Lecture 8: Time & Clocks. CDK: Sections TVS: Sections

Transcription

1 Lecture 8: Tme & Clocks CDK: Sectons TVS: Sectons

2 Topcs Synchronzaton Logcal tme (Lamport) Vector clocks We assume there are benefts from havng dfferent systems n a network able to agree the answers to tme-related questons. 28-Feb-11 COMP28112 Lecture 8 2

3 Synchronzaton Two parts: Dffculty of settng the same tme Clock drft.e. dffculty of mantanng synchronzaton once acheved 28-Feb-11 COMP28112 Lecture 8 3

4 UTC (Coordnated Unversal Tme) Internatonal Atomc Tme derved from clocks wth atomc oscllators, drft rate about 1 n 10^13 Astronomcal tme derved from stars, sun, etc. Slowng of earth s rotaton leads to dvergence UTC based on atomc tme, but wth occasonal nserton of leap seconds to keep t n step wth astronomcal tme UTC broadcast by terrestral rado and satellte (GPS) 28-Feb-11 COMP28112 Lecture 8 4

5 Computer Tme GPS recevers accurate to about 1 mcrosec. Recevers from terrestral statons, or over dedcated telephone lne to a few mllsec. In realty few computers n a network have ether of these ways of settng the tme And then there s drft (typcally 1 n 10^6 for nexpensve crystal clocks) 28-Feb-11 COMP28112 Lecture 8 5

6 Crstan s Clock Synchonzaton Wth a tme server, clents set ther own clocks by measurng the round-trp tme to process ther request, rtt, and addng half that to the tme n the reply Assumes tme-out = tme-back, more lkely to be true for short rtt If good estmate of mn transmsson tme avalable can estmate accuracy 28-Feb-11 COMP28112 Lecture 8 6

7 The Berkeley Algorthm 1 processor, the master, polls others (slaves) Slaves reply wth ther tmes Master estmates ther local tmes usng round-trp tmes (as above) Master averages all these (and own tme) elmnatng any tmes wth excessve rtt Also elmnates any clocks wrong wrt others 28-Feb-11 COMP28112 Lecture 8 7

8 The Berkeley Algorthm (cont.) Rather than send back correct tme, master sends back to each slave ts own delta (+/-) If the master fals, a dstrbuted electon algorthm exsts to elect one of the slaves as replacement Crstan s algorthm & the Berkeley algorthm desgned (prmarly) for ntranets 28-Feb-11 COMP28112 Lecture 8 8

9 Network Tme Protocol (NTP) Desgned for larger scale nternet Network of servers: Prmary (stratum 1) wth UTC clock Secondary (stratum 2), synchronzed wth prmary Can reconfgure e.g. f UTC source fals prmary can become secondary, etc. 28-Feb-11 COMP28112 Lecture 8 9

10 NTP Synchronzaton Three methods of synchronzaton Multcast mode Procedure call mode Symmetrc mode Multcast mode used on hgh-speed LANs Server sends tme to all servers on LAN at once Each reset clocks (assumng a small delay) Not hghly accurate 28-Feb-11 COMP28112 Lecture 8 10

11 Procedure-call mode Effectvely Crstan s algorthm Server accepts requests and reples wth the tme Used when multcast not supported or hgher accuracy requred 28-Feb-11 COMP28112 Lecture 8 11

12 Symmetrc mode Used where hghest accuracy s requred Messages exchanged, and data bult up to mprove accuracy of synchronzaton over tme. Each message sent contans tmng nfo about the prevous message receved (tme sent, tme receved) and tme t s sent 28-Feb-11 COMP28112 Lecture 8 12

13 CDK Fgure 11.4 Messages exchanged between a par of NTP peers Server B T -2 T -1 Tme m m' Tme Server A T - 3 T 28-Feb-11 COMP28112 Lecture 8 13

14 Usng the nformaton Use ths nformaton to estmate the offset between the two clocks, o, from the equatons (where t, t are transmsson tmes for m, m resp.) T T = + t Hence: T T = + t' o 1 o 28-Feb-11 COMP28112 Lecture 8 14

