Lecture 4: Layering as Optimization Decomposition

Transcription

1 CDS270: Omzaon Game and Layerng n Communcaon Newor Lecure 4: Layerng a Omzaon Decomoon Lun Chen 10/25/2006

2 Agenda Layerng a omzaon decomoon Layerng a omzaon decomoon Dual decomoon Cae udy Cro-layer rae conrol roung and chedulng degn n ad hoc wrele newor Oen ue 2

3 Layered roocol ac Archecure deermne unconaly allocaon Modularzaon: who doe wha How o connec or coordnae hem Newor ado a layered archecure alcaon ranor newor ln hycal Doe he ar o a ecc o he arcular alcaon Provde relable end-o-end ranmon congeon conrol Provde end-o-end ah beween wo end node roung Provde relable on-o-on ranmon channel acce Provde a ln or ranmng b beween wo node 3

4 S D alcaon ranor newor ln Each layer Conrol o a ube o decon varable Hde he comley o he layer below Provde well dened ervce o he layer above hycal 4

5 Each layer degned earaely and evolve aynchronouly Manage comley ued by he ucce o communcaon newor alcaon ranor newor ln hycal Doe he ar o a ecc o he arcular alcaon Provde relable end-o-end ranmon congeon conrol Provde end-o-end ah beween wo end node roung Provde relable on-o-on ranmon channel acce Provde a ln or ranmng b beween wo node 5

6 Each layer degned earaely and evolve aynchronouly Each layer omze ceran obecve alcaon ranor newor ln hycal Mnmze reone me web layou Mamze uly TCP/AQM Mnmze ah co IP Mamze hroughu Mnmze SINR mamze caace 6

7 Each layer abraced a an omzaon roblem Oeraon o a layer a drbued oluon Reul o one roblem layer are arameer o oher Oerae a deren mecale Alcaon: uly alcaon ranor newor ln hycal ma 0 ub o IP: roung U R c c X Phy: ower Ln: chedulng 7

8 Layerng moran oundaon or neworng Bu here lle quanave underandng o gude a yemac roce o degnng layered roocol ac. How o or how no o modularze and connec? How o acheve drbued conrol? How o elcly characerze and rade o degn obecve uch a ably erormance calably and robune ec? 8

9 Layerng a omzaon decomoon Each layer abraced a an omzaon roblem Oeraon o a layer a drbued oluon Reul o one roblem layer are arameer o oher Oerae a deren mecale alcaon ranor newor ln hycal o negrae varou roocol layer no a uned ramewor by regardng hem a drbued comuaon over he newor o olve ome global omzaon roblem. Deren layer carry ou drbued comuaon on deren ube o he decon varable ung local normaon o acheve ndvdual omaly. Taen ogeher hee local algorhm acheve a global omaly 9

10 General ramewor: uly mamzaon Movaon: uly mamzaon rovde a general ramewor or underandng TCP--drbued rmal-dual algorhm over he newor o mamze aggregae uly Kelly 98 Low Alcaon: uly alcaon ranor newor ln hycal ma ub o IP: roung U R c c X Phy: ower Ln: chedulng 10

11 Generalzed newor uly mamzaon Obecve uncon: Wha he end-uer and newor rovder care abou.e. uer uly & newor co Conran: Phycal and economc rercon Varable: Under he conrol o h degn Conan: Beyond he conrol o h degn alcaon ranor newor ln hycal ma R c ub o IP: roung Alcaon: uly U R c c X Phy: ower Ln: chedulng 11

12 Layerng a omzaon decomoon Newor Layer Inerace Layerng alcaon ranor newor ln hycal generalzed NUM ub-roblem uncon o rmal/dual varable decomoon mehod Deren vercal decomoon are maed o deren layerng cheme Horzonal decomoon can be urher carred ou whn one layer no drbued comuaon and conrol over geograhcally darae newor elemen 12

13 Mer romng o erve a a mahemacal heory o newor archecure revere engneerng Underand each layer n olaon aumng oher layer are degned nearly omally Underand neracon acro layer Incororae addonal layer Ulmae goal: enre roocol ac a olvng one gan omzaon roblem where ndvdual layer are olvng ar o 13

14 rovde a o-down aroach o degn he roocol ac orward engneerng Newor a an omzer End-uer alcaon ule lu newor co a he drver Elcly radeo degn obecve By careully choong obecve uncon By deren decomoon By degnng deren convergen algorhm Tranaren neracon beween varou layer Omaly n erm o ma uly 14

