͷܭըతΦʔτεέʔϦϯά '*5ୈճ৘ใՊֶٕज़ϑΥʔϥϜ $- 4FQ <>શࣗಈύϥϝʔλνϡʔχϯά͞ΜIUUQTCMPHNJSBLVJDPNFOUSZ

• ಛੑ೺ѲͷࣗಈԽ • ϑΟʔυόοΫ੍ޚʹΑΔݸผͷಛੑ೺ѲΛඞཁͱ͠ͳ͍Ξϓϩʔν[3][4] • ௚ۙͷϨεϙϯελΠϜ͕ۉߧ͢Δ఺ʹऩଋ͢ΔΑ͏ͳ୆਺ௐ੔ʹΑͬͯ ಛੑ೺Ѳ͕ෆཁͰ࣮ߦ࣌ʹޡࠩΛमਖ਼͢Δ͜ͱ͕Ͱ͖ͨ • ࠷దͳ୆਺ͷܾఆ͸୳ࡧతʢ໨ඪ஋ͱͷޡࠩͷେ͖͞(P)ɼաڈͷมԽ (I)ɼະདྷͷมԽ(D)ʹΑͬͯ”ͷΈ”୆਺Λࢉग़͢Δʣ • ଴ͪߦྻཧ࿦ʹΑΕ͹૭ޱར༻཰͕1Λ௒͑Δͱ଴ͪߦྻ͸ऩଋ͠ͳ͍ 12 ରࡦ: ΞϓϦέʔγϣϯಛੑͷ೺Ѳ <>:VTVLF.JZBLF 0QUJNJ[BUJPOGPS/VNCFSPGHPSPVUJOFT6TJOH'FFECBDL$POUSPM (PQIFS$PO.BSSJPUU.BSRVJT4BO%JFHP.BSJOB $BMJGPSOJB +VMZ <>ࡾ୐༔հ &CJSBΞΫηεෛՙʹԠͯ͡ܧଓతʹεέʔϦϯάج४Λ࠷దԽ͢Δ൚༻ΦʔτεέʔϦϯάػߏ ୈ࢛ճ8FCγεςϜΞʔΩςΫνϟݚڀձ ೥݄

• εέʔϦϯάͷ࣋ͭ2ͭͷ”஗Ε”ʹΑΓܥ͸ෆ҆ఆʹͳΓ͕ͪ • ೖྗͷ஗Ε: ෛՙ্ঢ͔Βαʔό୆਺Λݟੵ΋Δ·Ͱͷ࣌ؒࠩ • ग़ྗͷ஗Ε: αʔό୆਺ͷมߋࢦ͔ࣔΒىಈ·Ͱͷ࣌ؒࠩ • ͜ͷ஗Εʹରͯ͠ൃੜͨ͠଴ͪϦΫΤετ͕ܥͷ҆ఆੑΛ่͢ • ଴ͪߦྻཧ࿦ʹΑΕ͹૭ޱར༻཰͕1Λ௒͑Δͱ଴ͪߦྻ͸ऩଋ͠ͳ͍ 13 ՝୊2: “஗Ε”ͷߟྀ

• ஗ΕΛ࠷খԽ͢Δ • ೖྗͷ஗Εͷ࠷খԽ: มԽ఺ݕग़ • ग़ྗͷ஗Εͷ࠷খԽ: goroutine, CRIU [5] • ਫ਼౓ͷ؍఺΍γεςϜ੍໿ʹΑͬͯ0ʹ͸Ͱ͖ͳ͍ 14 ରࡦ: “஗Ε”ͷߟྀ <>দຊ྄հ ۙ౻Ӊஐ࿕ $3*6Λར༻ͨ͠)551ϦΫΤετ୯ҐͰίϯςφΛ࠶഑ஔͰ͖Δ௿ίετͰߴ଎ͳεέδϡʔϦϯάख๏ ݚڀใࠂΠϯλʔωοτͱӡ༻ٕ ज़ʢ*05ʣ 7PM*05 QQ 'FC

