cs/ee 143 Communication Networks

Transcription

1 cs/ee 143 Communicaion Neworks Chaper 3 Eherne Tex: Walrand & Parakh, 2010 Seven Low CMS, EE, Calech

2 Warning These noes are no self-conained, probably no undersandable, unless you also were in he lecure They are supplemen o no replacemen for class aendance

3 Agenda Eherne hisory/devices Swich Eherne forwarding able Spanning ree proocol Lile s heorem (informal proof)

4 Eherne Each (layer 2) nework full conneciviy: every node can reach every oher node broadcas capable: every node (inc. rouer) can broadcas o all oher nodes e.g. Eherne, WiFi, cable nework, ec.

5 Aloha nework (1970) Randomized muliple access Send on frequency f1; receive ack on frquency f2. If no ack afer imeou, wai a random ime and re-ransmi

6 Aloha nework (1970) Randomized muliple access If an ack is no ousanding, ransmi immediaely If no ack, re-ransmi afer a random delay

7 Aloha nework (1970) Randomized muliple access Max uilizaion (prob of success) ~ 1/e ~ 37%

8 Sloed Aloha uilizaion Model Sloed ime, fixed packe size, n saions 1 slo = 1 pk ransmission ime In each slo, each saion ransmis independenly wih probabiliy p Prob (slo has a successful ransmission) R(p) = np( 1 p) n 1

9 Sloed Aloha uilizaion max p R(p) = np( 1 p) n 1 0 = R'(p * ) = n( 1 p * ) n 1 n(n 1)p * ( 1 p * ) n 2 ( 1 p * ) = (n 1)p * p * = 1 n max uilizaion = R(p * ) " = $ 1 1 # n % ' & n 1 1 e as n

10 Sloed Aloha uilizaion max p R(p) = np( 1 p) n 1 0 = R'(p * ) = n( 1 p * ) n 1 n(n 1)p * ( 1 p * ) n 2 ( 1 p * ) = (n 1)p * p * = 1 n max uilizaion = R(p * ) " = $ 1 1 # n % ' & n 1 1 e as n

11 Sloed Aloha uilizaion max p R(p) = np( 1 p) n 1 0 = R'(p * ) = n( 1 p * ) n 1 n(n 1)p * ( 1 p * ) n 2 ( 1 p * ) = (n 1)p * p * = 1 n max uilizaion = R(p * ) " = $ 1 1 # n % ' & n 1 1 e as n

12 Unsloed Aloha uilizaion Model Fixed packe size, n saions Sloed ime of duraion τ << 1. pk ransmission ime lass 1/τ ime slos In each τ-slo, each saion ransmis independenly wih probabiliy p Small τ => approximaes unsloed operaion Prob (slo τ has a successful ransmission) R(p) = np( 1 p) n 1

13 Unsloed ALOHA uilizaion Prob (a pk ransmission sared in an arbirary τ-slo by saion 1 is successful) ( ) n 1 ( 1 p) n 1 S(p) = p 1 p = p 1 p K:= 2 1 ime slos τ ( ) ( n 1 )K

14 Unsloed ALOHA uilizaion Prob (a pk ransmission sared in an arbirary τ-slo by saion 1 is successful) ( ) n 1 ( 1 p) n 1 S(p) = p 1 p = p 1 p K:= 2 1 ime slos τ ( ) ( n 1 )K

15 Unsloed ALOHA uilizaion max p S(p) = p( 1 p) ( n 1 )K 0 = S'(p * ) = ( 1 p * ) ( n 1 )K ( 1 p * ) = (n 1)Kp * (n 1)Kp * ( 1 p * ) ( n 1 )K 1 p * = 1 (n 1)K +1

16 Unsloed ALOHA uilizaion max p S(p) = p( 1 p) ( n 1 )K 0 = S'(p * ) = ( 1 p * ) ( n 1 )K ( 1 p * ) = (n 1)Kp * (n 1)Kp * ( 1 p * ) ( n 1 )K 1 p * = 1 (n 1)K +1 reduces o sloed case If K=1

17 Unsloed ALOHA uilizaion uilizaion := n τ S(p* ) = n τ 1 " (n 1)K % $ ' # (n 1)K +1& ( n 1)K = n n 1 1 τ K + τ n 1 " $ 1 # 1 % ' (n 1)K +1& ( n 1)K 1 2e as n and τ 0 τ k = 2 τ

18 Unsloed ALOHA uilizaion uilizaion := n τ S(p* ) = n τ 1 " (n 1)K % $ ' # (n 1)K +1& ( n 1)K = n n 1 1 τ K + τ n 1 " $ 1 # 1 % ' (n 1)K +1& ( n 1)K 1 2e as n and τ 0 τ K = 2 τ

19 Unsloed ALOHA uilizaion uilizaion := n τ S(p* ) = n τ 1 " (n 1)K % $ ' # (n 1)K +1& ( n 1)K = n n 1 1 τ K + τ n 1 " $ 1 # 1 % ' (n 1)K +1& ( n 1)K 1 2e as n and τ 0 τ K = 2 τ

20 Eherne cable ( ) CSMA/CD (carrier sensing muliple access/collision deecion) 1. Wai ill channel is idle; wai for a random ime. 2. Transmi when he channel is idle following he random wai. 3. Abor if collision is deeced, and goo 1.