15 Dual decomoon 15 + l l l l l l c R U c R U ma mn ubec o ma Dual: Prmal: horzonal decomoon lnear and addve n R and c

16 ln IP ranor Prmal: Dual: ma 0 vercal decomoon c mn ma R ma 0 ma U 0 TCP rae conrol U hore ah roung + ma Throughu-mamal chedulng Congeon rce coordnae acro roocol layer mn R ubec o l R l l R c c l cπ c l l 16

17 Eamle Omal web layer: Zhu e al 01 HTTP/TCP: Chang Lu 04 alcaon ranor newor ln hycal TCP: Kelly e al 98 Low e al 99 TCP/IP: Wang e al 05 TCP/MAC: Chen e al 05 TCP/ower conrol: Xao e al 01 Chang 04 Rae conrol/roung/chedulng: Chen e al 05 Erylma e al 05 Ln e al 05 Neely e al 05 Chen e al

18 Agenda Layerng a omzaon decomoon Layerng a omzaon decomoon Dual decomoon Cae ude Cro-layer rae conrol roung and chedulng degn n ad hoc wrele newor Oen ue 18

19 Wha ad hoc wrele newor Baleeld communcaon Wrele LAN Communcaon nrarucure or auomaed vehcle Senor newor. Node equed wh wrele rado Peer-o-eer communcaon No bacbone nrarucure 19

20 Phycal and ln layer characerc Bandwdh-lmed Fber: one bundle ~ GHz Uable wrele ecrum ~ 3 GHz Should be ulzed ecenly Wrele channel me-varyng Unrelable wrele ln Wrele channel a hared medum and nererence-lmed Channel acce an ue Scheduled acce: hgh overhead Random acce: no ervce guaranee Aloha DCF 20

21 Eng roocol are no degned or wrele envronmen Perormance roblem: ecency and calably TCP hroughu degradaon Roung roocol un-calable More elc radeo beween hroughu and laency and ower Degn a general uroe newor? 21

22 Cro-layer degn Layered degn alcaon ranor newor ln hycal uncoordnaed Cro-layer degn alcaon ranor newor ln hycal Imrove erormance and acheve ecen reource allocaon 22

23 Cro-layer echnque Adave echnque Ln MAC newor and alcaon adaaon Reource managemen and allocaon ower conrol Dvery echnque Ln dvery anenna channel ec. Acce dvery Roue dvery Alcaon dvery Wha he rgh way o cro-layer degn Whch layer o ae acon: elmnae congeon Deren echnque wll no nerac adverely Acheve a good radeo: hroughu v delay v ower 23

24 Conrol baed ad hoc neworng Newor a drbued yem acro deren node and deren layer Deren echnque are caered and need o be u ogeher o ee hey really wor Perormance deend on oerang on and dynamc Conrol baed mehod Wha he roer merc/obecve uncon Wha he rgh layerng Tune obecve uncon and newor a realme o eec roer radeo n hroughu delay and ower 24

25 Newor degn by omzaon decomoon Man Obecve Redegn roocol ac accordng o conve omzaon heory 1. Omal earaon o concern 2.Alcaon-orened obecve uncon 3.Degned alo or robune congeon rce congeon conrol ranmon rae d uly uncon U d ouu queue d* o ervce ln o ranm roung chedulng ln wegh w conlc grah local congeon rce d d d neghbor congeon rce d λ d Dual decomoon ugge: Global reource allocaon decomoe o hree drbued ub-roblem neracng hrough congeon rce d d Provde a ramewor or bac rucure o ey algorhm o ad roocol degn and mlemenaon 25

26 Newor Model Conder a ac ad hoc wrele newor wh a e o N node and a e o logcal ln l L Each ln ha a ed caacy c l when acve The newor hared by a e S o ource ndeed by Alo deny low by denaon D N Some noaon: l v.. N N v.. [ ] S D L v.. 26

27 Model: Schedulably Prmary nererence: ln harng common node canno be acve mulaneouly Conlcon grah: caure conenon relaon among he ln o he newor Each vere rereen a ln An edge beween wo verce mean wo correondng ln canno ranm a he ame me

28 28 Indeenden e: he correondng ln can ranm mulaneouly Rereen ndeenden e a a -dmenonal rae vecor Feable rae regon e L e r = oherwe 0 e l c r l e l = = = Π 1 0 : e e e e e e a a r a r r

