Clock Synchronization

Transcription

1 Clock Synchronizaion Clock Synchronizaion Par, Chaper Roger Waenhofer ETH Zurich Disribued Compuing / Clock Synchronizaion / Overview / Moivaion Real World Clock Sources, Hardware and Applicaions Clock Synchronizaion in Disribued Sysems Theory of Clock Synchronizaion Proocol: PulseSync /

2 Moivaion Properies of Clock Synchronizaion Algorihms Logi al Ti e happe ed- efore Exernal vs. inernal synchronizaion Exernal sync: Nodes synchronize wih an exernal clock source (UTC) Inernal sync: Nodes synchronize o a common ime o a leader, o an averaged ime,... Deermine he order of evens in a disribued sysem Synchronize resources Physical Time One-sho vs. coninuous synchronizaion Timesamp evens ( , sensor daa, file access imes ec.) Synchronize audio and video sreams Measure signal propagaion delays (Localizaion) Wireless (TDMA, duy cycling) Digial conrol sysems (ESP, airplane auopilo ec.) Periodic synchronizaion required o compensae clock drif Online vs. offline ime informaion Offline: Can reconsruc ime of an even when needed Global vs. local synchronizaion (explained laer) A ura s. o erge e i e, B za i e odes, / World Time (UTC) / Aomic Clocks vs. Lengh of a Day Aomic Clock UTC: Coordinaed Universal Time SI definiion s := 99 oscillaion cycles of he caesium- aom Aoms are excied o oscillae a heir resonance frequency and cycles can be couned. Almos no drif (abou s in Million years) Geing smaller and more energy efficien! / /8

3 Access o UTC Wha is UTC, really? Radio Clock Signal Inernaional Aomic Time (TAI) Clock signal from a reference source (aomic clock) is ransmied over a long wave radio signal DCF saion near Frankfur, Germany ransmis a. khz wih a ransmission range of up o km Accuracy limied by he propagaion delay of he signal, Frankfur-Zurich is abou ms Special anenna/receiver hardware required Abou aomic clocks Abou naional laboraories Reduce clock skew by comparing and averaging UTC = TAI + UTC leap seconds (irregular roaion of earh) GPS USNO Time USNO vs. TAI difference is a few nanoseconds /9 Comparing (and Averaging) / Global Posiioning Sysem (GPS) Δ = + Δ = Δ Δ = Which is more accurae, GPS or Radio Clock Signal? Saion B Saion A Saellies coninuously ransmi own posiion and ime code Line of sigh beween saellie and receiver required Special anenna/receiver hardware required Time of fligh of GPS signals varies beween and 89ms Posiioning in space and ime! Δ = = + / /

4 GPS Localizaion GPS Localizaion Assuming ha ime of GPS saellies is correcly synchronized + + +, = =+ =+ =+ + = speed of ligh + +, Find leas squares soluion in and / Keeping GPS Saellies synchronized / Alernaive (Silly) Clock Sources AC power lines Use he magneic field radiaing from elecric AC power lines AC power line oscillaions are exremely sable (drif abou ppm, ppm = pars per million) Power efficien, consumes only 8 μw Single communicaion round required o correc phase offse afer iniializaion Sunligh Using a ligh sensor o measure he lengh of a day Offline algorihm for reconsrucing global imesamps by correlaing annual solar paerns (no communicaion required) / /

5 Clock Devices in Compuers Clock Drif Real Time Clock (IBM PC) Baery backed up.8 khz oscillaor + Couner Ge value via inerrup sysem +² -² E.g. TinyNodes have a maximum drif of - ppm (pars per million) HPET (High Precision Even Timer) Clock drif: random deviaion from he nominal rae dependen on power supply, emperaure, ec. rae Oscillaor: Mhz Mhz Up o ns resoluion! Schedule hreads Smooh media playback Usually inside Souhbridge This is a drif of up o μs per second or.8s per hour / Clock Synchronizaion in Compuer Neworks /8 Propagaion Delay Esimaion (NTP) Measuring he Round-Trip Time (RTT) Nework Time Proocol (NTP) Clock sync via Inerne/Nework (UDP) Publicly available NTP Servers (UTC) You can also run your own server! B Reques from A A Time according o A Propagaion delay = Θ= Packe delay is esimaed o reduce clock skew /9 Time according o B Answer from B and clock skew Θ can be calculaed + + = + /

