光パケット交換機のトラヒック理論（その2）
22
0
0
全文
(2) . శࡄࠤ࠶࠻឵ᯏߩ࠻ࡅ࠶ࠢℂ⺰㧔ߘߩ 2㧕 ̆ ৻⥸ಽᏓࡄࠤ࠶࠻㐳ߦኻߔࠆㄭૃ⸃ᴺ ̆ A Traffic Theory for Optical Packet Switches (Part 2) – Approximation Formulas for Generally Distributed Packet Length – ᵏม* Yasuji Murakami Abstract An all-optical network still remains a long way from realistic deployment. However, all-optical packet switches, in which optical packets are buffered and routed in optical form, are still expected to solve the problems of electronic bottlenecks and large power consumption in electronic routers.. An approximation is presented for. blocking probabilities and delays of optical buffers, where optical packets arrive in Poisson distribution at the inputs of the optical buffers and are generally distributed in packet length.. The approximation aims to provide a simple calculation tool for. optical buffer designs without requiring computer simulations or extensive iterative computations.. 㧝㧚ߪߓߦ ೨♿ᧃࠃࠅࠗࡦ࠲ࡀ࠶࠻࠻ࡅ࠶ࠢ߇Ფᐕ 1.5 ߩિ߮₸ߢჇᄢߒߡࠆ⁁ᴫߦኻ ᔕߔࠆߚ㧘વㅍⵝ⟎㧘឵ᯏߥߤᖱႎㅢାࡀ࠶࠻ࡢࠢߩ⸳ᛩ⾗߇⇇ਛߢᵴ⊒ߦⴕ ࠊࠇߡࠆ㧚శᵄ㐳ᄙ㊀વㅍᛛⴚ߇ㅴᱠߒߚ⚿ᨐ㧘ߎࠇࠄ⸳ᛩ⾗ߦࠃࠅࡀ࠶࠻ࡢࠢߩ 㜞ࠬ࡞ࡊ࠶࠻ߣ㜞ᐲߥᨵエᕈࠍᓧࠆ⚿ᨐߣߥߞߡࠆ㧚ߒ߆ߒߥ߇ࠄ㧘శવㅍᛛⴚߩ 㛳⇣⊛ߥ⊒ዷߦኻߒߡ㧘឵ᯏ㧘࡞࠲ߥߤߩࡀ࠶࠻ࡢࠢࡁ࠼ߢߪᧂߛ㔚᳇ಣℂߩ߹ ߹ߢࠆߚ㧘ォㅍ⢻ജߩ㒢⇇߇㗼ൻߔࠆࠃ߁ߦߥߞߚ㧚߹ߚ㧘IP ࡞࠲ߩ㔚ജᶖ⾌㊂ ߽ߎߩ߹߹Ⴧᄢࠍ⛯ߌࠇ߫㧘㔚ജࠦࠬ࠻߇ㆇ↪ࠦࠬ࠻ߩᄢ߈ߥᲧ㊀ࠍභࠆࠃ߁ߦߥࠆߣ ߣ߽ߦ㧘᷷ᥦൻࠍഥ㐳ߔࠆ⚿ᨐߣߥࠆ[1]㧚ᄢ߈ߊߪߎߩ 2 ߟߩ㗴ࠍ⸃ߔࠆᣇᴺߣ ߒߡ㧘శାภߩ߹߹ࡄࠤ࠶࠻ࠍಣℂߔࠆశࡄࠤ࠶࠻឵ᯏߩ⊓႐߇ᦼᓙߐࠇߡࠆ㧚ߔߥ ࠊߜ㧘శࡈࠔࠗࡃㅢାࠪࠬ࠹ࡓߦࠃࠅ 1 ࿁✢ߩવㅍㅦᐲ߇ 100Gbps ߦ㆐ߔࠆ⁁ᴫߦߥࠆ ߣ㧘વㅍ⢻ജߩ㜞శᛛⴚࠍ↪ߚశ឵ᯏ߇㧘ᰴઍߩ IP ࡞࠲ࠍᜂ߁ߎߣߦߥࠆߪ ߕߢࠆߣ߁ᦼᓙߢࠆ[2-3]㧚 นᄌ㐳 IP ࡄࠤ࠶࠻ߦኻᔕߔࠆߚ㧘㕖หᦼశࡄࠤ࠶࠻឵߇ᰴઍࠗࡦ࠲ࡀ࠶࠻ߩ ォㅍᛛⴚߦᔅ㗇ߢࠆߣߐࠇߡࠆ㧚ജࡐ࠻ߢߩࡄࠤ࠶࠻ⴣ⓭ࠍ࿁ㆱߔࠆߚߦߪశ శࡈࠔࠗࡃ ࡃ࠶ࡈࠔ߇ᔅⷐߢࠅ㧘శࡃ࠶ࡈࠔߦߪᄙߊߩឭ᩺߇ࠆ㧚ታᕈ߆ࠄߺࠆߣశ ㆃᑧ✢㧔optical fiber delay lines㧦FDL㧕ࠍ↪ߔࠆߎߣ߇ㄭߢࠆ㧚శࡃ࠶ࡈࠔߣߒ ߡߺߚ႐ว㧘FDL ߪᰴߩࠃ߁ߥ․ᓽࠍᜬߟ㧚 (1) FDL ߪߘߩ㐳ߐߦᲧߒߚ৻ቯ㊂ߩ⫾Ⓧᤨ㑆ߒ߆ᓧࠄࠇߥ㧚FDL ߢߩ⫾Ⓧᤨ㑆ߪ㧘 ̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̅̆̆̆̆̆̆ *ᄢ㒋㔚᳇ㅢାᄢቇ ᖱႎㅢାᎿቇㇱ ㅢାᎿቇ⑼ . 1- - .
(3) శࡈࠔࠗࡃ㐳ߦᲧߔࠆߩߢ㧘FDL 㐳ߩනࠍㆃᑧᤨ㑆ߢ⠨߃ࠆ㧚ߎࠇࠍᤨ ᤨ㑆☸ᐲ 㧔time granularity㧕ߣ߱㧚 (2) ⴣ⓭࿁ㆱߦ㑆ߦวࠊߥߌࠇ߫㧘ࡄࠤ࠶࠻ߪᑄ᫈ߐࠇࠆ㧚 㕖หᦼశࡄࠤ࠶࠻ߦኻᔕߔࠆశࡃ࠶ࡈࠔߩᕈ⢻ࠍ⹏ଔߔࠆߚ㧘ᄙߊߩ⸃ᨆᣇᴺ߇ឭ ᩺ߐࠇߡࠆ[4-9]㧚ߕࠇߩឭ߽᩺ᤨ㑆☸ᐲߩᢛᢙߩ FDL ࠍᢙᄙߊ↪ᗧߒߡ㧘ᤨ㑆☸ ᐲߩᦨㆡൻࠍ࿑ࠆ߽ߩߣߥߞߡࠆ㧚ߔߥࠊߜ㧘FDL ߩ㐳ߐಽᏓࠍߤߩࠃ߁ߦߔࠇ߫㧘ࡄ ࠤ࠶࠻ᑄ᫈₸ࠍᛥ߃ࠆߎߣ߇ߢ߈ࠆ߆߁ߣޔ㗴ߢࠆ㧚ߎࠇߦኻߒߡ㧘ㄭૃᢙ୯⸃[4-5]㧘 ᢙ୯ࠪࡒࡘ࡚ࠪࡦ[6-7]㧘ᜰᢙ㑐ᢙಽᏓࡄࠤ࠶࠻㐳ߦኻߔࠆ෩ኒ⸃[9]ߥߤߐ߹ߑ߹ߥข ࠅ⚵ߺ߇ߐࠇߡࠆ߇㧘ㅢߒߩࠃℂ⺰ᑼࠍᓧߡࠆࠊߌߢߪߥ㧚 ೨ႎ๔[10]ߢߪ㧘ᜰᢙ㑐ᢙಽᏓࡄࠤ࠶࠻㐳ߦኻߒߡ㧘శࡄࠤ࠶࠻឵ᯏࡃ࠶ࡈࠔߩᕈ⢻㧘 ౕ⊛ߦߪࡄࠤ࠶࠻ᑄ᫈₸ߣㆃᑧߦ㑐ߔࠆㅢߒߩࠃㄭૃᑼࠍᓧࠆߎߣߦᚑഞߒߚ㧚ᧄ ⺰ᢥߪ㧘೨ႎ๔ߩ⚿ᨐࠍ〯߹߃ߡߐࠄߦ৻⥸ൻߒ㧘৻⥸ಽᏓࡄࠤ࠶࠻㐳ߦኻߔࠆㄭૃᑼࠍ ਈ߃ߡࠆ㧚ߎߎߢߪ㧘ᣢ⊒[11]ߩౝኈࠍℂ⸃ߒ߿ߔᒻߦᢛℂߔࠆߣߣ߽ߦ㧘ዉߒ ߚㄭૃ⸃ߩ♖ᐲࠍ৻ጀߒߊ⺑ߔࠆ㧚. 㧞㧚ࡕ࠺࡞ߣቯℂ ᧄ⺰ᢥߢዉߔࠆࡄࠤ࠶࠻ᑄ᫈₸ߣㆃᑧߩㄭૃᑼߪ㧘ᢥ₂[6]߅ࠃ߮೨ႎ๔[10]ߩ⚿ᨐߦ ၮߠߊ߽ߩߢࠆ㧚ߒߚ߇ߞߡ㧘ᧄ▵ߢߪߘࠇࠄߩ⺰ᢥߦߡ⸥タߐࠇߚቯ⟵ߣᓧࠄࠇߚቯ ℂࠍ◲ẖߦ⸥ㅀߔࠆ㧚. 2.1 ࡕ࠺࡞ ᓙߜⴕߣߥࠆജࡃ࠶ࡈࠔ శࡈࠔࠗࡃㆃᑧ✢. ߦ FDL ࠍ↪ߔࠆ᭴ᚑࠍ㧘࿑ 1. 0. ߦ␜ߔ㧚㧝ߟߩജߦኻߒߡశࡄ ࠤ࠶࠻ߩⴣ⓭ࠍ࿁ㆱߔࠆߚ㧘 B. 1D. ᧄߩ FDL ࠍㆬᛯߢ߈ࠆ᭴ᚑߢ㧘i. . శࠬࠗ䏓࠴. 2D. ⇟⋡ߩ FDL ߪ i 1
(4) D 㧘1 d i d B. 3D. ߩㆃᑧࠍ↢ߓࠆ㧚ߎߎߢ ޔD ߪᤨ 㑆☸ᐲߢࠅ㧘శࡈࠔࠗࡃߩ㐳ߐ. B 1
(5) D. නࠍ L ߣߔࠆߣ㧘 D. 㨯㨯㨯. nL c 㧘. n 㧦శࡈࠔࠗࡃߩታലዮ᛬₸㧘c 㧦 ⌀ⓨਛߩశㅦߢࠆ㧚ߒߚ߇ߞߡ㧘. ࿑ 1㧚శࡈࠔࠗࡃㆃᑧ✢ߦࠃࠆశࡃ࠶ࡈࠔ. ߎߩశࡃ࠶ࡈࠔߢߪ㧘 0 㧘 1D 㧘. 2 D 㧘㨯㨯㨯㧘T. B 1
(6) D ߩ㔌ᢔ⊛. ߥㆃᑧᤨ㑆ߣߥࠆ⌕㗅ಣℂ㧔first come first service㧦FCFS㧕߇ⴕࠊࠇࠆ㧚T. B 1
(7) D. એߩㆃᑧᤨ㑆߇ᔅⷐߣߥࠆࡄࠤ࠶࠻ߪ⎕᫈ߐࠇࠆ㧚 ৻⥸⊛ߦߪ㧘⌕ߒߚࡄࠤ࠶࠻߇㧘ዋߥߊߣ߽ w ߩᓙߜᤨ㑆߇ᔅⷐߥߣ߈㧘ߎߩࡄࠤ. 2- - .