• ஗ΕΛ౿·͑ͨ४උ • ༧ଌతΞϓϩʔν: ΞΫηεස౓ͷ༧ଌϞσϧΛߏங[1] • Ϟσϧʹج͖ͮࣄલʹෛՙมಈΛ༧ଌɼ஗ΕΛߟྀͯ͠ࣄલʹىಈ • ຊ൪؀ڥͱͷޡࠩʹରॲͰ͖ͳ͍ • ൓ԠతΞϓϩʔν: εϛεͷ༧ଌ๏[6] • ϑΟʔυόοΫ੍ޚʹ͓͍ͯ஗ΕʹΑΔӨڹΛ౿·੍͑ͨޚྔΛࢉग़ • ਫ਼౓ͷߴ͍༧ଌϞσϧͷߏங͕ඞཁʢ௥ैʹ͸͜͜ͷࣗಈԽ͕ඞਢʣ 15 ରࡦ: “஗Ε”ͷߟྀ <>04NJUI $MPTFSDPOUSPMPGMPPQTXJUIEFBEUJNF $IFNJDBMFOHJOFFSJOHQSPHSFTT 7PM /P QQ

3. ଟ؀ڥͰͷӡ༻ੑΛߟྀͨ͠ ࣗ཯దԠܕΦʔτεέʔϦϯά੍ޚܥ

• ΞϓϦέʔγϣϯಛੑͷ೺ѲͷࣗಈԽͱ҆ఆੑͷཱ྆ 1. WebΞϓϦέʔγϣϯಛੑͱͯ͠ෛՙʹର͢Δ࣮ࢪྔͷؔ܎͕೺ѲͰ͖ Δ 2. ͜ΕΛෆඞཁͳෛՙΛ͔͚Δ͜ͱͳ࣮͘ߦ࣌ʹࣗಈͰ೺ѲͰ͖Δ 3. ೺Ѳͨ͠WebΞϓϦέʔγϣϯಛੑͱ࣮؀ڥʹޡ͕ࠩੜͨ͡৔߹ʹमਖ਼ Ͱ͖Δ 4. ͜ΕΛ࣮ݱ͢ΔϦΞΫςΟϒͳΞϓϩʔνͰൃੜ͢Δ”஗Ε”΁ରॲͰ͖Δ 17 ଟ؀ڥͰͷӡ༻ੑΛߟྀ͢Δ

• ϑΟʔυϑΥϫʔυ੍ޚΛத৺ͱ͠ɼ࣮؀ڥͷಛੑ೺Ѳɾ௥ैͷͨΊʹϑΟʔ υόοΫ੍ޚΛ૊ΈࠐΜͩ2ࣗ༝౓ͷΦʔτεέʔϦϯά੍ޚܥΛఏҊ • ಛੑ೺Ѳɾ௥ैͷࣗಈԽ • ଴ͪߦྻཧ࿦Λ༻͍ܾͨఆతͳ୆਺ࢉग़ɾ஗ΕิঈʹΑΔ҆ఆԽ 18 ࣗ཯దԠܕΦʔτεέʔϦϯά੍ޚܥ

