Distributed Systems: Time & Synchronization Lecture Notes, Study notes of Computer Science

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Computer Science 425

Distributed Systems

Lecture 4

Time & Synchronization

Reading: 10.1 10.

♣ A DS consists of a number of processes.

♣ Each process has a state (values of variables).

♣ Each process takes actions to change its state,

or to communicate (send, receive).

♣ An event is the occurrence of an action.

♣ Events within a process can be ordered by the

time of occurrence.

♣ In DS we also need to know the time order of events

on different processors & between different processes.

Processes and Events

Synchronizing Physical Clocks

• Ci(t):^ the reading of the software clock^ i^ when the real time is^ t.

• External synchronization: For a synchronization bound D>0 , and

for source S of UTC time,

for i=1,2,...,N and for all real times t in I.

Clocks Ci are accurate to within the bound D.

• Internal synchronization: For a synchronization bound D>0 ,

for i, j=1,2,...,N and for all real times t in I.

Clock Ci agree within the bound D.

∣S  t − Ci t ∣D ,

∣Ci  t − C j  t ∣D

♣ (^) Uses a time server to synchronize clocks

♣ (^) Time server keeps the reference time

♣ (^) Clients ask the time server for time & adjust their

clock, based on the response

For links with symmetrical latency:

Cristian’s Algorithm

adjusted-local-time = server-timestamp + (RTT / 2) or = server- timestamp + (RTT – server-latency) /2 local-clock-error = adjusted- local-time – local-time

RTT = response-received-time – request-sent-time

♣ (^) For positive clock errors, clock is advanced forward

accordingly. For negative clock errors, the clock

should be slowed down, not immediately adjusted.

♣For unusually long RTTs, repeat the time request

♣ (^) For non uniform RTTs, use adaptive, weighted average

Cristian’s Algorithm (2)

avg-clock-error 0 = local-clock-error

avg-clock-errorn = (Wn * local-clock-error) +

(1 – Wn) * local-clock-errorn-

♣ (^) Uses a designated server to synchronize

♣The designated server pools or broadcasts

to all machines for their time, adjusts times received for

RTT & latency, averages times, and tells each machine

how to adjust.

♣In some systems multiple time servers are used.

♣Avg. time is more accurate, but still drifts

Berkeley Algorithm

Messages Exchanged Between a Pair of NTP

Peers

Ti

Ti 2 Ti 1

Ti 3

Server B

Server A

Time

m m'

Time

Each message bears timestamps of recent message events: the local time when the previous NTP message was sent and received, and the local time when the current message was transmitted.

Theoretical Base for NTP

Ti

Ti 2 Ti 1

Ti 3

Server B

Server A

Time

m m'

Time

- oi : estimate of the actual offset between the two clocks - o : true offset of the clock at B relative to that at A - t and t’: actual transmission times for m and m’ - di : total transmission times for^ m and m’ ; d=t+t’

T i − 2 =T i− 3 t o

T i =T i− 1 t '− o

This leads to

di =t t ' =T i − 2 − T i− 3 T i− T i− 1

o=oi  t '− t /2, where

oi = T i − 2 − T i − 3 T i− 1 − T i / 2.

It can also be shown that

oi− di / 2 ≤o≤oi di / 2.

Events Occurring at Three Processes

p 1

p 2

p 3

a b

c d

e f

m (^1)

m (^2)

Physical time

Lamport Timestamps

a (^) b

c d

e f

m (^1)

m (^2)

1 2

3 4

1 5

p 1

p 2

p 3

Physical time

Vector Logical Clocks

 With Lamport Logical Time

e precedes f ⇒ timestamp(e) < timestamp (f), but timestamp(e) < timestamp (f) ~ ⇒ e precedes f

 Vector Logical time guarantees this:

 (^) All hosts use a vector of counters (logical clocks), ith^ element is the clock value for host i, initially all zero.  (^) Each host i, increments the ith^ element of its vector upon an event, and assigns the vector to the event.  (^) A send(message) event carries its vector timestamp (counter vector)  (^) For a receive(message) event,

Max(Vreceiver[j] , Vmessag[j]), if j is not self Vreceiver[j] = Vreceiver[j] + 1 otherwise

Vector Timestamps

a (^) b

c d

e f

m (^1)

m (^2)

(1,0,0) (2,0,0)

(2,1,0) (2,2,0)

(0,0,1) (2,2,2)

p 1

p 2

p 3

Physical time

Comparing Vector Timestamps

 (^) VT 1 = VT 2 ,

iff VT 1 [i] = VT 2 [i], i = 1, … , n

 VT 1 < VT 2 ,

iff VT 1 [i] < VT 2 [i], i = 1, … , n

 (^) VT 1 < VT 2 ,

iff VT 1 < VT 2 &

∃ j (1 < j < n & VT 1 [j] < VT 2 [j])

 VT 1 is concurrent with VT 2

iff not (VT 1 < VT 2 OR VT 2 < VT 1 )