(8) ࠶࠻ߪᰴߩࠃ߁ߦಣℂߐࠇࠆ㧚 (1) i 1
(9) D d w iD ߩߣ߈㧘 i 1
(10) ⇟⋡ߩ FDL ߦォㅍߐࠇࠆ㧚ߎߩߣ߈㧘వ㗡ߦߪ. . W. ªwº iD w 㧘 « » «D». iD 㧘. . 㧔1㧕. ߩⓨᦼ㑆 W ߇ઃടߐࠇࠆ㧚ߎߎߢ㧘 ªx º ߪ㧘 x ࠍ߃ࠆᦨዊᢛᢙࠍᗧߔࠆ㧚 (2) T. B 1
(11) D w ߩߣ߈㧘ᑄ᫈ߐࠇࠆ㧚. ࡐࠕ࠰ࡦജㆊ⒟ߣߒߚ FCFS ࠪࠬ࠹ࡓߢߪ㧘છᗧߩᤨ㑆ߢࠄߚߦ⌕ߒߚᗐࡄࠤ ࠶࠻߇ฃߌࠆᓙߜᤨ㑆ߪ㧘ታ㓙ߩᓙߜᤨ㑆ߣหߓ⛔⸘ಽᏓߦᓥ߁㧚ߎߎߢ㧘ታ㓙ߩᓙߜᤨ 㑆ߣߪ㧘ࡄࠤ࠶࠻߇⌕ߒߡ߆ࠄశࡃ࠶ࡈࠔౝߢṛߔࠆᤨ㑆ߢࠅ㧘ߘߩ⛔⸘ߪࡄࠤ࠶ ࠻ߏߣߦᢙ୯ࠪࡒࡘ࡚ࠪࡦߔࠆߎߣߦࠃߞߡᓧࠆߎߣ߇ߢ߈ࠆ㧚หߓ⛔⸘ߣߥࠆߩߪ㧘 ߊ߹ߢࡐࠕ࠰ࡦജㆊ⒟ࠍቯߒߡࠆߚߢࠅ㧘PASTA㧔Poisson arrivals see time averages㧕ߩ㑐ଥߦࠃࠆ㧚 ߘߎߢ㧘ᧄ⺰ᢥߢߪ㧘ታ㓙ߩᓙߜᤨ㑆ಽᏓߢߪߥߊ ᗐᓙߜᤨ㑆㧔virtual waiting time㧕. x ߦኻߔࠆ⏕₸ಽᏓࠍᛒ߁ߎߣߣߔࠆ㧚߹ߚ㧘ᗐᓙߜᤨ㑆ࠍ㧘శࡃ࠶ࡈࠔౝߦṛߔࠆ ᤨ㑆ߣቯ⟵ߔࠆߣ㧘శࡃ࠶ࡈࠔࠍ 1 ߟߩࠪࠬ࠹ࡓߣߚ႐ว㧘ߎࠇߪࠨࡆࠬᤨ㑆ࠍ ߚṛ ṛᤨ㑆㧔sojourn time㧕ߣߥࠆ㧚ࡄࠤ࠶࠻߇⌕ߔࠆߣ㧘ࠨࡆࠬ⚳ੌ߹ߢߦ x ᤨ㑆 ߆߆ࠆ㧚 ࡄࠤ࠶࠻߇శࡃ࠶ࡈࠔࠍ⚻↱ߔࠆ(1)ߩ႐ว㧘ⓨᦼ㑆߇ઃടߐࠇࠆಽ㧘឵ᯏߦ߆߆ࠆࡄ ࠤ࠶࠻⽶⩄ߪታ㓙ߩ⽶⩄ࠃࠅㆊߣߥࠆ㧚ⓨᦼ㑆ߪ㧘శࡃ࠶ࡈࠔ߇ⓨߩߣ߈⌕ߔࠆࡄࠤ ࠶࠻ߦߪઃടߐࠇߥ߇㧘శࡃ࠶ࡈࠔߦࡄࠤ࠶࠻߇⫾Ⓧߐࠇߡࠆߣ߈ߦߪઃടߐࠇࠆ㧚 ߘߎߢ㧘ⓨᦼ㑆ࠍߚࡄࠤ࠶࠻ࠍࠄߚߦ߁ߣޠߣߞߌ߬ޟฬ⒓ߢቯ⟵ߔࠆ㧚ߔߥࠊ ߜ㧘߬ߌߞߣߦߪ㧘 Ԙ శࡃ࠶ࡈࠔ߇ⓨߩߣ߈⌕ߔࠆࡄࠤ࠶࠻㧚ߎࠇࠍ㧘ೋᦼ⌕ࡄࠤ࠶࠻㧔first arrival packets㧕ߣ߮㧘ⓨᦼ㑆ࠍᜬߚߥ㧚 㕖ೋᦼ ԙ శࡃ࠶ࡈࠔߦࡄࠤ࠶࠻߇⫾Ⓧߐࠇߡࠆߣ߈⌕ߔࠆࡄࠤ࠶࠻㧚ߎࠇࠍ㧘㕖 ⌕ࡄࠤ࠶࠻㧔non-first arrival packets㧕ߣ߮㧘ⓨᦼ㑆ࠍࠎߛ㐳ߐߣߥࠆ㧚 ߩ㧞⒳㘃ߩࡄࠤ࠶࠻߇ࠆ㧚. 2.2 ή㒢㐳శࡃ࠶ࡈࠔߩℂ⺰ ᧄ⺰ᢥߦ↪ߔࠆ⏕₸ᄌᢙߣቯℂߦߟߡ㧘೨ႎ[10]ߦᓥ㧘◲ẖߦ⸥ㅀߔࠆ㧚ᦨೋߦ ή㒢㐳శࡃ࠶ࡈࠔߩ႐ว㧘ߔߥࠊߜ B o f ߩ႐วߢࠅ࠻࠶ࠤࡄޔᑄ᫈ߪߥޕ. O 㧦 ࡐࠕ࠰ࡦജߦ߅ߌࠆ⌕₸㧚 s0 㧦 ታࡄࠤ࠶࠻㐳㧚 g 0 x
(12) 㧦 s0 ߩ⏕₸ኒᐲ㑐ᢙ㧔pdf㧦probability density function㧕㧚. 3- - .
(13) G0 x
(14) 㧦 s0 ߩ⫾ⓍಽᏓ㑐ᢙ㧔CDF㧦Cumulative Distribution Function㧕㧚 f. s0 㧦 ᐔဋࡄࠤ࠶࠻㐳㧘ߒߚ߇ߞߡ ޔs 0. ³ xg x
(15) dx 㧚. 㧔2㧕. 0. 0. U 㧦 శࡄࠤ࠶࠻ߩ⽶⩄㧘ߒߚ߇ߞߡ ޔU. Os 0 㧚. l x
(16) 㧘 L x
(17) 㧦 W ߩ⏕₸ኒᐲ㑐ᢙ㧔pdf㧕ߣ⫾ⓍಽᏓ㑐ᢙ㧔CDF㧕㧚 sX 㧦 㕖ೋᦼ⌕ࡄࠤ࠶࠻ߩታലࡄࠤ࠶࠻㐳㧘ߒߚ߇ߞߡ ޔsX. s0 W 㧚. g x
(18) 㧘 G x
(19) 㧦 sX ߩ⏕₸ኒᐲ㑐ᢙ㧔pdf㧕ߣ⫾ⓍಽᏓ㑐ᢙ㧔CDF㧕㧘ߒߚ߇ߞߡ㧘 g x
(20) g 0 x
(21) l x
(22) {. f. ³ g x y
(23) l y
(24) dy 㧚 0. (3). f. ߎߎߢߺ⇥ߪ ޔㄟߺⓍಽ㧔convolution integral㧕ߢࠆ㧚. sX 㧦 㕖ೋᦼ⌕ࡄࠤ࠶࠻ߩᐔဋࡄࠤ࠶࠻㐳㧘ߒߚ߇ߞߡ㧘 f. sX. ³ xg x
(25) dx. s0 W. 0. s0 . D 㧚 (4) 2. v x
(26) 㧦߬ߌߞߣߩᗐᓙߜᤨ㑆 x ߦ߅ߌࠆ⏕₸ኒᐲ㑐ᢙ㧔pdf㧕㧚 V x
(27) 㧦߬ߌߞߣߩᗐᓙߜᤨ㑆 x ߦኻߔࠆ⫾ⓍಽᏓ㑐ᢙ㧔CDF㧕㧚 Q 㧦శࡃ࠶ࡈࠔ߇❥ᔔᦼ㑆ߦߥߣ߈㧘ߔߥࠊߜⓨߩߣ߈ߩ⏕₸㧚 U eq 1 Q 㧦߬ߌߞߣߦኻߔࠆ╬ଔ⽶⩄ߢ㧘ⓨᦼ㑆ࠍ⽶⩄ߦขࠅㄟࠎߛ߽ߩ㧚 ࠪࠬ࠹ࡓ߇ቯᏱ⁁ᘒ㧔steady-state㧕ߦࠆߣቯߒߡ㧘ᰴߩቯℂ߇ᓧࠄࠇߡࠆ[6,10]㧚 ഥቯℂ 1㧦╬ଔ⽶⩄ߣታ⽶⩄ߪᰴᑼߩ㑐ଥߣߥࠆ㧚 . U eq. U. (5). D 1 U 2s0. ᑼ(5)ߪ㧘 D ! 0 ߢࠇ߫ U eq ! U ߢࠆߎߣ㧘U 1 ߩ႐วߢ߽ U eq ! 1 ߣߥࠆߎߣ߇ࠅ ߃ࠆߎߣࠍᗧߔࠆ㧚 ቯℂ 1㧦߬ߌߞߣߩᗐᓙߜᤨ㑆 x ߦ߅ߌࠆ⏕₸ኒᐲ㑐ᢙ㧔pdf㧕v x
(28) ߪ㧘ࡌ࡞Ꮕᴺ[12]. 4- - .
