12. Traffic engineering

Transcription

1 12. Trffi engineering let12.ppt S Introution to Teletrffi Theory Spring

2 12. Trffi engineering Contents Topology Trffi mtrix Trffi engineering Lo lning 2

3 12. Trffi engineering Topology A teleommunition network onsists of noes n links Let N enote the set of noes inexe with n Let J enote the set of noes inexe with n Exmple: N = {,,,,e} J = {1,2,3,,12} e 5 7 link 1 from noe to noe link 2 from noe to noe Let j enote the pity of link j (ps) 3

4 12. Trffi engineering Pths We efine pth (= route) s set of onseutive links onneting two noes Let P enote the set of pths inexe with p Exmple: three pths from noe to noe : re pth onsisting of links 1 n e 5 7 green pth onsisting of links 11 n 6 lue pth onsisting of links 10, 8 n 6 4

5 12. Trffi engineering Pth mtrix Eh pth onsists of set of links This onnetion is esrie y the pth mtrix A,for whih element jp = 1 if j p, tht is, link j elongs to pth p otherwise jp = 0 Exmple: three olumns of pth mtrix

6 12. Trffi engineering Shortest pths If eh link j is ssoite with orreponing weight w j, the length l p of pth p is given y l p = w j j p With unit link weights w j = 1, pth length = hop ount Exmple: two shortest pths (with length 2) from noe to noe w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 e 6

7 12. Trffi engineering Contents Topology Trffi mtrix Trffi engineering Lo lning 7

8 12. Trffi engineering Trffi hrteristion Trffi Ciruit-swithe e.g. telephone trffi Pket-swithe e.g. t trffi Link Network Link Network 8

9 12. Trffi engineering Trffi mtrix (1) Trffi in network is esrie y the trffi mtrix T, for whih elementt nm tells the trffi emn (ps) from origin noe n to estintion noe m Aggregte trffi of ll flows with the sme origin n estintion t Aggregte trffi uring time intervl, e.g. usy hour or typil 5-minute intervl e Exmple: Trffi emn from origin to estintion is t (ps) 9

10 12. Trffi engineering Trffi mtrix (2) Below we present the trffi emns in vetor form Let K enote the set of originestintion pirs (OD-pirs) inexe with k Trffi emns onstitute vetor x, for whih elementx k tells the trffi emn of OD-pir k x k e Exmple: if OD-pir(,) is inexe with k, then x k = t 10

11 12. Trffi engineering Contents Topology Trffi mtrix Trffi engineering Lo lning 11

12 12. Trffi engineering Trffi engineering n network esign Trffi engineering = Engineer the trffi to fit the topology Given fixe topology n trffi mtrix, how to route these trffi emns? Network esign = Engineer the topology to fit the trffi 12

13 12. Trffi engineering Effet of routing on lo istriution Routing lgorithm etermines how the trffi lo is istriute to the links Internet routing protools (RIP, OSPF, BGP) pply the shortest pth lgorithms (Bellmn-For, Dijkstr) In MPLS networks, other lgorithms re lso possile More preisely: routing lgorithm etermines the proportions (splitting rtios) φ pk of trffi emns x k llote to pths p, φ=1/2 x φ=1/2 φ=0 e p P φ pk = 1 for ll k 13

14 12. Trffi engineering Link ounts Trffi on pth p etween OD-pir k is thus φ pk x k Link ounts y j re etermine y trffi emns x k n splitting rtios φ pk : y j = p P k K jp φ pk The sme in mtrix form: x k x y = 0 e y = 0 y = Aφx 14

15 12. Trffi engineering MPLS MPLS (Multiprotool Lel Swithing) supports trffi lo istriution to prllel pths etween OD-pirs In MPLS networks, there n e ny numer of prllel Lel Swithe Pths (LSP) etween OD-pirs These pths o not nee to elong to the set of shortest pths Eh LSP is ssoite with lel n eh MPLS pket is tgge with suh lel MPLS pkets re route through the network vi these LSP s (oring to their lel) Trffi lo istriution n e ffete iretly y hnging the splitting rtios φ pk t the origin noes 15

16 12. Trffi engineering OSPF (1) OSPF (Open Shortest Pth First) is n intromin routing protool in IP networks Link Stte Protool eh noe tells the other noes the istne to its neighouring noes these istnes re the link weights for the shortest pth lgorithm se on this informtion, eh noe is wre of the whole topology of the omin the shortest pths re erive from this topology using Dijkstr s lgorithm IP pkets re route through the network vi these shortest pths 16

