Policy optimization. Stochastic approach
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1 Polcy opmzo Sochc pproch
2 Dcree-me Mrkov Proce Sory Mrkov ch Sochc proce over fe e e S S {.. 2 S} Oe ep ro probbly: Prob j - p j Se ro me: geomerc drbuo Prob j T p j p - 2
3 Dcree-me Mrkov Proce Sory corollble Mrkov ch M Mrkov ch whoe ro probble p j re fuco of corollg vrble. 3
4 Dcree-me Mrkov Proce Servce Provder SP \ + o off P SP _o o 0 off \ + o off P SP _off o off 0 4
5 Dcree-me Mrkov Proce Servce Provder SP j p T SP j 5
6 Dcree-me Mrkov Proce Power coumpo d ervce re _o _off csp o 3 4 off 4 0 _o _off bsp o off 0 0 6
7 Dcree-me Mrkov Proce Servce Requeer SR \ + 0 P SR
8 8 Dcree-me Mrkov Proce Queue Q + < + < + < + < + oherwe Q r Z d r Z j f b Q r Z d r Z j f b r SQ j q P q 0 0 0
9 Dcree-me Mrkov Proce \ + 0 PS SQ S_oo \ + 0 PS SQ S_oo
10 Dcree-me Mrkov Proce \ + 0 PS SQ S_ooff \ + 0 PS SQ S_ooff
11 Dcree-me Mrkov Proce \ + 0 PS SQ S_offo \ + 0 PS SQ S_offo
12 Dcree-me Mrkov Proce \ + 0 PS SQ S_offoff \ + 0 PS SQ S_offoff
13 Dcree-me Mrkov Proce Power mger PM A corol procedure h ue commd A o he SP every me perod. The deco o whch commd o ue bed o he obervo of he yem hory up o H r q 2 r 2 q 2 r q 3
14 4 Dcree-me Mrkov Proce Power mger PM + + oherwe r Z q q f b p p r Z q q f b p p p p p q r q r ob p SR r r SP SR r r SP SQ q q SR r r SP j j 0 Pr
15 Dcree-me Mrkov Proce 5
16 Dcree-me Mrkov Proce Deco δ A he begg of me lce he PM oberve he hory H of he yem d corol he SP by ue commd wh probbly p H P δ p P p δ 6
17 Dcree-me Mrkov Proce Polcy π The equece of he deco ke by PM ech me ep decrbe he PM polcy. π [δ δ 2 ] Tro mr from perod 0 o perod uder polcy π P π P δ P P 2... δ δ 7
18 Dcree-me Mrkov Proce Mrkov ory polcy Polce where he deco do o deped o he ere hory H bu oly o he e of he yem rq me 8
19 Dcree-me Mrkov Proce Emple of rdomze d deermc Mrkov ory polcy 9
20 Dcree-me Mrkov Proce Co mr Epeced power coumpo level c δ p c p δ Performce pely d d q 20
21 Dcree-me Mrkov Proce Polcy opmzo Gve polcy d -dmeo row vecor P repreeg he e probbly drbuo of he yem he l me he probbly drbuo of he yem he fuure me p p P π 2
22 Dcree-me Mrkov Proce Soppg me Nˆ d dcou fcorβ Aume h he yem operg over fe me horzo Nˆ whch fe d rdom. Tme perod [0 Nˆ ]correpod o he wdow of ere eo A he begg of every perod he eo wll coue wh probbly 0 < β < E[ Nˆ ] - β - 22
23 23 Dcree-me Mrkov Proce Polcy opmzo ] [.. ] [ 2 : ] [.. ] [ : ] [ ] [ m m D d E c E PO C c E d E PO c P p c p c E d P p d p d E δ π δ π π δ π δ π π δ π δ δ π δ π δ δ π β β
24 24 Dcree-me Mrkov Proce Solvg Polcy opmzo problem A X A X y A y y A X A f f m A X ll for f D d f X ll for p f p f c f LP. / 0.. m : β
25 25 Couou-me Mrkov Proce Couou Mrkov proce pce dcree pce couou T S d T X X P X X X P ] [ ]... [
26 26 Couou-me Mrkov Proce Geeror MrGof -e Mrkov proce σ σ σ σ σ σ σ σ σ G j j j j p p p p j j j j j ; 2... ; lm lm σ σ σ σ
27 Couou-me Mrkov Proce Reque rrvl eve d reque ervce eve durg me ervl 0] re ochc proce wh Poo drbuo wh me λ. Reque er-rrvl me d he ervce me follow he epoel drbuo wh me / λ Tme eeded for he SP o wch from oe e o oher follow he epoel drbuo 27
28 Couou-me Mrkov Proce Servce requeor SR SR h oe reque geerg mode. The verge ervl me of reque geered by SR follow he epoel drbuo wh me vlue /λ 28
29 Couou-me Mrkov Proce Servce ProvderSP Se e S {.. 2 S} Aco e A Geeror mr G SP A 29
30 30 Couou-me Mrkov Proce Geeror mr eleme σ mr peed wchg oherwe of e deo he f j j j j j χ δ σ σ χ δ σ 0
31 Couou-me Mrkov Proce Geeror mr G SP G π SP G G AA SP IA SP G G AI SP II SP Mr G AA SP co he ro re for ro bewee cve e. Mr co he ro re for ro from y cve e o y cve e. G II SP d G IA SP re defed mlrly G AI SP 3