15 28-Feb-11 COMP28112 Lecture ) / ' ( 2 ) / ( ' t t o t t o T T T T o T T T T d + = + = + = + = Usng the fact that t and t are both >= 0, leads to 2 / 2 / d o d o o +

16 Data flterng NTP servers flters successve (o,d) values to dentfy best (lowest d value), and measure the relablty of the other server Each server wll nteract wth several peers dentfyng most relable ones Acheves accuraces of 10s of mllsec over nternet paths 28-Feb-11 COMP28112 Lecture 8 16

17 Logcal Tme (Lamport) In sngle processor, every event can be unquely ordered n tme usng the local clock What we want s to be able to do ths n a dstrbuted system, where synchronzaton between clocks s not suffcently good to use physcal tme 28-Feb-11 COMP28112 Lecture 8 17

18 Smple prncples If two events happen n the same process, they occur n the order gven by that process If a message s sent from 1 process to another, the event of sendng happens before the event of recevng These defne a partal orderng of events, gven by the happens-before relatonshp 28-Feb-11 COMP28112 Lecture 8 18

19 CDK Fgure 11.5 Events occurrng at three processes p 1 a b m 1 p 2 c d m 2 Physcal tme p 3 e f 28-Feb-11 COMP28112 Lecture 8 19

20 Logcal clocks A logcal clock s a monotoncally ncreasng software counter Each process keeps ts own, L, and uses t to tmestamp events L++ before each event Each message sent contans current L (as t) Each message receved sets L = max(l,t)+1 28-Feb-11 COMP28112 Lecture 8 20

21 Logcal clocks (cont.) Now f event e1 happens-before e2, L(e1) < L(e2) Note that the converse s not true,.e. we cannot deduce orderng from the tmestamps 28-Feb-11 COMP28112 Lecture 8 21

22 CDK Fgure 11.6 Lamport tmestamps for the events shown n CDK Fgure p 1 a b m 1 p c d m 2 Physcal tme p 3 1 e f 5 28-Feb-11 COMP28112 Lecture 8 22

23 Totally ordered logcal clocks Can make the orderng of events above total, so that there s an order between every par of events, by usng an orderng of process dentfers to resolve cases where logcal clocks are the same n dfferent processes Ths has no physcal realty, but can be used to control entry to crtcal sectons, etc. 28-Feb-11 COMP28112 Lecture 8 23

24 Vector Clocks A vector clock n a system wth n processes s an array of n ntegers Each process keeps ts own Messages between processes contan the vector clock of the sender as a tmestamp Each clock starts wth all ntegers 0 28-Feb-11 COMP28112 Lecture 8 24

25 Vector clocks (cont.) Events n process ncrement the th element n ts vector clock When process receves a tmestamp, t, n a message t resets each element n ts clock V[j] = max(v[j], t[j] ) for j = 1 n Ths operaton s referred to as a merge 28-Feb-11 COMP28112 Lecture 8 25

26 CDK Fgure 11.7 Vector tmestamps for the events shown n CDK Fgure 11.5 (1,0,0) (2,0,0) p 1 a b m 1 p 2 (2,1,0) (2,2,0) c d m 2 Physcal tme p 3 (0,0,1) e f (2,2,2) 28-Feb-11 COMP28112 Lecture 8 26

27 Comparng Vector clocks V1 = V2 ff V1[j] = V2[j] for all j V1 <= V2 ff V1[j] <= V2[j] for all j V1 < V2 ff V1 <= V2 & V1!= V2 Now f event e1 happened-before event e2, V(e1) < V(e2) And f V(e1) < V(e2), e1 happened-before e2 28-Feb-11 COMP28112 Lecture 8 27

28 Advantages and Dsadvantages We don t end up wth an arbtrary order when none s needed (e.g. between c and e n the fgures: nether V(c) < V(e) nor V(e) < V(c) ) Cost s the extra amount of data n a tmestamp. 28-Feb-11 COMP28112 Lecture 8 28