21 Eherne cable ( ) Truncaed binary exponenial backoff 1. Pick X uniformly a random from {0, 1,..., 2^n-1}, n = min (10, m), m = #collisions. Give up & declare error when m = Wai X x 512 bi imes (4,096 bis for 1G) 3. If collide, incremen m and repea.

22 Eherne cable ( ) Capure or winner-akes-all effec A saion ha collides is more likely o pick a larger random backoff ime. A saion ha successfully ransmis is more likely o pick a smaller backoff ime and hence more likely o successfully ransmi again

23 Eherne hub (1980s) CSMA/CD as in Eherne cable

24 Eherne hub (1980s) A saion wais a random muliples of T = 2 PROP before ransmiing When n saions ransmi independenly wih prob p, hen prob of success is <= 1/e when n is large Hence avg ime ill firs success = e T Uilizaion = TRANS / (TRANS + (e-1)t) = 1 / ( A), A = PROP/TRAN

25 Eherne swich Eherne swich eliminaes collision, provided swich buffer is big enough.

26 Eherne swich: forwarding able (Eherne) MAC address bi 2. Globally unique o MAC device, locaion independen (c.f. IP) 3. Broadcas address: 48 ones

27 Eherne swich: forwarding able x à y: [ y x daa ]

28 Agenda Eherne hisory/devices Swich Eherne forwarding able Spanning ree proocol Lile s heorem (informal proof)

29 Eherne swich rouing: STP Goal Operaion Example Performance x à y: [ y x daa ]

30 Spanning ree proocol Goal: for all swiches in a LAN o compue a shores-pah ree n used o roue layer-2 packes n one ree for enire LAN n rooed a he swich wih he smalles ID (MAC address) n decenralized, asynchronous, robus compuaion

31 Spanning ree proocol Three crieria 1. The roo swich always forwards messages on all is pors 2. Each swich compues is shores pah (in #bridges) o roo 3. All swiches conneced o a LAN elec a designaed swich for he LAN o send packes owards roo swich o A swich ha is no eleced for any of he LANs i is conneced o will no receive nor forward any daa packe

32 Spanning ree proocol n Swiches send packes asynchronously wih [ my ID curren roo ID disance o roo ] n A swich relays packes whose curren roo ID is he smalles i has seen so far (& smaller han is own curren roo ID ), and adds 1 o disance o roo n If he disances o roo on STP packes received by a swich on all is pors are he same or smaller han wha i believes is disance is, hen he swich sops forwarding n unil proocol converges Compleely decenralized, asynchronous, robus

33 STP: example I m 3 I hink roo is 3 my disance o roo is 0

34 STP: example I m 3 I hink roo is 3 my disance o roo is 0

35 STP: example a new iniiaion before previous converges

36 STP: example a new iniiaion before previous converges

37 STP: example a new iniiaion before previous converges

38 STP: example During ransien, B5 may connec o roo B1 eiher via B3 or B4 which should B5 use? Ans: use swich wih a smaller ID (B3)

39 Spanning ree for all swiches x à y: [ y x daa ]

40 STP: designaed swiches B4 believes is disance o roo B1 is 2 The STP packes from boh is pors have disances equal or less. So i does no forward and is no a designaed swich for neiher LAN Neiher B4 nor B5 will be involved in forwarding daa packes

41 Spanning ree proocol Performance n Unique pah beween every sourcedesinaion pah n Can poenially be bad since 2 swiches may communicae only via roo o e.g. in a ring of swiches, he swich wih he larges ID communicaes wih roo via he longes pah n Penaly is usually no oo bad since i is in a LAN

42 Agenda Eherne hisory/devices Swich Eherne forwarding able Spanning ree proocol Lile s heorem (informal proof)

43 Lile s law L = λt arrival rae: λ pks/s capaciy: µ pks/s (>λ) L pks

44 Lile s law α L( τ ) T i β τ α : #packes arrived by β : #packes depared by T i : delay of packe i L = α β : #packes in sysem a

45 Lile s law α L( ) β 0 T i L τ ( ) dτ

46 Lile s law α L( ) β T i i=1 β 0 T i L τ ( ) dτ

47 Lile s law α L( ) β T i i=1 β 0 T i L τ ( ) dτ α T i i=1

48 Lile s law α L( ) β T i i=1 β 0 T i L τ ( ) dτ α T i i=1 β 1 β β T i i=1 1 0 L τ ( ) dτ α 1 α α T i i=1

49 Lile s law α L( ) β T i λ T L λ T β 1 β β T i i=1 1 0 as L τ ( ) dτ α 1 α α T i i=1

50 Queueing sysem random arrival process wih rae λ pks/s µ random service ime wih average 1 s/pk µ o Lile s law L = λt o Verifies direcly for M/M/1, bu holds much more generally o Exremely useful because of is generaliy

51 M/M/1 queue Poisson arrival process wih rae λ pks/s µ Exponenial service ime wih average 1 s/pk µ 1 avg oal delay T = µ λ avg waiing ime 1 λ / µ Tq = T = µ µ λ avg #pks in sysem λ L = µ λ

52 Queueing sysem random arrival process wih rae λ pks/s µ random service ime wih average 1 s/pk µ L L = λt T T q = T 1 µ L q L = λ q T q T q