12. Traffic engineering

Transcription

1 lt2.ppt S-38. Introution to Tltrffi Thory Spring Topology Pths A tlommunition ntwork onsists of nos n links Lt N not th st of nos in with n Lt J not th st of nos in with j N = {,,,,} J = {,2,3,,2} link from no to no link 2 from no to no Lt j not th pity of link j (ps) W fin pth (= rout) s st of onsutiv links onnting two nos Lt P not th st of pths in with p thr pths from no to no : r pth onsisting of links n 3 grn pth onsisting of links n lu pth onsisting of links 0, 8 n

2 Pth mtri Shortst pths Eh pth onsists of st of links This onntion is sri y th pth mtri A,for whih lmnt jp = if j p, tht is, link j longs to pth p othrwis jp = 0 thr olumns of pth mtri If h link j is ssoit with orrponing wight w j, th lngth l p of pth p is givn y l p = w j j p With unit link wights w j =, pth lngth = hop ount two shortst pths (of lngth 2) from no to no w = w = w = w = w = w = w = w = w = w = w = w = Trffi hrtristion Ciruit-swith.g. tlphon trffi Trffi Pkt-swith.g. t trffi Link Ntwork Link Ntwork 8

3 Trffi mtri () Trffi mtri (2) Trffi in ntwork is sri y th trffi mtri T, for whih Blow w prsnt th trffi mns in vtor form lmnt t nm tlls th trffi mn (ps) from origin no n to stintion no m Aggrgt trffi of ll flows with th sm origin n stintion Aggrgt trffi uring tim intrvl,.g. usy hour or typil -minut intrvl Trffi mn from origin to stintion is t (ps) t LtK not th st of originstintion pirs (OD-pirs) in with k Trffi mns onstitut vtor, for whih lmnt k tlls th trffi mn of OD-pir k if OD-pir (,) is in with k, thn k = t k 9 0 Trffi nginring n ntwork sign = Enginr th trffi to fit th topology Givn fi topology n trffi mtri, how to rout ths trffi mns? Ntwork sign = Enginr th topology to fit th trffi 2

4 Efft of routing on lo istriution Link ounts Routing lgorithm trmins how th trffi lo is istriut to th links Intrnt routing protools (RIP, OSPF, BGP) pply th shortst pth lgorithms (Bllmn-For, Dijkstr) In MPLS ntworks, othr lgorithms r lso possil Mor prisly: routing lgorithm trmins th proportions (splitting rtios) φ pk of trffi mns k llot to pths p, φ pk = p P for ll k φ=/2 φ=/2 φ=0 3 Trffi on pth p twn OD-pir k is thus φ pk k Link ounts y j r trmin y trffi mns k n splitting rtios φ pk : y j = jpφ pk k p P k K Th sm in mtri form: y = Aφ y = /2 y = /2 y = /2 y = 0 y = /2 y = 0 MPLS OSPF () MPLS (Multiprotool Ll Swithing) supports trffi lo istriution to prlll pths twn OD-pirs In MPLS ntworks, thr n ny numr of prlll Ll Swith Pths (LSP) twn OD-pirs Ths pths o not n to long to th st of shortst pths Eh LSP is ssoit with ll n h MPLS pkt is tgg with suh ll MPLS pkts r rout through th ntwork vi ths LSP s (oring to thir ll) Trffi lo istriution n fft irtly y hnging th splitting rtios φ pk t th origin nos OSPF (Opn Shortst Pth First) is n intromin routing protool in IP ntworks Link Stt Protool h no tlls th othr nos th istn to its nighouring nos ths istns r th link wights for th shortst pth lgorithm s on this informtion, h no is wr of th whol topology of th omin th shortst pths r riv from this topology using Dijkstr s lgorithm IP pkts r rout through th ntwork vi ths shortst pths

5 OSPF (2) ECMP Routrs in OSPF ntworks typilly pply ECMP (Equl Cost Multipth) If thr r multipl shortst pths from no n to no m, thn no n tris to split th trffi uniformly to thos outgoing links tht long to t lst on of ths shortst pths Howvr, this os not imply tht th trffi lo is istriut uniformly to ll shortst pths! S th mpl on nt sli. Trffi lo istriution n fft only inirtly y hnging th link wights splitting rtios φ pk n not irtly hng u to ECMP, th sir splitting rtios φ pk my out of rh y = /2 y = /2 y = / y = / y = / y = / g y = /2 f y = /2 φ = / φ = / φ = /2 f g 8 Efft of link wights on lo istriution () Efft of link wights on lo istriution (2) mimum link lo mimum link lo w = w = w = w = w = w = w = w = w = w = w = w = φ = /2 φ = /2 φ = y = /2 y = 3/2 y = /2 y = /2 y = w = w = w = w = w = w = w = w = 2 w = w = w = w = 2 φ = /2 φ = /2 φ = /2 φ = /2 y = /2 y = /2 y = y = y = /2 y = /2 y = /2 link wight inrs 9 20

6 Lo lning prolm () Givn fi topology n trffi mtri, how to optimlly rout ths trffi mns? On pproh is to quliz th rltiv lo of iffrnt links, ρ j = y j / j Somtims this n on in multipl wys (uppr figur) Somtims it is not possil t ll (lowr figur) In this s, w my, howvr, try to gt s los s possil,.g. y minimizing th mimum rltiv link lo (ll: lo lning prolm) = = = = = g = = = f = = = = = = Lo lning prolm (2) Lo lning prolm (3) Lo Blning Prolm: Consir ntwork with topology (N,J), link pitis j, n trffi mns k. Dtrmin th splitting rtios φ pk so tht th mimum rltiv link lo is minimiz Minimiz sujt to y j m j J j y j = Ajpφ pk k j J k K φ pk = k K φ pk 0 p P, k K Lo Blning Prolm hs lwys solution ut this might not uniqu th sm mimum link lo is hiv with routs of iffrnt lngth th uppr routs r ttr u to smllr pity onsumption A rsonl uniqu solution is hiv y ssoiting ngligil ost with ll th hops long th pths us y = /2 y = /2 y = /2 y = 0 y = /2 y = /2 y = 0 y = /2 y = /2 y = 0 y = /2 y = /2 23 2

7 Lo lning prolm () Empl (): optiml solution Lo Blning Prolm with rsonl n uniqu solution: Consir ntwork with topology (N,J), link pitis j, n trffi mns k. Dtrmin th splitting rtios φ pk so tht th mimum rltiv link lo is minimiz with th smllst mount of rquir pity Minimiz sujt to y j m + ε y j' j J j j' J y j = Ajpφ pk k j J k K φpk = k K φpk 0 p P, k K = 2 = 2 = 2 = 2 = 2 = 2 = = = 2 = 2 = 2 = 2 φ = /2 φ = / φ = / ρ = / ρ = / ρ = / ρ = /8 ρ = / ρ = /8 2 2 Empl (2): link wights w = Empl (3): optiml link wights w = w = w = w = w = w = w = w = w = w = w = w = φ = /2 φ = /2 ρ = / ρ = / ρ = /2 ρ = / w = 2 w = 2 w = w = w = w = w = 3 w = 3 w = w = w = w = φ = /2 φ = /2 ρ = / ρ = / ρ = / ρ = / ρ = / 2 28