(29) ߦࠃࠆ⸃ᨆ߆ࠄ᳞ࠄࠇࠆ㧚ࠪࠬ࠹ࡓ߇ቯ⁁ᘒߦࠆߣ߈㧘ߔߥࠊߜ U eq 1 ߩߣ߈㧘. v x
(30) ߩࡊࠬᄌ឵Q T
(31) ߪᰴᑼߣߥࠆ㧚 v T
(32) *. OQ[1 g 0 * T
(33) ] T O[1 g * T
(34) ]. ߎߎߢ㧘 g 0. *. 㧔6㧕. T
(35) 㧘߅ࠃ߮ g * T
(36) ߪ㧘ߘࠇߙࠇ g 0 x
(37) 㧘߅ࠃ߮ g x
(38) ߩࡊࠬᄌ឵ߢࠆ㧚. ࡐ࠷ࠚ࠶ࠢࡅࡦࠠࡦᄌ឵ᣇ⒟ᑼ㧔the Pollaczek- ᑼ(6)ߪ㧘M/G/1 ࠪࠬ࠹ࡓߦ߅ߌࠆࡐ Khinchin transform equation㧕ߦኻᔕߔࠆ㧚ಽᲣ߇ T ߩߴ߈ਸ਼ߢࠄࠊߖࠆߩߢࠇ߫㧘 ㅒᄌ឵ߩߚߦߪ࿃ᢙಽ⸃ߢ߈ࠆߎߣ߇ᦸ߹ߒ㧚. 2.3 㒢శࡃ࠶ࡈࠔߩℂ⺰ 㒢㐳శࡃ࠶ࡈࠔߢߪ㧘ᗐᓙߜᤨ㑆 x ߇ᦨᄢ⸵ኈㆃᑧᤨ㑆ߢࠆ T. B 1
(39) D ࠍ߃. ࠆߣ㧘߬ߌߞߣߪᑄ᫈ߐࠇࠆ㧚ࠄߚߡ㧘߬ߌߞߣࠍಽ㘃ߔࠆߣ㧘ᰴߩ 3 ⒳㘃ߣߥࠆ㧚 (i) ೋᦼ⌕ࡄࠤ࠶࠻㧧ࡃ࠶ࡈࠔߪⓨߢࠆߩߢ x. 0 ߢࠅ㧘ㅢㆊࡄࠤ࠶࠻ߢࠆ㧘 (ii) 㕖ೋᦼ⌕ࡄࠤ࠶࠻ߢ߆ߟㅢㆊࡄࠤ࠶࠻㧘ߔߥࠊߜ 0 x d T 㧘 (iii) 㕖ೋᦼ⌕ࡄࠤ࠶࠻ߢ߆ߟᑄ᫈ߐࠇࠆࡄࠤ࠶࠻㧘 T x 㧚 㒢㐳శࡃ࠶ࡈࠔߦ߅ߌࠆ㑐ᢙࠍ㧘એਅߩࠃ߁ߦ㧘ਅઃ T ࠍᷝ߃ߡή㒢㐳శࡃ࠶ࡈࠔߩ ߘࠇࠄߣߔࠆ㧚ᑄ᫈ߐࠇߚ߬ߌߞߣߪࡃ࠶ࡈࠔౝߦሽߒߥߎߣ߇㧘ή㒢㐳ࡃ࠶ࡈ ࠔࡕ࠺࡞ߣߩ㆑ߢࠆ㧚. wT 㧦 ㅢㆊߒߚታࡄࠤ࠶࠻ߩߺ㧘ߔߥࠊߜ(i)ߣ(ii)㧘ࠍኻ⽎ߣߒ㧘ⓨᦼ㑆ࠍ߹ߥᐔဋ ㆃᑧᤨ㑆㧘. S T 㧦 ㅢㆊ߬ߌߞߣߩߺࠍኻ⽎ߣߒߚᐔဋ߬ߌߞߣ㐳㧘 PB 㧦 ⌕ోࡄࠤ࠶࠻ߦኻߔࠆ㐽Ⴇ⏕₸㧘߅ࠃ߮ࡄࠤ࠶࠻ᑄ᫈₸㧘៊ᄬ₸㧘 ቯℂ 3㧦 U eq 1 ߩߣ߈㧘ㅢㆊߔࠆታࡄࠤ࠶࠻ߩߺߩᐔဋㆃᑧᤨ㑆ߪᰴᑼߣߥࠆ㧚. V x
(40) Dª Q º dx «1 V T
(41) 2 ¬ V T
(42) »¼ 0. T. wT. T ³. 㧔7㧕. ߎߎߢ㧘ฝㄝߩ╙ਃ㗄ߪㅢㆊ߬ߌߞߣߩⓨᦼ㑆ߦࠃࠅ↢ߓߚㆃᑧߢࠅ㧘ߎࠇߪ࠲ࠗࡊ(ii). ߬ߌߞߣߩࡄࠤ࠶࠻㐳ᑧ㐳ಽߢࠆ㧚 ቯℂ 4㧦 U eq 1 ߩߣ߈㧘ࡄࠤ࠶࠻ᑄ᫈₸ߪᰴᑼߢਈ߃ࠄࠇࠆ㧚. 5- - .
(43) PB. 1. V T
(44) Q OS T V T
(45). 㧔8㧕. ߎߎߢ ST. s0 . Dª Q º 1 㧚 « 2 ¬ V T
(46) »¼. . 㧔9㧕. 㧚㧚㧚 ߢࠆ㧚ᑼ(8)ߩฝㄝ╙ੑ㗄ߪ㧘㒢㐳శࡃ࠶ࡈࠔߦ߅ߡ㧘ᗐᓙߜᤨ㑆߇ᦨᄢ⸵ኈㆃᑧ 㧚㧚㧚 ᤨ㑆 T B 1
(47) D ߣߥࠆ⏕₸ߢਈ߃ࠄࠇࠆ㧚ߎߩ㗄ߪ㧘⚿ዪ T B 1
(48) D ߦ߅ߌࠆή㒢㐳 శࡃ࠶ࡈࠔߩᗐᓙߜᤨ㑆 CDF ߩ୯ V T
(49) ߩ㑐ᢙߣߒߡࠄࠊߐࠇࠆ㧚. 㧟㧚 ㄭૃ⸃ᴺ 3.1 ⇼ૃ⽶⩄ߦࠃࠆᑄ᫈₸ߩዉ ᑼ(5)ࠃࠅ㧘శࡃ࠶ࡈࠔ߇ⓨߣߥࠆ⏕₸ Q ߪ Q. 1 U eq. D § · 1 O ¨ s 0 U eq ¸ 2 © ¹. ߢࠆߩߢ㧘ᑼ(9)ࠍ↪ࠆߣ㧘ᑼ(8)ߩฝㄝ╙ੑ㗄ߩಽᲣߪ㧘 Q OS T V T
(50). § D D D Q · § · ¸V T
(51) 1 O ¨ s 0 U eq ¸ O ¨¨ s0 2 2 2 V T
(52) ¸¹ © ¹ ©. D D· D· § · § § 1 O ¨ s 0 U eq Q
(53) ¸ O ¨ s 0 ¸V T
(54) 1 O ¨ s 0 ¸>1 V T
(55) @ 㧔10㧕 2 2¹ 2¹ © ¹ © © ߣߥࠆ⚿ߩߘޕᨐ㧘ᰴᑼࠍᓧࠆ㧚. PB. ª D ·º § «1 O ¨ s 0 2 ¸»>1 V T
(56) @ © ¹¼ ¬ D· § 1 O ¨ s 0 ¸>1 V T
(57) @ 2¹ ©. 㧔11㧕. ή㒢㐳శࡃ࠶ࡈࠔߢߩᄌᢙߩߺߢࠄࠊߐࠇࠆᑼ߇ᓧࠄࠇߚ㧚ߒߚ߇ߞߡ㧘ή㒢㐳శࡃ ࠶ࡈࠔࡕ࠺࡞ߢߩ⸃ࠍ᳞ࠇ߫㧘㒢㐳శࡃ࠶ࡈࠔߢߩ⸃ࠍᓧࠆߎߣ߇ߢ߈ࠆ㧚 ᑼ(11)ߪ㧘ㄭૃ⸘▚ࠍታⴕߔࠆߦߚࠅ㧘ᄙߊߩ␜ໂࠍ㑐ଥᑼߢࠆ㧚ࠄߚߦᡆ ૃ⽶⩄ U c ࠍᰴᑼߩࠃ߁ߦቯ⟵ߔࠆ㧚 . § ©. U c { O ¨ s0 . D· ¸ 2¹. §. U ¨¨1 ©. D · ¸ 2 s 0 ¸¹. (12). 6- - .
(58) ᡆૃ⽶⩄ࠍ↪ࠆߣ㧘ᑼ(11)ߪ PB. 1 U c
(59) >1 V T
(60) @ 1 U c>1 V T
(61) @. (13). ߣߥࠆ㧚M/G/1/K ࠪࠬ࠹ࡓߩᑄ᫈₸ PK ߇. PK. 1 U
(62) q K 1 Uq K. . (14㧕. ߢߐࠇࠆ[13-14]ߎߣࠍ⠨ᘦߔࠆߣ㧘ᑄ᫈₸ࠍ⸘▚ߔࠆ㓙ߦߪ ޔU ߦઍࠊߞߡ U c ࠍ↪ ࠆߎߣࠍ␜ໂߒߡࠆ㧚ߎߎߢ㧘ᑼ(14)ߩ q K ߪ㧘M/G/1 ࠪࠬ࠹ࡓߦ߅ߡࠪࠬ࠹ࡓౝቴᢙ ߇ K 1 એߣߥࠆ⏕₸ࠍ␜ߔ㧚 ᡆૃ⽶⩄ߪ㧘⌕ࡄࠤ࠶࠻ߔߴߡߦⓨᦼ㑆߇ઃടߐࠇߚ߽ߩߢ㧘᧤᧦ઙ U eq 1 ࠍḩ⿷ ߔࠆ㒢ࠅ╬ଔ⽶⩄ U eq ࠃࠅᄢ߈ߥ୯ߢࠆ㧚ߔߥࠊߜ㧘. U 1 U eq
(63). U c U eq. D 2s0. (15). ߣߥࠅ㧘᧤᧦ઙ U eq 1 ߪ U c 1 ߣ╬ଔߢࠆ㧚࿑㧞ߦ㧘⽶⩄ߦኻߔࠆ U c U eq ࠍ␜ߔ㧚. U eq. 1 ߣߥࠆ U ࠍ U max { 1 1 D 2 s 0
(64) ߣ߅ߊߣ㧘U c U eq ߪ߶߷ U max 2 ߢᦨᄢߣߥࠆ߇㧘. ߘߩ୯ߪ D ߩ 1/10 ⒟ᐲߢࠆ㧚. 3.2 ᜰᢙ㑐ᢙಽᏓࡄࠤ࠶࠻㐳 ᑼ(13)ࠍ↪ߡᑄ᫈₸ࠍ⸘▚ߔࠆߦߪ㧘V T
(65) ߩ୯߇ᔅⷐߢࠆ㧚ߔߥࠊߜή㒢㐳ࡃ࠶ࡈ ࠔࡕ࠺࡞ߦ߅ߌࠆᗐᓙߜᤨ㑆ಽᏓࠍ㧘ᓙߜᤨ㑆 x ߩ㑐ᢙᒻߢ᳞ࠆᔅⷐ߇ࠆ㧚ߎߩ㑐 ᢙߪᑼ(6)ߩ v. *. T
(66) ࠍࡊࠬㅒᄌ឵ߒߡ᳞ࠄࠇࠆ߇㧘ታ㓙ߩߣߎࠈࡊࠬㅒᄌ឵ߢ᳞. ࠄࠇࠆ㑐ᢙᒻߪ߈ࠊߡ㒢ࠄࠇߡࠆ㧚ⶄ㔀ߥ㑐ᢙࠍࡊࠬㅒᄌ឵ߔࠆߎߣߪ৻⥸ߦ ࿎㔍ߢࠅ㧘ᑼ(6)ࠍ↪ߡ⸘▚ߒߚࠍ⪺⠪ߩ⍮ࠆ㒢ࠅߥ㧚ᢥ₂[6]ߪ㧘ᑄ᫈₸߿ㆃᑧᤨ 㑆ߩ▚ߦߎߩᑼࠍ↪ߕߦᢙ୯ࠪࡒࡘ࡚ࠪࡦࠍⴕߞߡࠆ㧚 એਅߢߪ㧘శࡄࠤ࠶࠻㐳߇ᜰᢙ㑐ᢙಽᏓߔࠆ႐วߢߩㄭૃ⸃ࠍ᳞ࠆ㧚ߎߩ႐ว㧘ⓨᦼ 㑆߇ሽߔࠆߚ߬ߌߞߣࠨࡆࠬᤨ㑆ߪᜰᢙ㑐ᢙಽᏓߢߪߥ߇㧘ዉ߇ᦨ߽◲නߥࡕ. 7- - .