Kaburaya AutoScaler Architecture 19 Ts 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 ⇢r 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 µt 1 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 st 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 P(st, ) 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AAACknichVG7SgNBFD2u72fioxBsxBARizBRQbHyAWJhYRLzkCiyu050cV/sTgIa/AFtFQsrBQux8A9sbPwBi3yCpIxgY+HdzYJoMN5lZ86cuefMvVzF1jVXMFZpkVrb2js6u7p7evv6B0LhwaGMaxUdladVS7ecnCK7XNdMnhaa0HnOdrhsKDrPKker3n22xB1Xs8wtcWzzXUM+MLWCpsqCqMTaXjjCYsyP8UYQD0AEQWxa4SfsYB8WVBRhgMOEIKxDhktfHnEw2MTtokycQ0jz7zlO0UPaImVxypCJPaL1gE75gDXp7Hm6vlqlV3T6HVKOI8pe2T2rsRf2wN7Y559eZd/Dq+WYdqWu5fZe6Gw09fGvyqBd4PBb1UShUHa9sgp7pLqq29P5bNMeBQpY8HvTqFfbZ7yu1bpP6eSqllpMRsuT7JZVqd8bcn4mZ7P0rt4lePKaxhX/PZxGkJmJxWdjM4m5yNJKMLgujGECUzSdeSxhHZtI06sc57jApTQiLUrL0mo9VWoJNMP4EdLGF56qlXk= M AAACknichVG7SgNBFD2u72fioxBsxBARizBRQbHy0VgomMQ8JIrsrhNd3Be7k4AGf0BbxcJKwUIs/AMbG3/AIp8gKSPYWHh3syAajHfZmTNn7jlzL1exdc0VjFVapNa29o7Oru6e3r7+gVB4cCjjWkVH5WnV0i0np8gu1zWTp4UmdJ6zHS4bis6zytGqd58tccfVLHNLHNt815APTK2gqbIgKrGxF46wGPNjvBHEAxBBEJtW+Ak72IcFFUUY4DAhCOuQ4dKXRxwMNnG7KBPnENL8e45T9JC2SFmcMmRij2g9oFM+YE06e56ur1bpFZ1+h5TjiLJXds9q7IU9sDf2+adX2ffwajmmXalrub0XOhtNffyrMmgXOPxWNVEolF2vrMIeqa7q9nQ+27RHgQIW/N406tX2Ga9rte5TOrmqpRaT0fIku2VV6veGnJ/J2Sy9q3cJnrymccV/D6cRZGZi8dnYTGIusrQSDK4LY5jAFE1nHktYwybS9CrHOS5wKY1Ii9KytFpPlVoCzTB+hLT+Ba3slYA= P 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 max { 1 /Ts, µ} 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 µavg + µt 1 t + 1 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 µavg 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 t 1 + D ( t, 1 , t 1, µavg ) + D ( t, , t 1, µavg ) ⇢rµavg , where D ( t, , , µ ) = X i=1 (max { st iµ, 0 } ) 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

• αʔό୆਺SΛ࣍ࣜͰٻΊΔ • λ͸ฏۉ౸ண཰ʢreq/୯Ґ࣌ؒʣ • μ͸ฏۉαʔϏε཰ʢreq/୯Ґ࣌ؒʣ • ρ͸૭ޱར༻཰ʢ0<ρ<1ɽ0.7ҎԼΛਪ঑ʣ • ͭ·Γɼྲྀೖʹରͯ͠ॲཧೳྗΛ౿·͑ͯඞཁͳαʔό୆਺ΛٻΊΔ • λͱμ͸ϓϥϯτͷ؍ଌ݁Ռ͔Βಋग़ɼρ͸໨ඪ஋ͱ͢Δ 20 F: ϑΟʔυϑΥϫʔυ੍ޚ෦ S = /(⇢µ) 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

• ൓ԠతͳεέʔϦϯάͰ͸ෛՙ্ঢ͔Βαʔό୆਺ Λݟੵ΋Δ·Ͱͷ࣌ؒࠩʢೖྗͷ஗Εʣ͕ൃੜ • ͜ͷؒʹཷ·ͬͨະॲཧͷϦΫΤετΛߟྀ͢Δඞ ཁ͕͋Δ • ͜ͷະॲཧͷϦΫΤετ਺Λ࣍ࣜͰٻΊɼઌͷSΛ ٻΊΔࣜͷλʹՃ͑Δ 21 F: ϑΟʔυϑΥϫʔυ੍ޚ෦ʢೖྗͷ஗Εิঈʣ D ( t, 1 , t 1, µavg ) , where D ( t, , , µ ) = X i=1 (max { st iµ, 0 } ) 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 TUFQ

• εέʔϦϯάͰ͸αʔό୆਺ͷมߋࢦ͔ࣔΒىಈ· Ͱͷ࣌ؒࠩʢग़ྗͷ஗Εʣ͕ൃੜ • ͜ͷؒʹཷ·ͬͨະॲཧͷϦΫΤετΛߟྀ͢Δඞ ཁ͕͋Δ • ͜ͷະॲཧͷϦΫΤετ਺Λ࣍ࣜͰٻΊɼઌͷSΛ ٻΊΔࣜͷλʹՃ͑Δ 22 F: ϑΟʔυϑΥϫʔυ੍ޚ෦ʢग़ྗͷ஗Εิঈʣ D ( t, , t 1, µavg ) , where D ( t, , , µ ) = X i=1 (max { st iµ, 0 } ) 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 ЍTUFQ