32 Couou-me Mrkov Proce Servce re µ Repree he ervce peed of SP e. Epeced power coumpo C C pow power coumpo re of e ee pow + σ wchg eergy from e o S ee 32
33 Couou-me Mrkov Proce Queue Q Se e Q Q ble v Q rfer Q ble {q.. 02 Q} Q rfer {q Q} Geeror mr G SQ q where he SP e d q he co whe SP e d SQ e q 33
34 34 Couou-me Mrkov Proce Q q q Q G Q G Q G Q G G G G G G q q q q q q q q TT SQ q q TS SQ q q ST SQ q q SS SQ TT SQ TS SQ ST SQ SS SQ SQ : 0... : 0... : 0... : σ σ λ σ χ σ µ σ λ σ
35 Couou-me Mrkov Proce Power-Mged Syem SYS cor Whe he SQ ble e he SP c wch from cve e o cve e. 2 Whe he SQ ble e q Q SQ full he SP c wch from cve e o oher cve e wh loger wke up me. 35
36 Couou-me Mrkov Proce 3 Whe he SQ rfer e q Q Q- he SP c wch from cve e o oher cve e wh loger ervce me. 36
37 37 Couou-me Mrkov Proce Syem geeror mrg SYS [ ] [ ] j j SYS AI SP AA SP A SP Q ST SQ S TT SQ S A SP SS SQ SP SYS clculed re G of ere dgol The zero ll of vecor colum O zero ll of mr O G G G O I N O G I M G I N G M G G G cve cve 2 2 σ σ
38 38 Couou-me Mrkov Proce Teor um d produc B repecvely A d of order he d B I I A B A B B B B B A b b b b B A
39 Couou-me Mrkov Proce Co of he yem e Co Co C C pow lq C pow pow + + w C σ S lq where he e of w weghed vlue of dely ee SQ co 39
40 Couou-me Mrkov Proce Polcy Opmzo MIN π lm 0 X p π τ Co π dτ X By djug he weghed vlue he co equo he mmum power uder dffere dely cor c be cheve 40
41 Couou-me Mrkov Proce Polcy Opmzo workflow 4
42 Sem-Mrkov Proce 42
43 Sem-Mrkov Proce Probe eve occur by me E Prob + p + Tol elped me cludg he me pe he curre e σ j 0 j 43
44 Sem-Mrkov Proce Servce Requeor Uer behvor cceg he hrd dk: Reque er rrvl me follow mo cloely epoel drbuo E SR e λ SR 44
45 Sem-Mrkov Proce Servce Provder Hrd dk h 3 e: cve dle low-power dle. Servce me mo cloely follow epoel drbuo E SP e λ SP 45
46 Sem-Mrkov Proce Power mger PM corol ro bewee cve d lowpower dle. The ro bewee cve d low-power dle e be decrbed ug uform drbuo 0 0 E PM 0 0 oherwe 46
47 Sem-Mrkov Proce Queue Meured queue ze wh eperme o hrd dk ug uer rce mmum queue ze meured 9 job wh verge of
48 Sem-Mrkov Proce Syem e Syem e re chrcerzed by he power coumpo he e he umber of job he queue d he probbly drbuo defg he me pe he e. 48
49 Sem-Mrkov Proce Syem e ro 49
50 50 Sem-Mrkov Proce Co Mr d p c e du E k u S co α
51 5 Sem-Mrkov Proce Opmzo 0 } m{co d E p e m wh eleme m mr S S M v v M π π α π π π π
52 Polcy compro Eperme Evrome Peum II oebook compuer wh Fuju MHF 2043AT hrd dk rug be vero of Mcroof Wdow NT V5. Fler drver[7] for ech lgorhm re mplemeed o corol he power e of he hrd dk o record dk ccee d o lyze he performce mpc d power mgeme overhed of ech lgorhm 52
53 Polcy compro Dk prmeer P w P w w T d ec E d J T wu ec E wu J Reul Algorhm Pw T ec SM CM DM
54 Referece [] G. A. pleologo L. Be A. Boglolo G. De Mchel Polcy Opmzo for Dymc Power Mgeme hp://keboo.ford.edu/uer//reerch/dpm/ [2] Q. Qu d M. Pedrm Dymc Power Mgeme Bed o Couou-Tme Mrkov Deco Procee Deg Auomo Coferece pp [3] Tj Smuc Luc Be Gov De Mchel Eve Drve PM of Porble Syem hp://keboo.ford.edu/uer//reerch/dpm/ 54
55 Referece [4] U.Nry Bh Eleme Of Appled Sochc Procee Joh Wley&SoIc.984 [5] B.Mller Fe Se Couou Tme Mrkov Deco Procee Wh Fe Plg Horzo. SIAM J. Corol vol.5no. 2 pp [6] M.Puerm Fe Mrkov deco procee Joh Wley&SoIc.994 [7]Yug-Hg Lu Tj Smuc Gov De Mchel Sofwre corolled power mgeme hp://keboo.ford.edu/uer//reerch/dpm/ 55
56 Referece [8] Yug-Hg Lu Eu-Youg Chug Tj Smuc Luc Be Gov De Mchel Quve Compro of Power Mgeme Algorhm hp://keboo.ford.edu/uer//reerch/dpm/ [9] Tj Smuc Luc Be Peer Gly Gov De Mchel Dymc Power Mgeme of Lpop Hrd Dk Deg Auomo d Te Europe 2000 [0] Q. Qu Q.Wu d M. Pedrm Sochc modelg of Power-Mged Syem: Coruco d Opmzo USC EE-Syem Dep 56
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