(67) ⽶⩄䈱Ꮕ㩷 㱝㵭䋭㱝䌥䌱. 㪇㪅㪉 㪇㪅㪈㪏 㪇㪅㪈㪍 㪇㪅㪈㪋 㪇㪅㪈㪉 㪇㪅㪈 㪇㪅㪇㪏 㪇㪅㪇㪍 㪇㪅㪇㪋. D. 2 .0. D 1 .5 D 1 .0 D. D. 0 .8 D. 0 .6. D. 0 .4. 0 .2. 㪇㪅㪇㪉 㪇 㪇. 㪇㪅㪈. 㪇㪅㪉. 㪇㪅㪊. 㪇㪅㪋. 㪇㪅㪌. 㪇㪅㪍. 㪇㪅㪎. 㪇㪅㪏. 㪇㪅㪐 㪈㪅㪇. ⽶⩄㩷 㱝 ࿑ 2㧚ᡆૃ⽶⩄ߣ╬ଔ⽶⩄ߣߩᏅ ࠺࡞ߢࠆߣᕁࠊࠇࠆ㧚 ࿑ 3 ߦ␜ߔࠃ߁ߦ㧘శࡄࠤ࠶࠻㐳ߪᐔဋ୯ s0 ߩᜰᢙ㑐ᢙಽᏓ㧘ⓨᦼ㑆ߪ >0, D @ ߩ㑆ߢߩ ဋ৻ಽᏓߣቯߔࠆ㧚ฦ⏕₸ኒᐲ㑐ᢙߣߘߩࡊࠬᄌ឵ߪ㧘ᰴᑼߣߥࠆ㧚. g 0 x
(68) l x
(69). 1. 1 x s0 * 㧘 g 0 T
(70) e s0. s 0T 1. 1 >u x
(71) u x D
(72) @㧘 l * T
(73) D. (16). 㧘 . 1 1 e DT 㧚 DT.
(74). (17㧕. ߎߎߢ㧘u x
(75) ߪනࠬ࠹࠶ࡊ㑐ᢙߢࠆ㧚ᑼ(3)ߦ߅ߌࠆ⇥ߺㄟߺⓍಽߪ㧘ࡊࠬᄌ឵ߢ ߪනߥࠆⓍߣߥࠆߚ㧘. g * T
(76). g 0 T
(77) l * T
(78) *. 1. 1 1 e DT s 0T 1 DT.
(79). (18). ߢࠆ㧚ᑼ(16)㧘(18)ࠍᑼ(6)ߦઍߔࠆߣᰴᑼࠍᓧࠆ㧚. ª. º » ¬ s0T 1¼ ª º 1 1 T O «1 1 e DT » ¬ s 0T 1 DT ¼. OQ «1 . v. *. T
(80). 1.
(81). 8- - . (19).
(82) 1 s0. 1 D. 0. 0. 0 ࡄࠤ࠶࠻㐳 x. D. 0 ⓨᦼ㑆㐳 x. (a)ࡄࠤ࠶࠻㐳ಽᏓ. (b)ⓨᦼ㑆㐳ಽᏓ. ࿑ 3 ࡄࠤ࠶࠻㐳ߣⓨᦼ㑆㐳ߩ⏕₸ኒᐲಽᏓ ᑼ(19)ࠍࡊࠬㅒᄌ឵ߔࠇ߫ㆃᑧᤨ㑆ߦ㑐ߔࠆ⏕₸ኒᐲ㑐ᢙࠍᓧࠆߎߣ߇ߢ߈ࠆ㧚 ߒ߆ߒߥ߇ࠄ㧘ᑼ(19)ߩ␜⊛ߥㅒᄌ឵ࠍ᳞ࠆߎߣߪ࿎㔍ߢࠆߩߢ ޔDT 1 ߣߒ . 1 DT 2 1 e DT | 1 O DT
(83) DT 2. >.
(84). @. (20). ߢㄭૃߒߡ㧘 DT
(85) એߩߴ߈ਸ਼ࠍήⷞߔࠆ㧚ᑼ(19)ߪ߈ࠊߡ◲නൻߐࠇߡ 2. v * T
(86). OQ 1 T s0. OQ. ª D ·º § «1 O ¨ s 0 2 ¸» © ¹¼ ¬. (21). 1 T 1 U c
(87) s0. ߣߥࠅ㧘ߘߩㅒᄌ឵ߪᰴᑼߣߥࠆ㧚 v x
(88). OQe 1 U c
(89) x s. (22). 0. >. @.
(90). ᑼ(21)ߦ߅ߌࠆㄭૃߢߪ O DT
(91) ࠍήⷞߒߚ㧚ߎࠇߪ㧘ᑼ(22)ࠃࠅ O 1 U c
(92) D s 0
(93) ࠍ 2. 2. ήⷞߔࠆߎߣߣห╬ߢࠆ㧚ߎߩ᧦ઙߪ㧘 D ߇ s0 ߦኻߒߡᭂߡዊߐ߆㧘⽶⩄ U c ߇ 1 ߦㄭߊ㊀႐วߦ⋧ᒰߔࠆ㧚ߒߚ߇ߞߡ㧘ᑄ᫈₸߇ᄢ߈႐วߩㄭૃߢࠆ㧚 CDF ߪ㧘ᑼ(22)ࠃࠅ x. V x
(94). V 0
(95) ³ OQe 1 U c
(96) [ s0 d[ 1 U eq e 1 U c
(97) x s0. (23). 0. ߣߥࠅ㧘ᑼ(5)ߩ╬ଔ⽶⩄㧘ᑼ(12)ߩᡆૃ⽶⩄ࠍ↪ߚ߈ࠊߡ◲නߥᑼߣߥࠆ㧚 ᑼ(23)ߪ㧘M/M/1 ࠪࠬ࠹ࡓߦ߅ߌࠆቴߩᓙߜᤨ㑆ಽᏓ㑐ᢙߣหᒻߢࠆ[15]㧚ߚߛߒ㧘 Ყଥᢙߩ⽶⩄ U ߇╬ଔ⽶⩄ U eq ߣߥࠅ㧘ᜰᢙㇱߢߪ⽶⩄߇ᡆૃ⽶⩄ U c ߣ⟎߈឵ࠊߞߡ. 9- - .
(98) ࠆߜ߇߇ࠆ㧚ᡆૃ⽶⩄ U c ߇㧘ᗐᓙߜᤨ㑆 x ߩ⫾ⓍಽᏓ㑐ᢙߦ߅ߌࠆᜰᢙㇱಽ㧔ߎࠇ ᧃ┵ಽᏓ㧔tail distribution㧕ߦ⋧ᒰߔࠆ㧕ߦ߅ߌࠆ⽶⩄ߣߥࠆℂ↱ߪ㧘એਅߩ ߪࠊࠁࠆᧃ ࠃ߁ߦ⠨߃ࠄࠇࠆ㧚 ⽶⩄߇ᄢ߈႐วߦߪ㧘ߔߴߡߩࡄࠤ࠶࠻ߪశࡃ࠶ࡈࠔࠍ⚻↱ߒߡജߐࠇࠆ㧚․ߦ㧘 ᑄ᫈ߐࠇࠆ⏕₸ࠍ㗴ߣߔࠆࠃ߁ߥ႐㕙ߢߪ㧘శࡃ࠶ࡈࠔ߇Ᏹߦḩ᧰ߢࠆ⁁ᴫߢࠆߩ ߢ㧘ࡄࠤ࠶࠻ߦߪᔅߕⓨᦼ㑆߇ઃടߐࠇߚ⁁ᘒߣߥࠆ㧚ታ㓙㧘ᗐᓙߜᤨ㑆 x ߩ⏕₸ኒᐲ 㑐ᢙߦኻߔࠆၮᧄᑼ(6)ߢߪ㧘ಽᲣߩࠨࡆࠬᤨ㑆ߦ㑐ߔࠆಽᏓ㑐ᢙߣߒߡ㧘㕖ೋᦼ⌕ࡄ ࠤ࠶࠻ߩࠨࡆࠬᤨ㑆㑐ᢙ g x
(99) ߇↪ࠄࠇߡࠆ㧚 ᑼ(23)ࠍᑼ(13)ߦઍߒߡ㧘ᜰᢙ㑐ᢙಽᏓߦኻߔࠆᦨೋߩᑄ᫈₸ㄭૃᑼ PB , M 1 ࠍᓧࠆ㧚. . PB , M 1. 1 U c
(100) U eq e 1 U c
(101) T s 1 U cU eq e 1 U c
(102) T. 0. (24). s0. 3.3 ৻⥸ಽᏓࡄࠤ࠶࠻㐳 ᜰᢙ㑐ᢙಽᏓߦ߅ߡߪ㧘ᓙߜᤨ㑆ߩ⚥ⓍಽᏓ߇න⚐ߥᜰᢙ㑐ᢙߣߥࠆߎߣࠍ೨▵ߢ ࠄ߆ߦߒߚ㧚GI/GI/1 ࠪࠬ࠹ࡓߦ߅ߡ㧘ᓙߜᤨ㑆ಽᏓࠍන⚐ߥᜰᢙ㑐ᢙߢㄭૃߔࠆߎߣ ߦኻߒߡ߹ߢߦ♖ജ⊛ߥ⎇ⓥ߇ߥߐࠇߡࠆ[16-20]㧚GI/GI/1 ࠪࠬ࠹ࡓߣߪ㧘ቴߩ ⌕㑆㓒߇⁛┙ߢဋ৻ߦಽᏓߒߡ߅ࠅ㧔iid㧦independent and identically distributed㧕㧘ޘ ߩቴߩࠨࡆࠬᤨ㑆߽⁛┙ߢဋ৻ߦಽᏓߒߡࠆࡕ࠺࡞ߢࠆ㧚ߐࠄߦ㧘⌕㗅ಣℂࠍ ቯߔࠆ㧚ߎߩࠪࠬ࠹ࡓߦ߅ߡ㧘ቴ߇⌕ߒߚᤨὐߢߩᗐᓙߜᤨ㑆 w ߇ x એਅߢࠆ⏕ ₸ P x ! w
(103) { W x
(104) ࠍᰴᑼߢㄭૃߔࠆ㧚. W A x
(105) 1 Ce Kx (25) ߎߎߢ㧘 K ࠍᷫ₸㧔decay rate㧕㧘 C ࠍቯᢙ㧔constant㧕ߣ߱㧚ᑼ(25)ߪ㧘 x ߇㕖Ᏹߦ ᄢ߈ߊ㧘⽶⩄ a ߇㊀㧔1 ߦㄭ㧕႐วߦߪࠃㄭૃߢࠆߎߣ߇ࠄ߆ߦߐࠇߡࠆ㧚 ᑼ(23)ߢߪ㧘ᷫ₸ߪ 1 U c
(106) s0 㧘ቯᢙߪ U eq ߣߥߞߡࠆ㧚߽ߒ㧘 W x
(107) | W A x
(108). (26). ߢࠆߥࠄ߫㧘ᐔဋᓙߜᤨ㑆 w ࠍ↪ߡ㧘 f. w. f. dW A ³ xdWA x
(109) ³ x dx dx 0. W A 0
(110). 0. f. CK ³ xe Kx dx 0. 1 C 1 a. C. K. 㧘 . (27). (28). ࠃࠅ㧘 C. a. (29). - 10 .
