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Time (and Global State)

3

Time – basics

We want to know when something happened - Physical and logical clocks.

Algorithms may depend upon clock synchronization.No global notion of time.

4

Time – system model

N processes: Each executes on a single processor. No shared memory. Only communication means is exchange of messages.

pi has state si.An event is the occurrence of a single action, i.e.:

An internal state-transforming action by pi, or a communication action.

e i e’ if e occurs before e’ in pi.

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Time – clocks

Each computer has its own physical clock.The software clock Ci can be used to timestamp any

event at pi.Problems: Clock skew and clock drift.

Network

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Time – Coordinated Universal Time (UTC)

International standard for timekeeping.Based on atomic time.Synchronizes with astronomical time using leap

seconds.UTC signals are synchronized and broadcast

regularly from land-based radio stations and satellites.

Computers with receivers attached can synchronize their clocks with these timing signals.

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Synchronizing physical clocks – basics

External synchronization: For each i, synchronize Ci with an authoritative, external source of time.

Internal synchronization: For each i,j, synchronize Ci and Cj with each other.

Other issues: Correctness, monotonicity, faulty clocks, crash failures, arbitrary failures.

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Synchronizing physical clocks – in a synchronous system

Internal synchronization.Sender sends local time t to receiver.Receiver ideally sets time to: t + T(trans).T(trans) in [min,max].Receiver sets time to: t + (max+min)/2.

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Synchronizing physical clocks – Cristian’s algorithm

mr

mtp Time server,S

p records total round-trip time T(round);p sets its time to t+T(round)/2;If minimal transmission time is known, accuracy can be calculated.Problem: single point of failure.

External synchronization

Cristian’s algorithm

Compensate for delays Note times:

request sent: T0

reply received: T1

Assume network delays are symmetric

server

clienttime

request reply

T0 T1

Tserver

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Cristian’s algorithm

Client sets time to:server

clienttime

request reply

T0 T1

Tserver

= estimated overhead in each direction

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Error bounds

If minimum message transit time (Tmin) is known:

Place bounds on accuracy of result

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Error bounds

server

clienttime

request reply

T0 T1

Tserver

Tmin Tmin

Earliest time message arrives

Latest time message leaves

range = T1-T0-2Tmin

accuracy of result =

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Cristian’s algorithm: example

Send request at 5:08:15.100 (T0)

Receive response at 5:08:15.900 (T1) Response contains 5:09:25.300 (Tserver)

Elapsed time is T1 -T0

5:08:15.900 - 5:08:15.100 = 800 msec

Best guess: timestamp was generated400 msec ago

Set time to Tserver+ elapsed time

5:09:25.300 + 400 = 5:09.25.70014

Cristian’s algorithm: example

If best-case message time=200 msec

server

clienttime

request reply

T0 T1

Tserver

200 200

800

Error =

T0 = 5:08:15.100T1 = 5:08:15.900Ts = 5:09:25.300Tmin = 200msec

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Synchronizing physical clocks – the Berkeley algorithm

Internal synchronization. A coordinator computer chosen to act as master.Master periodically polls the other computers (the slaves). Slaves send back their clock values to master.Master calculates an average (taking the roundtrip times

into account).Master sends the amount by which each individual slave’s

clock requires adjustment. The algorithm eliminates readings from faulty clocks. Algorithm has provisions for ignoring readings from clocks

whose skew is too great, Compute a fault-tolerant average

Berkeley Algorithm: example

3:25 2:50 9:10

3:00

1. Request timestamps from all slaves

3:252:50

9:10

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Berkeley Algorithm: example

3:25 2:50 9:10

3:00

2. Compute fault-tolerant average:

3:252:50

9:10

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Berkeley Algorithm: example

3:25 2:50 9:10

3:00

3. Send offset to each client

-0:20+0:15

-6:05

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Synchronizing physical clocks – the Network Time Protocol (NTP) aims

Provide a service enabling clients across the Internet to be synchronized accurately to UTC.

Provide a reliable service that can survive lengthy losses of connectivity.

Enable clients to resynchronize sufficiently frequently to offset the rates of drift found in most computers.

Provide protection against interference with the time service, whether malicious or accidental.

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Synchronizing physical clocks – NTP architecture

1

2

3

2

3 3

Note: Arrows denote synchronization control, numbers denote strata.

- A network of servers located across the Internet.

- Primary servers connected directly to time source.

- Secondary servers synchronized with primary servers.

- Servers connected in logical hierarchy, synchronization subnet.

- Three modes of sync.: Multicast, procedure-call, symmetric (H.W.).

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Synchronizing physical clocks – NTP peers message exchange

Ti

Ti-1Ti-2

Ti- 3

Server B

Server A

Time

m m'

Time

T(i-3): Time when previous message sent.T(i-2): Time when previous message was received.T(i-1): Time when this message (just received) was sent.T(i): Time when this message was received.

SNTP

Roundtrip delay:

d = (T4-T1) - (T2-T3)

server

clienttime

request reply

T1

T2

T4

T3

Time offset:

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SNTP example

server

clienttime

request reply

T1=1100

T2=800

T4=1200

T3=850

Time offset:

Offset =

((800 - 1100) + (850 - 1200))/2

=((-300) + (-350))/2

= -650/2 = -325

Set time to T4 + t= 1200 - 325 = 875

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Cristian’s algorithm

server

clienttime

request reply

T1=1100

T2=800

T4=1200

T3=850

Offset = (1200 - 1100)/2 = 50

Set time to Ts + offset= 825 + 50 = 875

Ts=825

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Logical time and logical clocks – happened-before relation (self study)

If two events occurred at the same process pi, then they occurred in the order in which pi observes them (->i).

Whenever a message is sent between processes, the event of sending the message occurred before the event of receiving the message.

Transitive relation.

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Logical time and logical clocks – happened-before example (self study)

p1

p2

p3

a b

c d

e f

m1

m2

Physicaltime

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Logical time and logical clocks – Lamport logical clocks and timestamps (self study)

A Lamport logical clock is a monotonically increasing software counter.

Each process pi keeps its own logical clock Li which is used to apply Lamport timestamps to events.

To capture the happened-before relation ->, processes update their logical clocks and transmit the values of their logical clocks in messages as follows: Before each event at pi: Li := Li+1 When pi sends a message m, it piggybacks t=Li. When pj receives (m,t): Lj := max(Lj,t)+1.

e -> e’ => L(e) < L(e’).

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Logical time and logical clocks – Lamport timestamps example (self study)

a b

c d

e f

m1

m2

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3 4

51

p1

p2

p3

Physical time

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Logical time and logical clocks – Vector timestamps example (self study)

a b

c d

e f

m1

m2

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

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

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

p1

p2

p3

Physical time

Vi[i]: The number of events that pi has timestamped;Vi[j]: The number of events that have occurred at pj that pi has potentially been affected by, j <> i.

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Summary

TimeSynchronization of physical clocks:

In a synchronous system. Cristian’s method. The Berkeley algorithm. The Network Time Protocol (NTP).

Logical time and logical clocks (self study): The happened-before relation. Lamport’s logical clocks and Lamport’s timestamps. Vector timestamps.