29 Model: Rae conran 29 :caacy o ln allocaed o he low wh denaon Schedulably conran where Rae conran = D Π D N L L : : : : Flow neced no newor caacy allocaed o ncomng ranve low caacy allocaed o Ougong low

30 Model: Problem ormulaon 30 Each ource aan a connuou nondecreang concave uly when ranmng a rae Formulae reource allocaon U Π D N U L L.. ma : :

31 Cro-layer Degn va Dual Decomoon 31 Inroduce Lagrangan dual Dual uncon non-derenable he ubgraden o dual uncon.e.. By ubgraden mehod we oban g D D + g = Π + = U D L L D N.. ma : : = + ] [ 1 : : L L γ

32 Rae Conrol 32 The Lagrangan dual can be decomoed no wo ubroblem Soluon o he r ubroblem rae conrol ource adu rae accordng o local congeon rce Π = = D U D.. ma ma ' U =

33 Jon Schedulng and Roung 33 The econd ubroblem equvalen o For each ln nd denaon uch ha and dene Schedulng: chooe uch ha Roung: over ln end an amoun o b or denaon accordng o ~ ~ L w arg ma ~ Π w = arg ma Π = D.. ma ma 2

34 Summary o Cro-layer Algorhm Congeon rce + 1 = [ + γ + ] : L : L + TCP rae conrol Queue a node Roung Schedulng 34

35 Convergence Analy Subgraden may no be a drecon o decen bu ha an angle le han 90 wh all decen drecon The yem wll converge o he omal bu no mono-oncally wh a conan eze. Conour o D P+rg P* P+1=[+rg] + P 35

36 * Denon 1: Le be an omal value o he dual varable. The aoremenoned cro-layer algorhm wh conan eze ad o converge acally o or any δ > 0 here * e a eze γ uch ha lmud D * δ 1 where : = τ he average rce by τ = 1 me. 36

37 Theorem 2: D * lmud D * +γg 2 / 2 Theorem 3: P * lmn P P * γg 2 / 2 Guaranee he ably and average rce and ource rae converge o correondng omal value reecvely when eze mall enough. 37

38 Eenon o he Newor wh Tme-varyng Channel Aume me loed channel ae h an..d. ne ae roce wh drbuon qh. A each channel ae h we have a eable rae regon Eend aoremenoned cro-layer algorhm o handle me-varyng channel only wh a modcaon o chedulng ~ arg ma w 1 Π h L Queon: ably? revere-engneered o olve any omzaon roblem? Πh 38

39 Reerence Syem 39 Dene mean eable rae regon Dene deal reerence yem roblem Characerze he algorhm wh reec o he reerence yem } : { h h r h r h q r r h Π = = Π Π D N U L L.. ma : :

40 Sably 40 Congeon rce evolve accordng o a Marov chan Proo by ochac Lyaunov analy Theorem 4: Denoe dual uncon o he reerence roblem by wh an omal rce. Conder Lyaunov uncon we oban where D * A A G G V E V V E c Ι + Ι = + = ] 1] [ ] [ γ γ 2 * 2 * ma } : { 2 * A G D D = = γ δ δ 2 2 * V = = + ] [ 1 : : L L γ

41 Perormance Denoe he ae o he Marov chan n he eady ae by and correondng ource rae by Theorem 5: D * D E[ ] D * + γg 2 / 2 Theorem 6: P * P E[ ] P * γg 2 / 2 Provde a general echnque and reul regardng ably and omaly o dual algorhm n a me-varyng envronmen. 41

42 Summary Jon rae conrol roung chedulng algorhm or wrele newor Subgraden algorhm Eenon o me-varyng channel dual oluon o conve G.NUM reman able and omal on average under Marov model ochacally varyng conran e Only ece a general rucure and ey comonen or cro-layer degn and many ue reman Imlemenaon ue: uly uncon eze congeon rce and queung meage ang Need boom-u aroach or mlemenaon 42

43 Agenda Layerng a omzaon decomoon Layerng a omzaon decomoon Dual decomoon Cae ude Cro-layer rae conrol roung and chedulng degn n ad hoc wrele newor Oen ue 43

44 Uly degn.e. how o model he uer or alcaon need Inelac rac Delay enve rac me-baed uly Nonconve roblem Nonconcave obecve uncon Nonconve conran Sably under delay Iue relaed o conrol lane Imlemenaon and managemen comley Evolvably 44