(111) a w. K. (30). ࠍᓧࠆ㧚․ߦ㧘M/G/1 ࠪࠬ࠹ࡓߢߪ㧘ᐔဋᓙߜᤨ㑆 w ߣߒߡᰴᑼߩࡐ ࡐ࠷ࠚ࠶ࠢࡅࡦࠠ ࡦߩᐔဋ୯ᑼ㧔Pollaczek-Khinchin mean value formula㧕[21]ࠍᓧߡࠆ㧚. s a 1 Cb. w. 2.
(112). 㧔31㧕. 2 1 a
(113) 2. ߎߎߢ ޔC b ߪࠨࡆࠬᤨ㑆ߩಽᢔ㧔variance㧕ࠍࠨࡆࠬᤨ㑆ᐔဋ s ߩੑਸ਼ߢⷙᩰൻ ߒߚ߽ߩߢࠆ㧚ߒߚ߇ߞߡ㧘M/G/1 ࠪࠬ࠹ࡓߦ߅ߌࠆᗐᓙߜᤨ㑆⚥ⓍಽᏓߪ. ª 2 1 a
(114) x º 1 a exp « » 2 «¬ 1 C b s »¼. W x
(115). (32). ߣߥࠆ㧚ᑼ(32)ࠍዉߔࠆߦᒰࠅ㧘↪ߚㄭૃߪᑼ(25)ߩߺߢࠆ㧚 ᑼ(23)ߢߪ㧘ቯᢙ C ߪ╬ଔ⽶⩄ U eq ߢࠅ㧘ᷫ₸ߦ߅ߌࠆ⽶⩄ߪᡆૃ⽶⩄ U c ࠍ↪ߡ ࠆ㧚ߘߎߢ㧘ᑼ(6)ߩ⸃ߣߒߡᰴᑼߢㄭૃߔࠆ㧚. ª 2 1 U c
(116) x º 1 U eq exp « » 2 «¬ 1 C g sX »¼. (33). s. (34). V x
(117) ߎߎߢ㧘. Cg. 2. X. 2. sX. 2.
(118) s. s0 D 2. ᑼ(4)ࠃࠅ sX. 2. X. 㧘. U c O ߢࠆ㧚ᑼ(13)ߩᑄ᫈₸ߪ 1 V T
(119) ߦ߶߷Ყߔࠆߩߢ㧘 2. ᷫ₸߇ᄢ߈ߣᜰᢙ㑐ᢙ⁁ߦᑄ᫈₸ߪዊߐߊߥࠆ㧚ߔߥࠊߜ㧘ಽᢔ୯ C g ߇ዊߐ߶ߤ ᑄ᫈₸ߪዊߐߊߥࠆ㧚 ᑼ(34)ߦ߅ߌࠆಽᢔࠍ㧘ฦࡄࠤ࠶࠻㐳 ಽᏓߦߟߡ᳞ࠆ㧚 (1) ᜰᢙ㑐ᢙಽᏓ. 1 D. ࡄࠤ࠶࠻㐳ಽᏓࠍᰴᑼߣߔࠆߣ. g x
(120). 1 x s0 e s0. g 0 x
(121). ᑼ(3㧕ࠃࠅ㧘 g x
(122) ߪ࿑㧠ߦ␜ߔࠃ߁ߦ. g x
(123). 0 0. 1 1 e x s0 for 0 d x d D D.
(124). D x. ࿑ 4. ᜰᢙ㑐ᢙಽᏓߦ߅ߌࠆ g x
(125). - 11 .
(126) 1 D s0 e 1 e x s0 for D x D. .
(127). 2. ߣߥࠅ㧘ᰴᑼߦࠃ߁ߦᜰᢙ㑐ᢙಽᏓߦኻߔࠆಽᢔ C g ,M ࠍᓧࠆ㧚. ª 2 1 § D ·2 º 2 « s 0 ¨ ¸ » sX 3 © 2 ¹ ¼» ¬«. 2. C g ,M. (35). ߎߎߢ㧘. 1 C. 2 g ,M.
(128) s. X. s0. 4§ D 2 ¨¨ 3 © 2s0. · ¸¸ ¹. 2. § D · ¨¨1 ¸¸ ! 2 © 2s0 ¹. ߢ ࠆ ߩ ߢ 㧘 ⓨ ᦼ 㑆 ߦ 㑐 ߔ ࠆ ಽ ᢔ O D 2s 0
(129). 1 U c
(130) s0 ࠃࠅዊߐ㧚߹ߚ ޔO D.
(131) ߇ ข ࠅ ࠇ ࠄ ࠇ 㧘 ᷫ ₸ ߪ ᑼ (23) ߩ. 2.
(132). 2s0
(133) ߇ขࠅࠇࠄࠇߡࠆߎߣ߆ࠄ㧘ᑼ(23)ࠃࠅ 2. ♖ᐲ߇㜞ߣ߃ࠆ㧚 (2). ࿕ቯ㐳ಽᏓ. g 0 x
(134). 1 D. G x s0
(135) g x
(136). ࠃࠅ㧘࿑㧡ߦ␜ߔ g x
(137). l x s0
(138). ߣߥࠅ㧘ߘߩಽᢔߪᰴᑼߣߥࠆ㧚 C g ,D. 2. (3). 1§ D· ¨ ¸ 3© 2 ¹. 0. 0. s0 D. s0 x. 2 2. sX (36). ࿑ 5. ࿕ቯ㐳ߦ߅ߌࠆ g x
(139). ဋ৻ಽᏓ. ࡄࠤ࠶࠻㐳߇ࠆ[0㧘 2s 0 ]ߩ▸࿐ౝߢဋ৻ߦಽᏓߒߡࠆߣߔࠆߣ㧘. g 0 x
(140). 1 >u x
(141) u x 2s0
(142) @ 㧘 2s0. ߐࠄߦ g x
(143) ߪ࿑ 6 ߩบᒻߣߥࠅ. g x
(144). g x
(145). x for 0 d x d D 2s0 D. 1 2s0. 0. 0. 2s0. D. 2s0 D. x 1 2s0. for D x d 2s 0. ࿑ 6. ဋ৻ಽᏓߦ߅ߌࠆ g x
(146). - 12 .
(147) 1 > 2s0 D
(148) x@ for 2s0 x d 2s 0 D 2s0 D. 0. . for 2 s 0 D x 㧘. ߘߩಽᢔߪᰴᑼߣߥࠆ㧚. C g ,U. 2 1ª 2 §D· º 2 « s 0 ¨ ¸ » sX 3 ¬« © 2 ¹ ¼». 2. (37). ߎࠇࠄ 3 ߟߩಽᢔߩ߁ߜ㧘ᑼ(36)ߩ࿕ቯ㐳ಽᏓ߇ᦨዊߢࠆߩߢ㧘ߘߩᑄ᫈₸ߪᦨዊߣ ߥࠆ㧚 (4). ⶄᢙ࿕ቯ㐳ಽᏓ. ࠗࡦ࠲ࡀ࠶࠻ߢォㅍߐࠇࠆ IP ࡄࠤ࠶࠻ߢߪ㧘40ޔ552ޔ576ޔ1500 ࡃࠗ࠻ߥߤ․ቯࡄ ࠤ࠶࠻㐳ߩ߽ߩ߇ୟ⊛ߢࠆ[22]㧚ታ㓙ߩ IP ࡀ࠶࠻ࡢࠢࠍᮨᡆߔࠆߦߪ㧘ⶄᢙߩ․ ቯࡄࠤ࠶࠻㐳ߩߺߢォㅍࡄࠤ࠶࠻߇᭴ᚑߐࠇߡࠆߣ⠨߃ࠆᔅⷐ߇ࠆ㧚. n ߩ․ቯࡄࠤ࠶࠻㐳ࠍߘࠇߙࠇ s i i 1,2,, n
(149) 㧘ߘࠇߙࠇߩ⌕₸ࠍ Oi i 1,2, , n
(150) ߣ߅ߊ㧚ኒᐲಽᏓ㑐ᢙߪ n. g 0 x
(151). ¦ p G x s
(152) i. i. i 1. ߣߥࠆ㧚ߎߎߢ pi. Oi. Oi 㧘 O O. n. ¦O. n. ¦O. i. 㧘ߢࠅ. i 1. i. i 1. n. s0. n. ¦ps ¦ i i. i 1. i 1. Oi s i O. n U 㧘 U { ¦ Oi s i O i 1. ߢࠆ㧚ߐࠄߦ g x
(153). n. ¦ p l x s
(154) i. i. i 1. 1 C g , MD. 2. 2 2 ªn § D· 1§ D· º 2 «¦ pi ¨ si ¸ ¨ ¸ » sX 2¹ 3 © 2 ¹ ¼» ¬« i 1 ©. ߣߥࠆ㧚. - 13 . (38).
