Time ( and Global State )

1. 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.

5. 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.

6. 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.

7. 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.

8. 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.

9. m r m t p Time server,S Synchronizing physical clocks – Cristian’s algorithm External synchronization 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.

10. Tserver Cristian’s algorithm Compensate for delays • Note times: • request sent: T0 • reply received: T1 • Assume network delays are symmetric server request reply client time T0 T1

11. Tserver server request reply client time T0 T1 Cristian’s algorithm Client sets time to: = estimated overhead in each direction

12. Error bounds If minimum message transit time (Tmin) is known: Place bounds on accuracy of result

13. range = T1-T0-2Tmin Tmin Tmin Earliest time message arrives Latest time message leaves Error bounds Tserver server request reply client time T0 T1 accuracy of result =

14. 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 generated 400 msec ago • Set time to Tserver+ elapsed time 5:09:25.300 + 400 = 5:09.25.700

15. 200 200 Cristian’s algorithm: example If best-case message time=200 msec T0 = 5:08:15.100 T1 = 5:08:15.900 Ts = 5:09:25.300 Tmin = 200msec Tserver server request reply client time T0 T1 800 Error =

16. 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

17. 3:25 2:50 9:10 3:00 Berkeley Algorithm: example 3:25 9:10 2:50 1. Request timestamps from all slaves

18. 3:25 2:50 9:10 3:00 Berkeley Algorithm: example 3:25 9:10 2:50 2. Compute fault-tolerant average:

19. 3:25 2:50 9:10 3:00 Berkeley Algorithm: example -0:20 -6:05 +0:15 3. Send offset to each client

20. 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.

21. 1 2 2 3 3 3 Note: Arrows denote synchronization control, numbers denote strata. Synchronizing physical clocks – NTP architecture - 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.).

22. Server B T T i -2 i-1 Time m m' Time Server A T T i - 3 i Synchronizing physical clocks – NTP peers message exchange 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.

23. SNTP Roundtrip delay: d = (T4-T1) - (T2-T3) T2 T3 server request reply client time T1 T4 Time offset:

24. SNTP example Offset = ((800 - 1100) + (850 - 1200))/2 =((-300) + (-350))/2 = -650/2 = -325 Set time to T4 + t= 1200 - 325 = 875 T2=800 T3=850 server request reply time client T1=1100 T4=1200 Time offset:

25. Cristian’s algorithm Offset = (1200 - 1100)/2 = 50 Set time to Ts + offset= 825 + 50 = 875 T2=800 T3=850 server request reply Ts=825 time client T1=1100 T4=1200

26. 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.

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

28. 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’).

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

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

31. Summary • Time • Synchronization 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.