6 Messages Experience ier in he Delay ier Measuremens Problem: ier in he message delay Differen radio chips use differen paradigms Lef is a CC radio chip which generaes an inerrup wih each bye. Righ is a CC radio chip ha generaes a single inerrup for he packe afer he sar frame delimier is received. Various sources of errors (deerminisic and non-deerminisic) - ms - ms - ms SendCmd Access Transmission Recepion Callback - ms In wireless neworks propagaion can be ignored (<¹s for m). Soluion: Timesamping packes a he MAC layer ier i he essage dela is redu ed o a fe lo k i ks Sill here is quie some variance in ransmission delay because of laencies in inerrup handling (picure righ). / Clock Synchronizaion in Compuer Neworks (PTP) / Hardware Clock Disribuion Synchronous digial circuis require all componens o ac in sync Precision Time Proocol (PTP) is very similar o NTP Commodiy nework adapers/rouers/swiches can assis in ime sync by imesamping PTP packes a he MAC layer Packe delay is only esimaed on reques 9 Synchronizaion hrough one packe from server o cliens! Some newer hardware (G Inel cards, 88) can imesamp any packe a he MAC layer The bigger he clock skew, he longer he clock period The clock signal ha governs his rhyhm needs o be disribued o all componens such ha skew and wire lengh is minimized Opimize rouing, inser buffers (also o improve signal) Achieving skew of abou microsecond / /

7 Clock Synchronizaion Tricks in Wireless Neworks Bes ree for ree-based clock synchronizaion? A Reference Broadcas Synchronizaion (RBS) Synchronizing aomic clocks Sender synchronizes se of clocks Θ S Finding a good ree for clock synchronizaion is a ough problem Spanning ree wih small (maximum or average) srech. B Example: Grid nework, wih n = m nodes. Time-sync Proocol for Sensor Neworks (TPSN) Nework Time Proocol Esimaing round rip ime o sync more accuraely B A In general, finding he minimum max srech spanning ree is a hard problem, however approximaion algorihms exis Timesamp packes a he MAC Layer o improve accuracy No maer wha ree you use, he maximum srech of he spanning ree will always be a leas m (jus ry on he grid). Flooding Time Synchronizaion Proocol (FTSP) Precision Time Proocol / Clock Synchronizaion Tricks (GTSP) Varians of Clock Synchronizaion Algorihms Synchronize wih all neighboring nodes Tree-like Algorihms e.g. FTSP Broadcas periodic ime beacons, e.g., every s No reference node necessary Disribued Algorihms e.g. GTSP How o synchronize clocks wihou having a leader? Follow he node wih he fases/slowes clock? Idea: Go o he average clock value/rae of all neighbors (including node iself) / Bad local skew / All nodes consisenly average errors o all neigbhors /8

8 FTSP vs. GTSP: Global Skew FTSP vs. GTSP: Local Skew Nework synchronizaion error (global skew) Neighbor Synchronizaion error (local skew) Pair-wise synchronizaion error beween any wo nodes in he nework Pair-wise synchronizaion error beween neighboring nodes Synchronizaion error beween wo direc neighbors: FTSP (avg:. μs) GTSP (avg:. μs) FTSP (avg:. μs) GTSP (avg:.8 μs) /9 / Global vs. Local Time Synchronizaion Theory of Clock Synchronizaion Common ime is essenial for many applicaions: Assigning a imesamp o a globally sensed even (e.g. earhquake) Given a communicaion nework.. Each node equipped wih hardware clock wih drif Message delays wih jier Precise even localizaion (e.g. shooer deecion, muliplayer games) wors-case (bu consan) TDMA-based MAC layer in wireless neworks Coordinaion of wake-up and sleeping imes (energy efficiency) / Goal: hro ize Clo ks Logi al Clo ks Boh global and local synchronizaion! /

9 Time Mus Behave! Formal Model Hardware clock Hv() = s[,] hv( ) d wih clock rae hv() [-²,+²] Time (logical clocks) should no be allowed o sand sill or jump Logical clock Lv( ) which increases a rae a leas and a mos Clock drif ² is ypically small, e.g. ² ¼- for a cheap quarz oscillaor Logical clocks wih rae less han eha e differe l s hro izer Message delays [,] Employ a synchronizaion algorihm o updae he logical clock according o hardware clock and messages from Time is neighbors Le s e ore areful a d a iious : Logical clocks should always move forward Someimes faser, someimes slower is OK. Bu here should be a minimum and a maximum speed. As close o correc ime as possible! Neglec fixed share of delay, normalize jier Hv Time is Time is Lv? / Synchronizaion Algorihms: Amax Synchronizaion Algorih s: A E a ple Amax Quesion: How o updae he logical clock based on he messages from he neighbors? Idea: Minimizing he skew o he fases neighbor Allow = The problem of Amax is ha he clock is always increased o he maximum value Idea: Allow a consan slack γ beween he maximum neighbor clock value and he own clock value The algorihm Amax ses he local clock value Li() o max, max Se he clock o he maximum clock value received from any neighbor (if larger han local clock value) forward new values immediaely Opimum global skew of abou D Poor local propery Wors-case clock skew beween wo neighboring nodes is sill Θ D independen of he choice of γ! Firs all essages ake i e u i he e ha e a fas essage! Fases Hardware Clock New ime is D+x Time is D+x New ime is D+x Time is D+x How can we do beer? skew D! Time is D+x Adjus logical clock speeds o cach up wih fases node (i.e. no jump)? Idea: Take he clock of all neighbors ino accoun by choosing he average value? Clock value: D+x Old clock value: D+x- / Old clock value: x+ Old clock value: x / /