(155) 㧠㧚 ᢙ୯ 4.1 ㄭૃᑼߩ♖ᐲ ᑼ(33)ߪ㧘ᓙߜᤨ㑆 x ߇චಽᄢ߈ߊߡ㧘㊀⽶⩄㧔heavy traffic㧕ߩ႐วߢߩㄭૃߢ ࠆ㧚ߎߩ⸘▚ᑼߩ♖ᐲࠍ᳞ࠆߚ㧘ᢥ₂[6]ߢߩࠪࡒࡘ࡚ࠪࡦ⚿ᨐ߅ࠃ߮ᢥ₂[9]ߢߩ ᜰᢙ㑐ᢙಽᏓߩ෩ኒ⸃ߣᲧセߔࠆ㧚 ᓙߜᤨ㑆 x ߇ᄢ߈ߊ㧘㊀⽶⩄ߩ႐วߩߣߒߡ㧘B=256㧘ǹ㧩0.8 ߦ߅ߌࠆࡄࠤ࠶࠻ ᑄ᫈₸ࠍ FDL ☸ᐲ D ߦኻߒߡ࿑ 7 ߦ␜ߔ㧚ታ✢ߪࡄࠤ࠶࠻㐳ಽᏓ߇ᜰᢙ㑐ᢙಽᏓ㧘⎕✢ ߪဋ৻ಽᏓ㧘߅ࠃ߮ὐ✢ߪ࿕ቯ㐳ߩ႐วߩㄭૃ⸘▚⚿ᨐࠍߘࠇߙࠇ␜ߔ㧚ᑄ᫈₸ߩ⸘▚ߦ ߪ㧘ᑼ(13)ߣ(33)ࠍ↪㧘ฦಽᏓߩᷫ₸ߦߪᑼ(35)㧘ᑼ(36)㧘߅ࠃ߮ᑼ(37)ߩಽᢔᑼࠍ↪ ߚ㧚߹ߚ㧘ᐔဋࡄࠤ࠶࠻㐳ߢࠆ s0 ࠍᤨ㑆න㧘ߔߥࠊߜ s 0. 1 ߣߒߚ㧚ਣ㧘ࡃ࠷㧘ਃ. ⷺߩฦශߪ㧘ᢥ₂[6]ߢߩࠪࡒࡘ࡚ࠪࡦ⚿ᨐߢࠆ㧚࿕ቯ㐳ಽᏓߩ႐วߩ⺋Ꮕ߇ᦨ߽ᄢ ߈߇㧘ߘࠇߢ߽ 25㧑એౝߦ߹ߞߡ߅ࠅ㕖Ᏹߦࠃㄭૃߢࠆߎߣ߇ℂ⸃ߐࠇࠆ㧚 ࿑ 8 ߪ㧘⽶⩄ߦኻߔࠆᑄ᫈₸⸘▚⚿ᨐࠍ␜ߔ㧚ᓙߜᤨ㑆 x ߪᲧセ⊛ዊߐ႐ว B㧩32 ߣ ߒߡ᳞ߚ㧚✢ߣ⸥ภߩᗧߪ㧘࿑ 7 ߣห᭽ߢࠆ㧚⽶⩄߇シ㧔light traffic㧕ߣ߈㧘ᜰ ᢙ㑐ᢙ㧘ဋ৻ಽᏓ㧘࿕ቯ㐳ߩ㗅ߦ♖ᐲߩᖡ⚿ᨐߣߥߞߡ߅ࠅ㧘ߚߣ߃߫⽶⩄߇ 0.3 ߩߣ ߈㧘ဋ৻ಽᏓ㧘࿕ቯ㐳ߩᑄ᫈₸ߪ㧘ࠪࡒࡘ࡚ࠪࡦ⚿ᨐࠃࠅ 1 ᩴ⒟ᐲᄢ߈ߥ୯ߢࠆ㧚 ߚߛߒ㧘⽶⩄߇ 0.7 એߣߥࠆߣߘߩ⺋Ꮕߪ 10㧑એౝߣߥࠅ㧘ࠃㄭૃߢࠆߎߣߪℂ⸃ ߐࠇࠆ㧚ᜰᢙ㑐ᢙಽᏓߩ႐วߦߪ㧘⽶⩄߇ዊߐ႐วߢ߽ㄭૃ♖ᐲߪࠃߊ㧘ߔߴߡߩ႐ว 㪈㪅㪇. 㪙㫃㫆㪺㫂㫀㫅㪾㩷㫇㫉㫆㪹㪸㪹㫀㫃㫀㫋㫐 ᑄ᫈₸ PB. 㪈㪇㪄㪈. B. 256. U. 0.8. 㪈㪇㪄㪉 㪈㪇㪄㪊. ᜰᢙ㑐ᢙಽᏓ. 㪈㪇㪄㪋. ဋ৻ಽᏓ. 㪈㪇㪄㪌. ࿕ቯ㐳ಽᏓ. 㪄㪍. 㪈㪇. 㪈㪇㪄㪎. 㪇㪅㪇 㪇㪅㪇㪌 㪇㪅㪈㪇 㪇㪅㪈㪌. 㪇㪅㪉㪇. 㪇㪅㪉㪌. 㪇㪅㪊㪇 㪇㪅㪊㪌 㪇㪅㪋㪇 㪇㪅㪋㪌. FDL ☸ᐲ D 㪝㪛㪣㩷㪾㫉㪸㫅㫌㫃㪸㫉㫀㫋㫐㩷 ࿑ 7.. FDL ☸ᐲ D ߦኻߔࠆᑄ᫈₸. 㧔ታ✢ߪࡄࠤ࠶࠻㐳ಽᏓ߇ᜰᢙ㑐ᢙಽᏓ㧘⎕✢ߪဋ৻ಽᏓ㧘߅ࠃ߮ὐ✢ߪ࿕ቯ 㐳ߩ႐วߩㄭૃ⸘▚⚿ᨐࠍ㧘ਣ㧘ࡃ࠷㧘ਃⷺߩฦශߪᢥ₂[6]ߢߩࠪࡒࡘࠪ ࡚ࡦ⚿ᨐߘࠇߙࠇ␜ߔ㧚㧕. - 14 .
(156) 㪈㪅㪇. B. 32. D. 0 .3. 㪄㪈. ᑄ᫈₸ PB. 㪙㫃㫆㪺㫂㫀㫅㪾㩷㫇㫉㫆㪹㪸㪹㫀㫃㫀㫋㫐. 㪈㪇. ᜰᢙ㑐ᢙ. ဋ৻ 㪄㪉. 㪈㪇. 㪈㪇㪄㪊 㪈㪇㪄㪋. ࿕ቯ㐳 㪄㪌. 㪈㪇. 㪈㪇㪄㪍 㪈㪇㪄㪎 㪇㪅㪊. 㪇㪅㪋. 㪇㪅㪌. 㪇㪅㪍. 㪇㪅㪎. 㪇㪅㪏. ⽶⩄ ǹ 㪦㪽㪽㪼㫉㪼㪻㩷㫃㫆㪸㪻 ࿑ 8. ⽶⩄ U ߦኻߔࠆᑄ᫈₸ 㧔ታ✢ߣ⸥ภߪ࿑ 7 ߣหߓᗧߢࠆ㧚㧕. ߢ 20㧑એౝߩ♖ᐲࠍᓧߡࠆ㧚ᑄ᫈₸ߩ୯ߣߒߡߪ㧘ࠪࡒࡘ࡚ࠪࡦ⚿ᨐࠃࠅᄢ߈ߊ⸘ ▚ߐࠇࠆߎߣ߆ࠄ㧘ᦨᖡߩ⸳⸘୯ߣߒߡߪ↪ߢ߈ࠆ㧚 ᜰᢙ㑐ᢙಽᏓߦ߅ߌࠆ♖ᐲࠍ㧘ߐ߹ߑ߹ߥ⽶⩄ U ߣ FDL ᢙ B ߩ୯ߦኻߒߡ⏕ߒߚ㧚 ࿑ 9 ߪ㧘B㧩32 ߦ߅ߌࠆᑄ᫈₸ࠍ㧘ߐ߹ߑ߹ߥ U ߣ FDL ☸ᐲ D ߦኻߒߡ᳞ߚ⚿ᨐߢ ࠆޕή㒢㐳శࡃ࠶ࡈࠔࡕ࠺࡞ߦ߅ߌࠆ᧤᧦ઙ U eq 1 ࠃࠅ ޔD ߦߪᰴᑼߩᦨᄢ୯ Dmax ߇ ሽߔࠆ[10]. Dmax. 2s 0 1 U 1
(157). 㧔39㧕. ታ✢ߪㄭૃ⸘▚⚿ᨐߢࠅ㧘ਣߪᢥ₂[6]ߢߩࠪࡒࡘ࡚ࠪࡦ⚿ᨐߢࠆ㧚⽶⩄߇シ U 0.4 ߩ႐วߢ߽ޔචಽߥ♖ᐲࠍߞߡࠆޕ ᑄ᫈₸ࠍᦨዊߣߔࠆ D ߩ୯ Dopt ߪ㧘⽶⩄ߩ୯ߦࠃࠅ⇣ߥࠆߎߣ㧘 Dopt ઃㄭߢߪ D ߩᄌ ൻߦኻߒߡᑄ᫈₸ߪ㊰ᗵߢࠆߎߣ㧘FDL ᢙ B ߩ୯߅ࠃ߮ࡄࠤ࠶࠻㐳ಽᏓߦߪ߹ࠅᓇ㗀 ࠍ߁ߌߥߎߣߩߤߥޔᕈ⾰߇⍮ࠄࠇߡࠆ[6]㧚࿑ 7㧘࿑ 9 ߣᰴߦ␜ߔ࿑ 10 ߆ࠄޔDopt ߩ ୯ߣߘߩᕈ⾰ࠍ⺒ߺขࠆߎߣ߇ߢ߈ࠆ㧚ߚߣ߃߫㧘U. U. 0.8 ߦ߅ߡ Dopt | 0.25 ߢࠆ߇㧘. 0.4 ߢߪ Dopt | 1.4 ߢࠅ㧘⽶⩄ߦࠃࠅ D ߩᦨㆡ୯ߪ⇣ߥࠆ㧚. - 15 .
(158) 㪈. U. 㪄㪈. 㪙㫃㫆㪺㫂㫀㫅㪾㩷㫇㫉㫆㪹㪸㪹㫀㫃㫀㫋㫐 ᑄ᫈₸ PB. 㪈㪇. B. 0 .8. U. 32. 0 .7. 㪈㪇㪄㪉 U. 㪈㪇㪄㪊. 0 .6. U. 0 .5. 㪄㪋. 㪈㪇. U. 0 .4. 㪈㪇㪄㪌 㪈㪇㪄㪍 㪈㪇㪄㪎 㪇. 㪇㪅㪌. 㪈㪅㪇. 㪈㪅㪌. 㪉㪅㪇. 㪉㪅㪌. 㪊㪅㪇. 㪝㪛㪣㩷㪾㫉㪸㫅㫌㫃㪸㫉㫀㫋㫐㩷㪛 FDL ☸ᐲ D ࿑ 9. B㧩32 ߦ߅ߌࠆᑄ᫈₸ 㧔ታ✢ߣㄭૃ⸘▚⚿ᨐ㧘ฦ⸥ภߪࠪࡒࡘ࡚ࠪࡦ⚿ᨐ[6]ߢࠆ㧚㧕. 㪈. ᑄ᫈₸ PB 㪙㫃㫆㪺㫂㫀㫅㪾㩷㫇㫉㫆㪹㪸㪹㫀㫃㫀㫋㫐. 㪈㪇㪄㪇㪌. B. 5. B. 20. 㪈㪇㪄㪈㪇 B. 㪈㪇. 50. 㪄㪈㪌. U. 0.25. 㪈㪇㪄㪉㪇 㪇㩷. 㪈㪅㪇. 㪉㪅㪇 FDL ☸ᐲ D 㪝㪛㪣㩷㪾㫉㪸㫅㫌㫃㪸㫉㫀㫋㫐㩷㪛. ࿑ 10. ǹ㧩0.25 ߦ߅ߌࠆᑄ᫈₸ 㧔ታ✢ߪㄭૃ⸘▚㧘⎕✢ߪ෩ኒ⸃[9]ࠍ␜ߔ㧚㧕. - 16 . 㪊㪅㪇. 㪋㪅㪇.
