Real-Time Course. Clock synchronization. June Peter van der TU/e Computer Science, System Architecture and Networking

Transcription

1 Real-Time Course Clock synchronization 1

2 Clocks Processor p has monotonically increasing clock function C p (t) Clock has drift rate For t1 and t2, with t2 > t1 (1-ρ)(t2-t1) <= C p (t2)-c p (t1) <= (1+ρ)(t2-t1) Suppose C p (t) = C q (t) = C, and ρ = 2 µs/s = Worst case: C p (t+1s) = C C q (t+1s) = C

3 Synchronous Systems Bounded communication times Kind of global clock C p (t) C q (t) < ε p and q identify processors 3

4 Clock Drifts Given t2, t1, with t2 = t1 + Maximum drift between p and q at t2, when: C p (t2) = C p (t1) + (1+ρ).(t2-t1) C q (t2) = C q (t1) + (1-ρ).(t2-t1) At t2, difference between p and q clock values C p (t2) - C q (t2) = 2.ρ. 4

5 Synchronization interval Clocks not synchronized when: C p (t2) - C q (t2) = 2.ρ. > ε Before time units expired, clocks must be synchronized Thus: 2.ρ. < ε Given that ε = 50 µs, ρ given by manufacturer, can be calculated 5

6 Clock Synchronization Three types of clock implementations: 1. Central clock: special purpose connection 2. Centrally controlled clock: local clocks with central reference clock 3. Distributed clocks: local clocks agree In all cases, synchronization is never perfect 6

7 Central clock broadcast C q (t2) q Time C p (t1) Fixed transmission delay: δ Set C q (t2) equal to C p (t1) + δ t1 δ t2 P What is C p (t2) C q (t2)? 7

8 Central clock broadcast (2) What is C p (t2) C q (t2)? C p (t2) C q (t2) = C p (t2) C p (t1) + C p (t1) - C q (t2) = C p (t2) C p (t1) + C p (t1) (C p (t1) + δ) = C p (t2) C p (t1) - δ Use: δ.(1- ρ) < C p (t2) C p (t1) < δ.(1+ ρ) δ.(1- ρ) - δ < C p (t2) C p (t1) - δ < δ.(1+ ρ) - δ - δ.ρ < C p (t2) C q (t2) < δ.ρ 8

9 Central clock broadcast (3) p q1 q2 q2 - δ.ρ < C p (t) C qx (t) < δ.ρ -2.δ.ρ < C q1 (t) C q2 (t) < 2.δ.ρ 9

10 q Central clock request C q (t) C q (t4) a b p d d time t1 t2 t t3 t4 C p (t1) C p (t2) C p (t3) C p (t4) t2-t1 = t4-t3 = d is minimum transmission time 10

11 Central clock request (2) Given in p is: C p (t1), C p (t4) and C q (t) What is C p (t4) - C q (t4) First calculate C q (t4) based on C q (t) (t4-t)(1- ρ) < C q (t4) C q (t) < (t4-t)(1+ ρ) { t4 t = d + b} (d+b)(1- ρ) < C q (t4) C q (t) < (d+b)(1+ ρ) { 0 <= b <= t4-t1-2d } d.(1- ρ) < C q (t4) C q (t) < (t4-t1-d)(1+ ρ) {(t4-t1)(1- ρ) < C p (t4) C p (t1) } {(t4-t1)< (C p (t4) C p (t1))/(1- ρ) } 11

12 Central clock request (3) d.(1- ρ) < C q (t4) C q (t) < (t4-t1-d)(1+ ρ) {(t4-t1)< (C p (t4) C p (t1))/(1- ρ) } d.(1- ρ) < C q (t4) C q (t) < (C p (t4) C p (t1)).(1+ ρ)/(1- ρ) -d.(1+ ρ) {substitute: 2K = (C p (t4) C p (t1)).(1+ ρ)/(1- ρ) } d.(1- ρ) < C q (t4) C q (t) < 2K - d.(1+ ρ) 12

13 Central clock request (4) Take C p (t4) = C q (t) + K ρd C q (t4) - C p (t4) = C q (t4) - C q (t) + C q (t) - C p (t4) = = -K + ρ d + C q (t4) - C q (t) {d.(1- ρ) < C q (t4) C q (t) < 2K - d.(1+ ρ)} -K - d < C q (t4) - C p (t4) < K + d 13

14 Probabilistic clock synchronization Transmission time has a given distribution Send several requests to server. Use value obtained with shortest communication time to synchronize clocks 14

15 Distributed clock synchronization Failure of central clock results in failure of clock synchronization High reliability requirement and a well defined clock failure probability leads to distributed clock synchronization protocol 15

16 Distributed clock synchronization (2) Synchronized clock c p (t) is given by: c p (t) = C p (t) + FIX p Where: C p (t) is clock function FIX p is repetitively calculated constant FIX p calculation is based on convergence function CF(c p (t), c 1 (t) c 2 (t).. c N (t) ) 16

17 Distributed clock synchronization (3) Clock synchronization algorithm FIX p := 0 WHILE TRUE DO await next synchronization collect c 1 (t) c 2 (t).. c N (t) FIX p := CF(c p (t), c 1 (t),c 2 (t).. c N (t)) - C p (t) OD 17

18 Distributed clock synchronization (3) Assume that m out of N processors can fail Egocentric Average CF EA (t p, t 1, t 2.. t N ) = 1/N Σ i=1.n x i Where: t i is value obtained from processor i by processor p x i = t i if t p t i < ε x i = t p otherwise 18

19 Distributed clock synchronization (4) Calculate largest difference after synchronization between correct processors p and q - Faulty processor, f, can send different clock values to p and q. - Assume t q > t p Worst behavior On processor p: t f =t p ε On processor p: t f = t q + ε 19

20 Distributed clock synchronization (5) Calculate T p and T q, values after synchronization T p = 1/N( Σ f t f + Σ i t i ) On processor p: Σ f t f = m(t p ε) On processor q: Σ f t f = m(t q + ε) Assume Σ i t i is same on both p and q T q T p =1/N( m(t q + ε) - m(t p ε))= m/n(t q -t p + 2ε) {t q -t p < ε} T q T p < 3mε/N required: m < N/3 20