10 Local Skew: Overview of Resuls Enforcing Clock Skew u E er od s expecaion, five years ago solved All naural algorihms [Locher e al., DISC ] Blocking algorihm Lower bound of logd / loglogd [Fan & Lynch, PODC ] v D logd D Dynamic Neworks! [Kuhn e al., SPAA 9] Kappa algorihm [Lenzen e al., FOCS 8] Messages beween wo neighboring nodes may be fas in one direcion and slow in he oher, or vice versa. Tigh lower bound [Lenzen e al., PODC 9] A consan skew beween neighbors may be hidde. In a pah, he global skew may be in he order of D/. / Local Skew: Lower Bound = Add Local Skew: Upper Bound ℎ = =x ℎ = ℎ = skew in ime, Surprisingly, up o small consans, he (log( -)/² D) lower bound can be mached wih clock raes [, ] (ough par, no included) We ge he following picure [Lenzen e al., PODC 9]: Higher clock raes ime (all ℎ = ) a leas Consider a subpah of lengh = =+ max rae +² + (²) + ² large local skew (log D) (log/² D) (log/² D) (log/² D) messing wih clock raes and messages Skew reduces by a mos skew in + ℎ = Aferwards: Coninue execuion for Add /8 = Repea his rick (+½,-¼,+½,-¼, log Theorem: (log β wih a leas ime a leas β We can have boh smooh and accurae clocks! skew remains D imes skew skew in subpah D) skew beween neighbors... because oo large clock raes will amplify he clock drif ². /9 In pracice, we usually have /² ¼ > D. In oher words, our iniial inuiion of a consan local skew was no enirely wrong! /

11 Back o Pracice: Synchronizing Nodes How accuraely can we synchronize wo nodes? Sending periodic beacon messages o synchronize nodes Message delay jier affecs clock synchronizaion qualiy Beacon inerval B = ^r y r reference clock ^r = jier jier y(x) = ^r + clock offse relaive clock rae (esimaed) x Beacon inerval B / / Muli-hop Clock Synchronizaion Clock Skew beween wo Nodes Lower Bound on he clock skew beween wo neighbors Nodes forward heir curren esimae of he reference clock Each synchronizaion beacon is affeced by a random jier ^r y r ^r Error in he rae esimaion: ier in he message delay Beacon inerval Number of beacons k... d d Sum of he jier grows wih he square-roo of he disance sddev( d) = d sddev() Synchronizaion error: Single-hop: Muli-hop: x Beacon inerval B / /

12 Linear Regression (e.g. FTSP) The PulseSync Proocol FTSP uses linear regression o compensae for clock drif Send fas synchronizaion pulses hrough he nework Speed-up he iniializaion phase ier is amplified before i is sen o he nex hop Faser adapaion o changes in emperaure or nework opology y r Beacon ime B Example for k= ^r synchronizaion error FTSP Expeced ime = D B/ y(x) = ^r + Beacon ime B clock offse relaive clock rae (esimaed) PulseSync x Expeced ime = D pulse Beacon inerval B pulse / / The PulseSync Proocol () FTSP vs. PulseSync Remove self-amplificaion of synchronizaion error Global Clock Skew Fas flooding canno compleely eliminae amplificaion y r Maximum synchronizaion error beween any wo nodes FTSP PulseSync Example for k= synchronizaion error ^r y(x) = ^r + clock offse relaive clock rae (esimaed) Beacon inerval B Synchronizaion Error x The green line is calculaed using k measuremen poins ha are saisically independen of he red line. Average (>s) Maximum (>s) / FTSP PulseSync.9 µs. µs 9 µs 8 µs /8

13 FTSP vs. PulseSync Credis The Nework Time Proocol was originally designed by David L. Mills, 98. The Precision Time Proocol sandard was defined by an IEEE working group for precise neworked clock synchronizaion under ohn Eidson,. The Reference Broadcas Synchronizaion scheme was firs inroduced by eremy Elson, Lewis Girod and Deborah Esrin,. The Flooding Time Synchronizaion Proocol is due o Miklos Maroi e al.,. TPSN is due Saurabh Ganeriwal e al.,. GTSP is due Philipp Sommer e al., 9. Local skew resuls by Fan & Lynch, Lenzen, Locher, Kuhn, e al. Approximaion algorihms for minimum max srech spanning ree, e.g. Emek and Peleg,. PulseSync was proposed by Lenzen e al., 9. Sychnronizaion Error vs. disance from roo node FTSP PulseSync /9 Tha s all! Quesions & Commens? Roger Waenhofer ETH Zurich Disribued Compuing / /