(159) ࿑ 10 ߪ㧘FDL ᢙ B ࠍࡄࡔ࠲ߣߒߡシ⽶⩄ U. 0.25 ߩ႐วߦ߅ߌࠆᑄ᫈₸⸘▚⚿. ᨐࠍ␜ߔ㧚 B ߩ୯ߪ㧘෩ኒ⸃[9]ߣᲧセߢ߈ࠆࠃ߁ߦㆬᛯߒߚ㧚ታ✢ߪㄭૃ⸘▚㧘⎕✢ߪ෩ ኒ⸃⸘▚ߩ⚿ᨐߢࠆ㧚 B. 50 ߩ႐ว㧘෩ኒ⸃ߣᲧセߒߡㄭૃ⸘▚⚿ᨐߪᦨᄢ 50 㜞. ୯ࠍ␜ߔ߇ ޔB ߇ዊߐߊߥࠆߦߟࠇ㧘ᑄ᫈₸߇߇ࠆߣ߽ߦ♖ᐲߪჇߔ㧚 ߎࠇࠄߩ⚿ᨐࠃࠅ㧘ㄭૃ⸘▚ߪ෩ኒ⸃ࠃࠅᏱߦ㜞୯ࠍ␜ߔߩߢ㧘ᑄ᫈₸ߩᦨᖡ୯ࠍ᳞ ࠆߦߪᧄឭ᩺ㄭૃ⸘▚ߪലߢࠆߎߣ߇ࠊ߆ࠆ㧚߹ߚ㧘ᑄ᫈₸߇ᄢ߈ߊߥࠆߣ♖ᐲ߇ Ⴧߔߎߣ߽ߥὐߢࠆ㧚 ᐔဋㆃᑧᤨ㑆ߪ㧘ᑼ(33)ࠍ↪ࠆߣ㧘ᑼ(7)ࠃࠅ wT. ª 1 º § 1 D ·ª Q º ¨¨ ¸¸ «1 T «1 » » ¬ V T
(160) ¼ © K 2 ¹ ¬ V T
(161) ¼. (40). ࠃࠅ⸘▚ߢ߈ࠆ㧚ᓙߜᤨ㑆 x ߇ᄢ߈ߊ㧘㊀⽶⩄㧔heavy traffic㧕ߩ႐วߩߣߒߡ㧘B=256㧘 ǹ㧩0.8 ߦ߅ߌࠆᐔဋㆃᑧᤨ㑆ࠍ࿑ 11 ߦ␜ߔ㧚✢ߣ⸥ภߩᗧߪ㧘࿑ 7 ߣห᭽ߢࠆ㧚ߔ ߴߡߩಽᏓߦ߅ߡ߽♖ᐲߪ߈ࠊߡ㜞ߊ㧘⺋Ꮕߪᦨᄢߢ߽ 2㧑ߢ⺒ߺขࠅ♖ᐲ⒟ᐲߢ ࠆ㧚 ᓙߜᤨ㑆 x ߇Ყセ⊛ዊߐ႐ว B㧩32 ߣߒߡ᳞ߚᐔဋㆃᑧᤨ㑆ࠍ㧘࿑ 12 ߦ␜ߔ㧚⽶ ⩄߇シ㧔light traffic㧕ߣ߈߶ߤࠪࡒࡘ࡚ࠪࡦ⚿ᨐࠃࠅᄢ߈ߊ⸘▚ߐࠇߡࠆ߇㧘ߘ ߩᏅߪ࿕ቯ㐳㧘⽶⩄ 0.4 ߩߣ߈߇ᦨᄢߢ 20㧑ߢࠆ㧚ߔߴߡ⽶⩄ߦኻߒߡ㧘ࠪࡒࡘࠪ ࡚ࡦ⚿ᨐࠃࠅࠊߕ߆ߦᄢ߈ߊ⸘▚ߐࠇߡࠆ߇㧘ࠃ৻⥌ࠍߖߡࠆ㧚ᄢ߈୯ߦࠪࡈ ࠻ߒߡࠆߎߣ߆ࠄ㧘ᦨᖡ୯ࠍ᳞ࠆߎߣߦߪ↪ߢ߈ࠆ㧚. 㪍㪇 B. U. 256. 0.8. Ɇ. 㪘㫍㪼㫉㪸㪾㪼㩷㪻㪼㫃㪸㫐㩷 ᐔဋㆃᑧᤨ㑆 WT. 㪌㪇 㪋㪇 ᜰᢙ㑐ᢙಽᏓ 㪊㪇 㪉㪇. ဋ৻ಽᏓ. 㪈㪇 ࿕ቯ㐳ಽᏓ 㪇 㪇. 㪇㪅㪈. 㪇㪅㪉. 㪇㪅㪊. 㪇㪅㪋. 㪝㪛㪣㩷㪾㫉㪸㫅㫌㫃㪸㫉㫀㫋㫐㩷㪛 FDL ☸ᐲ D ࿑ 11. FDL ☸ᐲ D 㧘 B. 256 ߦኻߔࠆᐔဋㆃᑧᤨ㑆. 㧔ታ✢ߣ⸥ภߪ࿑ 7 ߣหߓᗧߢࠆ㧚㧕. - 17 . 㪇㪅㪌.
(162) 㪋㪅㪇. B. 32. D. 0.3. Ɇ. 㪘㫍㪼㫉㪸㪾㪼㩷㪻㪼㫃㪸㫐 ᐔဋㆃᑧᤨ㑆 WT. 㪊㪅㪌 㪊㪅㪇. ᜰᢙ㑐ᢙ. 㪉㪅㪌 㪉㪅㪇. ဋ৻. 㪈㪅㪌 㪈㪅㪇. ࿕ቯ㐳. 㪇㪅㪌 㪇 㪇㪅㪊. 㪇㪅㪋. 㪇㪅㪍. 㪇㪅㪌. 㪇㪅㪎. 㪇㪅㪏. ⽶⩄ ǹ. 㪦㪽㪽㪼㫉㪼㪻㩷㫃㫆㪸㪻 ࿑ 12. FDL ☸ᐲ D 㧘 B. 32 ߦኻߔࠆᐔဋㆃᑧᤨ㑆. 㧔ታ✢ߣ⸥ภߪ࿑ 7 ߣหߓᗧߢࠆ㧚㧕. 4.2 ታ࠻ࡅ࠶ࠢ߳ߩㆡ↪ ታߩ IP ࡀ࠶࠻ࡢࠢߢߪ㧘․ቯࡄࠤ࠶࠻㐳ߦࡇࠢࠍᜬߟಽᏓߣߥߞߡࠆߎߣߪ ࠃߊ⍮ࠄࠇߡࠆ㧚ߘߎߢ㧘ⶄᢙ࿕ቯ㐳ಽᏓߢߩᑄ᫈₸ࠍ᳞ࠆ㧚 Case.1 2 ࡄࠤ࠶࠻㐳 s1. 64 ࡃࠗ࠻㧘 s 2. 1518 ࡃࠗ࠻㧘ࠃߞߡ s 0. 791 ࡃࠗ࠻㧘 p1. p2. 0.5. Case.2 3 ࡄࠤ࠶࠻㐳 s1. p1. 64 ࡃ ࠗ ࠻ 㧘 s 2 p2. p3. 582 ࡃ ࠗ ࠻ 㧘 s3. 1518 ࡃ ࠗ ࠻ 㧘 ࠃ ߞ ߡ s 0. 721 ࡃ ࠗ ࠻ 㧘. 13. ߎߎߢ㧘ߎࠇࠄߩࡄࠤ࠶࠻ߦߪࠗࠕ 2 ߦ߅ߌࠆࠗࠨࡀ࠶࠻ࡈࡓࠍᗐቯߒߡࠆ㧚 ߒߚ߇ߞߡ㧘ᦨ⍴ 64 ࡃࠗ࠻㧘ᦨ㐳 1518 ࡃࠗ࠻ߢࠆ㧚 B=256㧘ǹ㧩0.8 ߦ߅ߌࠆࡄࠤ࠶࠻ᑄ᫈₸ࠍ㧘࿑ 13 ߦ␜ߔ㧚ᄥ✢ߩታ✢ߪ 2 ࡄࠤ࠶࠻㐳 ಽᏓ㧘ᄥ✢ߩὐ✢ߪ 3 ࡄࠤ࠶࠻㐳ಽᏓ㧘߅ࠃ߮⚦✢ߪ࿑ 7 ߣห᭽㧘ታ✢㧘⎕✢㧘ὐ✢ߢᜰ ᢙ㑐ᢙ㧘ဋ৻ಽᏓ㧘࿕ቯ㐳ߩ႐วࠍߘࠇߙࠇ␜ߔ㧚2 ࡄࠤ࠶࠻㐳㧘3 ࡄࠤ࠶࠻㐳ಽᏓߪ㧘 ᜰᢙ㑐ᢙಽᏓߣဋ৻ಽᏓߣߩ㑆ߦ⟎ߒ㧘2 ࡄࠤ࠶࠻㐳ಽᏓߩᣇ߇ᑄ᫈₸ߪᄢ߈㧚ࡄࠤ ࠶࠻㐳ಽᏓߦ߅ߌࠆಽᢔ߇ᄢ߈ߚߢࠆ㧚ታ㓙ߩ IP ࡀ࠶࠻ࡢࠢߢߪ㧘3 ࡄࠤ࠶࠻ 㐳ಽᏓߣဋ৻ಽᏓࠍว⸘ߒߚಽᏓߣߥߞߡࠆߚ㧘ࡄࠤ࠶࠻㐳ಽᏓࠍታ᷹ߒߚ⚿ᨐࠍᱜ ⏕ߦᤋߔࠆߣ㧘࿑ 13 ߦ␜ߔࠃ߁ߦ㧘3 ࡄࠤ࠶࠻㐳ಽᏓߣဋ৻ಽᏓߣߩ㑆ߦ⟎ߔࠆߣ. - 18 .
