The Transport Layerjohanl/educ/2IN20/clocksynchro.pdf · June 2004 Peter van der [email protected]...

June 2004 Peter van der [email protected]/e Computer Science, System Architecture and Networking

1

Real-Time CourseClock synchronization


2

Clocks

Clock has drift rateFor t1 and t2, with t2 > t1(1-ρ)(t2-t1) <= Cp(t2)-Cp(t1) <= (1+ρ)(t2-t1)

Processor p has monotonically increasing clock functionCp(t)

Suppose Cp(t) = Cq(t) = C, and ρ = 2 µs/s = 2.10-6

Worst case:Cp(t+1s) = C+1 + 2.10-6

Cq(t+1s) = C+1 - 2.10-6


3

Synchronous Systems

• Bounded communication times• Kind of global clock

• | Cp(t) – Cq(t) | < ε

• p and q identify processors


4

Clock Drifts

Given t2 , t1, with t2 = t1 + ∆

Maximum drift between p and q at t2, when:Cp(t2) = Cp(t1) + (1+ρ).(t2-t1)

Cq(t2) = Cq(t1) + (1-ρ).(t2-t1)

At t2, difference between p and q clock valuesCp(t2) - Cq(t2) = 2.ρ. ∆


5

Synchronization interval

Clocks not synchronized when:Cp(t2) - Cq(t2) = 2.ρ. ∆ > ε

Before ∆ time units expired, clocks must be synchronizedThus: 2.ρ.∆ < εGiven that ε = 50 µs, ρ given by manufacturer,∆ can be calculated


6

Clock Synchronization

Three types of clock implementations:

1. Central clock: special purpose connection2. Centrally controlled clock: local clocks

with central reference clock3. Distributed clocks: local clocks agree

In all cases, synchronization is never perfect


7

Central clock broadcast

Fixed transmission delay: δSet Cq(t2) equal to Cp(t1) + δ

What is Cp(t2) – Cq(t2) ?

Time

Cp(t1)

Cq(t2)

δt1 t2

q

P


8

Central clock broadcast (2)

What is Cp(t2) – Cq(t2) ?

Use: δ.(1- ρ) < Cp(t2) – Cp(t1) < δ.(1+ ρ)

Cp(t2) – Cq(t2) =Cp(t2) – Cp(t1) + Cp(t1) - Cq(t2) =Cp(t2) – Cp(t1) + Cp(t1) – (Cp(t1) + δ) =Cp(t2) – Cp(t1) - δ

δ.(1- ρ) - δ < Cp(t2) – Cp(t1) - δ < δ.(1+ ρ) - δ- δ.ρ < Cp(t2) – Cq(t2) < δ.ρ


9

Central clock broadcast (3)

p

q1 q2 q2

- δ.ρ < Cp(t) – Cqx(t) < δ.ρ-2.δ.ρ < Cq1(t) – Cq2(t) < 2.δ.ρ


10

Central clock request

p

q

time t1 t2 t t3 t4

a b

d d

Cq(t)

Cp(t1) Cp(t2) Cp(t3) Cp(t4)

t2-t1 = t4-t3 = d is minimum transmission time

Cq(t4)


11

Central clock request (2)

Given in p is: Cp(t1), Cp(t4) and Cq(t)What is Cp(t4) - Cq(t4)

First calculate Cq(t4) based on Cq(t) (t4-t)(1- ρ) < Cq(t4) – Cq(t) < (t4-t)(1+ ρ) { t4 – t = d + b}(d+b)(1- ρ) < Cq(t4) – Cq(t) < (d+b)(1+ ρ) { 0 <= b <= t4-t1-2d }d.(1- ρ) < Cq(t4) – Cq(t) < (t4-t1-d)(1+ ρ) {(t4-t1)(1- ρ) < Cp(t4) – Cp(t1) }{(t4-t1)< (Cp(t4) – Cp(t1))/(1- ρ) }


12


d.(1- ρ) < Cq(t4) – Cq(t) < (t4-t1-d)(1+ ρ) {(t4-t1)< (Cp(t4) – Cp(t1))/(1- ρ) }

d.(1- ρ) < Cq(t4) – Cq(t) < (Cp(t4) – Cp(t1)).(1+ ρ)/(1- ρ) -d.(1+ ρ){substitute: 2K = (Cp(t4) – Cp(t1)).(1+ ρ)/(1- ρ) }

d.(1- ρ) < Cq(t4) – Cq(t) < 2K - d.(1+ ρ)


13


Take Cp(t4) = Cq(t) + K – ρd

Cq(t4) - Cp(t4) = Cq(t4) - Cq(t) + Cq(t) - Cp(t4) == -K + ρ d + Cq(t4) - Cq(t) {d.(1- ρ) < Cq(t4) – Cq(t) < 2K - d.(1+ ρ)}

-K - d < Cq(t4) - Cp(t4) < K + d


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


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


16

Distributed clock synchronization (2)

Synchronized clock cp(t) is given by:cp(t) = Cp(t) + FIXp

Where:Cp(t) is clock functionFIXp is repetitively calculated constant

FIXp calculation is based on convergence function CF(cp(t), c1(t) c2(t) ….. cN(t) )


17


Clock synchronization algorithm

FIXp := 0WHILE TRUE DO

await next synchronizationcollect c1(t) c2(t) ….. cN(t) FIXp := CF(cp(t), c1(t),c2(t) ….. cN(t)) - Cp(t)

OD


18


Assume that m out of N processors can fail

Egocentric AverageCFEA(tp, t1, t2 ….. tN) = 1/N Σi=1.N xiWhere:ti is value obtained from processor i by

processor pxi = ti if |tp – ti| < εxi = tp otherwise


19


Calculate largest difference after synchronization between correct processors p and q- Faulty processor, f, can send different clock

values to p and q.- Assume tq > tp

Worst behavior

On processor p: tf = tp – εOn processor p: tf = tq + ε


20


Calculate Tp and Tq, values after synchronization

Tp = 1/N( Σf tf + Σi ti )On processor p: Σf tf = m(tp – ε)On processor q: Σf tf = m(tq + ε)Assume Σi ti is same on both p and q

Tq – Tp =1/N( m(tq + ε) - m(tp – ε))=m/N(tq - tp + 2ε)

{ tq - tp < ε}Tq – Tp < 3mε/N required: m < N/3

The Transport Layerjohanl/educ/2IN20/clocksynchro.pdf · June 2004 Peter van der [email protected]...

Documents

Transcript of The Transport Layerjohanl/educ/2IN20/clocksynchro.pdf · June 2004 Peter van der [email protected]...