• εέʔϦϯάʹඞཁͳύϥϝλΛࣗಈ͔ͭܧଓతʹٻΊΔͨΊʹϓϥϯτ͔Β ಘ࣮ͨଌ஋ΛF෦ʹϑΟʔυόοΫ͢Δ • ࠷େεϧʔϓοτͱͯ͠ͷμ͸௿ෛՙ࣌ʹ͸ٻΊΔ͜ͱ͕Ͱ͖ͳ͍ͨΊϨεϙ ϯελΠϜ(Ts)ͷٯ਺͔ΒεϧʔϓοτΛٻΊΔ • ҰํͰߴෛՙ࣌ʹ͸1/Ts͕ஶ͘͠௿Լ͢Δ͜ͱ͔ΒઌͷSΛٻΊΔ͔ࣜΒඞཁ Ҏ্ͷαʔό୆਺͕ಋ͔Εͯ͠·͏ • ͜ΕΛճආ͢ΔͨΊʹߴෛՙ࣌͸μΛ༻͍ΒΕΔΑ͏྆ऀͷ͏ͪେ͖͍΋ͷΛ ར༻͢Δ 23 M: ϑΟʔυόοΫ੍ޚ෦ʢλͷ௥ैɼμͷਪఆɾ௥ैʣ

Kaburaya AutoScaler Architectureʢ࠶ܝʣ 24 Ts 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 ⇢r AAACl3ichVFLLwNRFP46XvUuNsRGNEQsmjtIiI2GRLrU0ofUIzPjaod5ZWbapBp/wMpOsCKxEAv/wMbGH7DwE8SyEhsLZx6JIDiTufe73z3fd8/JkS1NdVzGniJCU3NLa1u0vaOzq7unN9bXn3PMiq3wrGJqpl2QJYdrqsGzrupqvGDZXNJljefl/SXvPl/ltqOaxppbs/imLpUMdVdVJJeo3IZdNrfs7VicJZgfIz+BGII4wlgxY3fYwA5MKKhAB4cBl7AGCQ59RYhgsIjbRJ04m5Dq33McooO0FcrilCERu09riU7FkDXo7Hk6vlqhVzT6bVKOYIw9smvWYA/shj2z91+96r6HV0uNdjnQcmu792hw9e1flU67i/Kn6g+FTNlBZU/slup6WZ8s5v/s0cUu5vzeVOrV8hmvayXwqR6cNFbnM2P1cXbJXqjfC3K+J2ej+qpcpXnmnMYlfh/OT5CbSojTian0TDy5GA4uimGMYoKmM4skUlhBll7dwzFOcSYMCQvCspAKUoVIqBnAlxDSHyNYl9o= t 1 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 µt 1 AAACmnichVG7SgNBFD1Z3++ojaBFMCgiGGZVUKxEG8UmD2MMSQy766iL+2J3EtDgD9haWKiFgoVY+Ac2Nv6AhZ8glgo2Ft5sFkSD8S47c+bMPWfu5aqOoXuCseeQ1NTc0trW3tHZ1d3T2xfuH9jw7JKr8bRmG7a7qSoeN3SLp4UuDL7puFwxVYNn1P3l6n2mzF1Pt611ceDwgqnsWvqOrimCqGzeLG1VxJR8VAxHWYz5EakHcgCiCCJuh++RxzZsaCjBBIcFQdiAAo++HGQwOMQVUCHOJaT79xxH6CRtibI4ZSjE7tO6S6dcwFp0rnp6vlqjVwz6XVJGMMae2A17Y4/slr2wzz+9Kr5HtZYD2tWaljvFvuOh1Me/KpN2gb1vVQOFStm1yp7ZHdX1mp3MZRr2KLCDeb83nXp1fKbatVbzKR+evqUWkmOVcXbFXqnfS3J+IGer/K5dJ3jyjMYl/x5OPdiYjskzsenEbHRxKRhcO4YxigmazhwWsYI40vSqiROc40IakZakVWmtliqFAs0gfoS0/gWpzJjp st AAAClHichVHLSsNAFD3Gd320KojgplgUcVEmVVDERVEEV1Jb2yr1QRKnNZgmIZkWavEHBLe6cKXgQlz4B27c+AMu+gnSZQU3LrxNA6Ki3pCZM2fuOXMvV7UN3RWM1dqk9o7Oru6e3kBf/8BgMDQ0nHGtkqPxtGYZlrOlKi43dJOnhS4MvmU7XCmqBs+qRyvN+2yZO65umZuiYvPdolIw9byuKYKolLsn9kMRFmVehH8C2QcR+JGwQg/YwQEsaCihCA4TgrABBS59OchgsInbRZU4h5Du3XOcIEDaEmVxylCIPaK1QKecz5p0bnq6nlqjVwz6HVKGMcme2S1rsCd2x17Y+69eVc+jWUuFdrWl5fZ+8HQs9favqki7wOGn6g+FStmtymrsnuqqb8/ksn/2KJDHgtebTr3aHtPsWmv5lI8vGqnF5GR1il2zOvV7Rc6P5GyWX7WbDZ68pHHJ34fzE2RiUXk2GtuYi8SX/cH1YBwTmKbpzCOONSSQplcLOMM5LqRRaUlakVZbqVKbrxnBl5DWPwAXC5aM µ 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 P(st, ) 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 F 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 M 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 P 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 max { 1 /Ts, µ} 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 µavg + µt 1 t + 1 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 µavg 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 t 1 + D ( t, 1 , t 1, µavg ) + D ( t, , t 1, µavg ) ⇢rµavg , where D ( t, , , µ ) = X i=1 (max { st iµ, 0 } ) 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 αʔό୆਺ͷࢉग़ + ೖग़ྗ஗Εิঈ μͷਪఆɾ௥ै λͷ௥ै ρͷࢦఆ