(163) 㪈㪅㪇 B. 256. U. 0 .8. 㪄㪈. ᑄ᫈₸ PB. 㪙㫃㫆㪺㫂㫀㫅㪾㩷㫇㫉㫆㪹㪸㪹㫀㫃㫀㫋㫐. 㪈㪇. 㪉㩷 䊌䉬䉾䊃㐳 㪄㪉. 㪈㪇. 㪊㩷 䊌䉬䉾䊃㐳 㪄㪊. 㪈㪇. ᜰᢙ㑐ᢙ. 㪈㪇㪄㪋 㪈㪇㪄㪌. ဋ৻. ࿕ቯ㐳. 㪄㪍. 㪈㪇. 㪇㪅㪇. 㪇㪅㪇㪌. 㪇㪅㪈㪇 㪇㪅㪈㪌 㪇㪅㪉㪇 㪇㪅㪉㪌. 㪇㪅㪊㪇. 㪇㪅㪊㪌. 㪇㪅㪋㪇. 㪇㪅㪋㪌. FDL ☸ᐲ D 㪝㪛㪣㩷㪾㫉㪸㫅㫌㫃㪸㫉㫀㫋㫐㩷㪛 ࿑ 13. B. 256 㧘 U. 0.8 ߦ߅ߌࠆᑄ᫈₸. 㧔ᄥ✢ߪ 2 ࡄࠤ࠶࠻㐳㧘3 ࡄࠤ࠶࠻㐳ಽᏓ㧘⚦✢ߪᜰᢙ㑐ᢙ㧘ဋ৻㧘 ࿕ቯ㐳ಽᏓࠍߘࠇߙࠇ␜ߔ㧚㧕. ⠨߃ࠄࠇࠆ㧚. 㧡㧚 ߅ࠊࠅߦ ᧄ⺰ᢥߢߪ㧘৻⥸ಽᏓࡄࠤ࠶࠻㐳ߦኻߒߡశࡄࠤ࠶࠻឵ᯏࡃ࠶ࡈࠔߦ߅ߌࠆᑄ᫈₸ߣ ㆃᑧᤨ㑆ࠍਈ߃ࠆㄭૃᑼࠍ⏕┙ߒߚ㧚ᓧࠄࠇߚㄭૃᑼߪ㧘ࠗࡦ࠲ࡀ࠶࠻㧘NGN㧔next generation networks㧦ᰴઍᖱႎㅢାࡀ࠶࠻ࡢࠢ㧕ߥߤ㧘ታ㓙ߩࡄࠤ࠶࠻ࡀ࠶࠻ࡢ ࠢߦ↪ߔࠆశࡄࠤ࠶࠻឵ᯏࠍ⸳⸘ߔࠆߢജߥᱞེߦߥࠆ߽ߩߣ⏕ାߒߡࠆ㧚ᓧ ࠄࠇߚ⚿ᨐߪએਅߩߣ߅ࠅߢࠆ㧚 1). శࡃ࠶ࡈࠔߦ߅ߌࠆᑄ᫈₸ࠍ◲ଢߦ⸘▚ߔࠆ⋡⊛߆ࠄ㧘ᡆૃ⽶⩄ࠍࠄߚߦቯ⟵ߒߚ㧚 ߎߩᡆૃ⽶⩄ߪ㧘M/G/1/K ࠪࠬ࠹ࡓߦ߅ߌࠆ⽶⩄ߦઍࠊࠆ߽ߩߢࠆ㧚. 2). ৻⥸ಽᏓࡄࠤ࠶࠻㐳ߦኻߒߡ㧘ᗐᓙߜᤨ㑆ߩ⫾ⓍಽᏓ㑐ᢙ CDF ࠍ᳞ࠆㄭૃᑼࠍ ዉߒߚ㧚ߎߩㄭૃᑼߪ㧘ᓙߜᤨ㑆߇චಽᄢ߈ߊߡ㧘⽶⩄߇㊀ߣ߈߶ߤലߢࠆ㧚. 3). ⽶⩄߇ 0.7 એߩߣ߈㧘ㄭૃᑼߦࠃࠆᑄ᫈₸⸘▚⚿ᨐߪ㧘ࠪࡒࡘ࡚ࠪࡦ⚿ᨐ߿෩ ኒ⸃⸘▚⚿ᨐߣᲧセߒߡ 10㧑એౝߩ৻⥌ࠍߺߖߚ㧚ߒ߆ߒߥ߇ࠄ㧘⽶⩄߇シ႐วߦ ߪ♖ᐲ߇ᖡߊ㧘⽶⩄ 0.3 ߢࠪࡒࡘ࡚ࠪࡦ⚿ᨐߩ 10 ߩ୯ߣߥߞߡࠆ㧚. 4). ᑄ᫈₸߇㜞ߣ♖ᐲߪࠃߊߥࠅ㧘⽶⩄߇シߊߡ♖ᐲ߇ᖡ႐วߦ߅ߡ߽㧘Ᏹߦ෩ኒ ⸃ࠃࠅ㜞ᑄ᫈₸ߢࠆߚ㧘᳞ߚㄭૃᑼߪᦨᖡ୯ࠍ᳞ࠆߎߣߦലߢࠆ㧚. ߐࠄߦ㧘ᓟߩ⺖㗴ߣᕁࠊࠇࠆ࠹ࡑߪએਅߩߣ߅ࠅߢࠆ㧚. - 19 .
(164) i) シ⽶⩄ߦ߅ߌࠆㄭૃ⸘▚♖ᐲߩะ ii) U ! 1 ߩ㊀⽶⩄ߩ႐วߦ߅ߌࠆᑄ᫈₸⸘▚ iii) ఝవᮭઃ߈శࡄࠤ࠶࠻឵ᯏߩ᭴ᚑឭ᩺ߣߘߩ࠻ࡅ࠶ࠢℂ⺰ iv) ࡀ࠶࠻ࡢࠢోߢࠬ࡞ࡊ࠶࠻ะ╷ߩឭ᩺ߣߘߩ࠻ࡅ࠶ࠢℂ⺰ ߥߤߢࠆ㧚 ෳ⠨ᢥ₂ [1] R. S Tucker, “The Role of Optical and Electronics in High-Capacity Routers,” IEEE J. Lightwave Technol., Vol. 24, No. 12, pp. 4655-4673, 2006. [2] R. S Tucker et al, “Evolution of WDM Optical IP networks: A Cost and Energy Perspective,” IEEE J. Lightwave Technol., Vol. 27, No. 3, pp. 243-252, 2009. [3] G. Grasso et al, “Role of Integrated Photonics Technologies in the Realization of Terabit Nodes,” J. Opt. Commun. Netw., Vol. 1, No. 3, pp. B111-B119, 2009. [4] F. Callegati, “Optical Buffers for Variable Length Packets,” IEEE Commun. Lett., Vol. 4, No. 9, pp. 292-294, 2000. [5] Xiaohua Ma, “Modeling and Design of WDM Optical Buffers in Asynchronous and Variable-Length Optical Packets Switches,” Optical Commun., No. 269, pp. 53-63, 2007. [6] Jianming Liu et al., “Blocking and Delay Analysis of Single Wavelength Optical Buffer with General Packet Size Distribution,” IEEE J. Lightwave Technol., Vol. 27, No. 8, pp. 955-966, 2009. [7] H. E. Kankaya and N. Akar, “Exact Analysis of Single-Wavelength Optical Buffers with Feedback Markov Fluid Queues,” J. Opt. Commun. Netw., Vol. 1, No. 6, pp. 530-542, 2009. [8] W.Rogiest, D. Fiems, K.Laevens, and H. Bruneel, “Modeling the Performance of FDL Buffers with Wavelength Conversion”, IEEE Trans. Commun., Vol. 57, No. 12, pp. 3703-3711, 2009. [9] W. Rogiest, and H. Bruneel, “Exact Optimization Method for an FDL Buffer with Variable Packet Length”, IEEE Photon. Technol. Lett., Vol. 22, No. 4, pp. 242-244, 2010. [10] ᵏม㧘̌ࡄࠤ࠶࠻឵ᯏߩ࠻ࡅ࠶ࠢℂ⺰㧔ߘߩ㧝㧕̆ᜰᢙ㑐ᢙಽᏓࡄࠤ࠶࠻㐳 ߦኻߔࠆㄭૃ⸃ᴺ̆̍㧘ᄢ㒋㔚᳇ㅢାᄢቇ⎇ⓥ⺰㓸㧔⥄ὼ⑼ቇ✬㧕㧘╙ 46 ภ㧘p.9-30 (2011) [11] Murakami Y., “An Approximation for Blocking Probabilities and Delays of Optical Buffer With General Packet-Length Distributions,” IEEE J. Lightwave Technol., Vol. 30, No. 1, pp. 54-66, 2012. [12] Percy H. Brill, “A Brief Outline of the Level Crossing Method in Stochastic Models,” CORS Bulletin Vol. 34, No. 4, pp. 1-8, 2000. [13] for example, Villy B. Iversen, “Teletraffic Engineering and Network Planning”, Technical University of Denmark, p. 270, 2010㧚 [14] Ṛᩮືޔદ⮮ᄢテޔየ┨ᴦ㇢⪺ޟጤᵄ⻠ᐳࠗࡦ࠲ࡀ࠶࠻ 5 ࡀ࠶࠻ࡢࠢ⸳⸘. - 20 .
(165) ℂ⺰ޠጤᵄᦠᐫ㧔2001 ᐕ㧕ޔp.58ޔᑼ(2.42)ޕ [15] for example, L. Kleinrock, “Queueing Systems, Vol. 1: Theory”, p.203, John Wiley & Sons, New York, 1975. [16] W. Feller, “An Introduction to the Theory of Probability and its Applications,” NewYork: John Wiley, 1966, 1971. [17] A. A. Fredricks, “A Class of Approximations for the Waiting Time Distribution in a GI/G/1 Queueing System,” Bell Syst. Tech. J. Vol. 61, pp. 295-325, 1982. [18] J. Abate, G. L. Choudhury, and W. Whitt, “Exponential approximations for tail probabilities in queues, I: Waiting Times,” Oper. Res., Vol. 43, No. 3, pp. 885-901, 1995. [19] Y. Jiang, C-K. Tham, C-C. Ko, “An Approximation for Waiting Time Tail Probabilities in Multiclass Systems,” IEEE Commu. Lett., Vol. 5, No. 4, pp. 175-177, 2001. [20] L. Kleinrock, “Queueing Systems, Vol. II: Computer Applications”, John Wiley & Sons, New York, 1976. [21] ߚߣ߃߫㧘᜕⪺ߒߐ߿ޟᖱႎ឵Ꮏቇޠർ 㧔2009 ᐕ㧕㧘p.66㧘ᑼ(2.51)㧚 [22] Fei Xue et al., “Design and Experimental Demonstration of a Variable-Length Optical Packet Routing System With Unified Contention Resolution,” IEEE J. Lightwave Technol., Vol. 22, No. 11, pp. 2570-2581, 2004.. - 21 .
(166) .
(167)
関連したドキュメント
Index Terms—Chaos, external cavity, optical feedback (OFB), pulsation, semiconductor lasers, time delay..
An essential feature of CNIS is phase synchronization without frequency locking: even in the case of oscillators with different frequencies, their phases become almost always locked
This study was carried out to realize an active optical cable AOC integrated with Si-LSIs, proposed by an optical integrated circuit of a low-loss high-refractive-index
However for the SOA which does not have the facet mirrors, several authors have theoretically predicted that the inputted optical signal can reveal the larger amplification factor
In order to linearly sweep the optical frequency, the beat signal of a simple reference interferometer made of a piece of single-mode optical fiber is phase-compared
After calibration using OpenCV, the rate of distortion improved and became ≤ 5% at the point 5 cm from the center of the image. Next, we measured MTF of the prototype optical
Standard domino tableaux have already been considered by many authors [33], [6], [34], [8], [1], but, to the best of our knowledge, the expression of the
Then it follows immediately from a suitable version of “Hensel’s Lemma” [cf., e.g., the argument of [4], Lemma 2.1] that S may be obtained, as the notation suggests, as the m A