17 12. Trffi engineering OSPF (2) Routers in OSPF networks typilly pply ECMP (Equl Cost Multipth) If there re multiple shortest pths from noe n to noe m, then noe n tries to split the trffi uniformly to those outgoing links tht elong to t lest one of these shortest pths However, this oes not imply tht the trffi lo is istriute uniformly to ll shortest pths! See the exmple on next slie. Trffi lo istriution n e ffete only iniretly y hnging the link weights splitting rtios φ pk n not iretly e hnge ue to ECMP, the esire splitting rtios φ pk my e out of reh 17

18 12. Trffi engineering ECMP y = x/4 y = x/4 x y = x/4 e y = x/4 g f φ = 1/4 φ = 1/4 φ = 1/2 e f g 18

19 12. Trffi engineering Effet of link weights on lo istriution (1) mximum link lo w = 1 w = 1 w = 1 w = 1 w = 1 x w = 1 w = 1 x w = 1 w = 1 w = 1 w = 1 w = 1 e φ = 1/2 φ = 1/2 φ = 1 e y = 3x/2 y = x e 19

20 12. Trffi engineering Effet of link weights on lo istriution (2) mximum link lo w = 1 w = 1 w = 1 w = 1 w = 1 x w = 1 w = 1 x w = 2 w = 1 w = 1 w = 1 w = 2 e φ = 1/2 φ = 1/2 φ = 1/2 e φ = 1/2 y = x y = x e link weight inrese 20

21 12. Trffi engineering Contents Topology Trffi mtrix Trffi engineering Lo lning 21

22 12. Trffi engineering Lo lning prolem (1) Given fixe topology n trffi mtrix, how to optimlly route these trffi emns? One pproh is to equlize the reltive lo of ifferent links, ρ j = y j / j Sometimes this n e one in multiple wys (upper figure) Sometimes it is not possile t ll (lower figure) In this se, we my, however, try to get s lose s possile, e.g. y minimizing the mximum reltive link lo (lle: lo lning prolem) x = 1 = 1 = 1 = 1 e = 1 g = 1 = 1 = 1 f = 1 x = 1 = 1 = 1 = 1 = 2 22

23 12. Trffi engineering Lo lning prolem (2) Lo Blning Prolem: Consier network with topology (N,J), link pities j, n trffi emns x k. Determine the splitting rtios φ pk so tht the mximum reltive link lo is minimize Minimize sujet to y φ mx j J j p P pk = φ y j j 0 = 1 p P k K pk A jp φ pk x k j J k K p P, k K 23

24 12. Trffi engineering Lo lning prolem (3) Lo Blning Prolem hs lwys solution ut this might not e unique Exmple: the sme mximum link lo is hieve with routes of ifferent length the upper routes re etter ue to smller pity onsumption A resonle unique solution is hieve y ssoiting negligile ost with ll the hops long the pths use x y = 0 e x y = 0 e y = 0 24

25 Trffi engineering Lo lning prolem (4) Lo Blning Prolem with resonle n unique solution: Consier network with topology (N,J), link pities j, n trffi emns x k. Determine the splitting rtios φ pk so tht the mximum reltive link lo is minimize with the smllest mount of require pity = = + K k P p K k J j x A y y pk P p pk P p K k k pk jp j J j j y J j j j, 0 1 sujet to mx Minimize φ φ φ ε

26 12. Trffi engineering Exmple (1): optiml solution = 2 = 2 = 2 = 2 = 2 x = 2 = 1 = 1 = 2 = 2 = 2 = 2 e φ = 1/2 φ = 1/4 φ = 1/4 e ρ = x/4 ρ = x/4 ρ = x/4 ρ = x/8 e ρ = x/4 ρ = x/8 26

27 12. Trffi engineering Exmple (2): link weights w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 x w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 w = 1 e φ = 1/2 φ = 1/2 e ρ = x/4 ρ = x/4 ρ = x/2 e ρ = x/4 27

28 12. Trffi engineering Exmple (3): optiml link weights w = 1 w = 2 w = 2 w = 1 w = 1 x w = 1 w = 3 w = 3 w = 1 w = 1 w = 1 w = 1 e φ = 1/2 φ = 1/2 e ρ = x/4 ρ = x/4 ρ = x/4 e ρ = x/4 ρ = x/4 28

29 12. Trffi engineering THE END 29