3. ධՁ

• ϓϥϯτͷγϛϡϨʔλʢޙड़ʣΛ࢖ͬͯఏҊख๏ʹΑΔΦʔτεέʔϦϯά ͷࣗ཯ɾదԠͷੑೳΛධՁ͢Δ • ϓϥϯτ͸଴ͪߦྻϞσϧ(M/M/S)ʹै͏΋ͷͱ͢Δ • ୯Ґ࣌ؒ͸1ඵ • ϓϥϯτͷγϛϡϨʔγϣϯִؒDT=0.00001(0.01ms) • ρ = 0.7Ͱݻఆ 26 ධՁ

଴ͪߦྻγϛϡϨʔλʢࣄ৅-ࣄ৅ਐߦํࣜʣ 27 • ্ه͸M/M/S Ϟσϧ: ρ = 1.0 ( λ = 0.2, μ = 0.1, S = 2 ) Ͱͷ݁Ռ • ແݶͷੑೳΛ࣋ͭϩʔυόϥϯαʔΛԾఆ͢ΔʢϘτϧωοΫʹ͸ͳΒͳ͍ʣ

μ ͷਪఆɾ௥ै 28 • μ=1000Λ250step໨Ҏ߱ɼ1500 ΁มߋ • ࣮ࡍͷ μ ͕ෆ໌ͳঢ়ଶ͔ΒఏҊख ๏Ͱ௿ෛՙ࣌ɼߴෛՙ࣌ͷ͍ͣΕ ΋ݕग़ɾ௥ै • ಛʹߴෛՙ࣌ͷ1/Tsͷ௿ԼΛճආ • ௥ैੑೳͷ޲্ͷͨΊશظؒͰ͸ ͳ͍ۙ͘ظؒʹΑΔฏۉ͕ඞཁ

؍ଌɾਪఆͨ͠ύϥϝλʹΑΔεέʔϧੑೳ 29 • 500step௨ͯ͠ཧ૝తͳαʔό୆਺ ͱͷ୆਺ͷ͕ࠩ-46୆ • ʢϓϥϯτͱϞσϧͷલఏ͕ಉ͡ Ͱ͋Ε͹ʣ؍ଌɾਪఆͨ͠ύϥϝʔ λΛ༻͍ͨϞσϧͷεέʔϧ͸ਫ਼౓ ྑ͘ػೳ͢Δ

ೖྗͷ஗ΕʹΑΔ଴ͪϦΫΤετ਺ͷ૿Ճ 30 • લड़ͷγϛϡϨʔγϣϯ݁Ռʹ͓ ͍ͯɼϦΫΤετ਺ͷ૿Ճ࣌ʹɼ ଴ͪϦΫΤετ͕ൃੜ͠ɼࡹ͖͖ Δ·Ͱʹ࣌ؒΛཁ͍ͯ͠Δ͜ͱ͕ Θ͔Δ • ͷ΂଴ͪϦΫΤετ਺͸10,170Ͱ ͋ͬͨ • ఏҊख๏ͷ஗ΕิঈػߏʹΑΔվ ળΛਤΔ

஗Εิঈʢೖྗʣ 31 • ؍ଌ࣌఺Ͱൃੜͨ͠଴ͪΛॲཧՄ ೳͳαʔό୆਺Λ༧ଌ • ͷ΂଴ͪϦΫΤετ਺͕10,170͔ Β6,735·Ͱ࡟ݮ • ऩଋੑೳͷ޲্ʢ࣍εςοϓ΁ͷ ࣋ͪӽ͠ແ͠ʣ • ϨεϙϯελΠϜ΋վળ ೖྗ஗ΕิঈOFF ೖྗ஗ΕิঈON

ग़ྗͷ஗ΕʹΑΔ଴ͪϦΫΤετ਺ͷ૿Ճ 32 • લड़ͷγϛϡϨʔγϣϯͰαʔό ىಈ·Ͱͷ஗Ε͕6step(6secޙ)Ͱ ͋ͬͨͱ͢Δͱ଴ͪϦΫΤετ਺ ͕૿Ճ͢Δ • ͷ΂଴ͪϦΫΤετ਺͸311,821 Ͱ͋ͬͨ • ఏҊख๏ͷ஗ΕิঈػߏʹΑΔվ ળΛਤΔ

஗Εิঈʢग़ྗʣ 33 • αʔόىಈ·Ͱʹൃੜ͢Δ଴ͪΛ ॲཧՄೳͳαʔό୆਺Λ༧ଌ • ͷ΂଴ͪϦΫΤετ਺͕311,821 ͔Β182,373·Ͱ࡟ݮ • ऩଋੑೳͷ޲্ ← ೖྗ஗ΕิঈOFF ↑ ೖྗ஗ΕิঈON

34

35

5. ·ͱΊ

• ΦʔτεέʔϦϯάͱ։ൃӡ༻ऀؒͷؔ܎ΛͳΊΒ͔ʹ͢ΔͨΊͷଟ؀ڥͰͷ ӡ༻Λߟྀͨࣗ͠཯దԠܕΦʔτεέʔϦϯά੍ޚܥΛఏҊ • M/M/SϞσϧΛલఏͱͨ͠ϓϥϯτγϛϡϨʔλʹΑͬͯ͜ΕΒ͕ୡ੒Մೳ ͳ͜ͱΛࣔͨ͠ • ࠓޙ͸ϓϥϯτʹ࣮ࡍͷWebαʔό/ΞϓϦέʔγϣϯαʔόΛద༻ͨ͠ධՁ ΛਐΊΔ • ·ͨɼఏҊख๏Ͱ͸ೖྗͷ஗Εʹ൐͍୯Ґ࣌ؒ಺ʹ଴ͪϦΫΤετ͕ඞͣൃੜ ͢ΔͨΊมԽ఺ݕग़ͳͲͰ஗Ε࣌ؒࣗମΛ୹ॖ͢Δํࣜ΋ݕ౼͍ͨ͠ 37 ·ͱΊ

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