Time And Global States

1. Time And Global States By Jeevan Varma Anga

2. Layout • Significance of Time. • Definitions • Some Algorithms

3. Significance • Consistent Electronic commerce transactions. • To understand how distributed executions unfold. • To determine global state.

4. Events • An Event is an occurrence of a single action that a process carries out as it executes – a communication action or a state-transformation action. History(pi)=<ei0,ei1,ei2,ei3…..>

5. Clocks • Electronic Devices that count oscillations occurring in a crystal at a definite frequency, and that typically divide this count and store the result in a counter register. • Clock Skew. • Clock drift.

6. Synchronizing Physical Clocks • External Synchronization • Internal Synchronization

7. Synchronization in a synchronous system (Internal Sync.): • One process sends the time t on its local clock to the other in a message m. • The receiving process could set its clock to the time t+TRANS where TRANS is the time taken to transmit m between them. • TRANS = min + x • U(1-1/n) where u= (min+max)/2

8. Cristian’s method(External Sync.) • Uses a time server. mr mt P Time Server, S • P sets its time to t+Tround/2 • Assumes that the elapsed time is split equally before and after S sent placed t in mt

9. Berkeley Algorithm (Internal Sync.) • A coordinator acts as master while others act as slaves. • Master polls slaves and receives their local clock times. • Master calculates average. • Master sends the slaves + or – value. • Faulty clocks are eliminated by identifying significant adverse values. • When a master fails, new master is elected.

10. Network Time Protocol(NTP) • NTP defines an architecture for a time service and a protocol to distribute time information over the internet. • Features: • To provide a service enabling clients across the Internet to be synchronized accurately to UTC. • To provide a reliable service that can survive lengthy losses of connectivity. • To enable clients to resynchronize sufficiently frequently to offset the rates of drift found in most computers. • To provide protection against interference with the time service, whether malicious or accidental.

11. 1 Strata Level 1 2 2 • For each pair of messages sent between two servers, the NTP calculates an offset oi, which is an estimate of the actual offset between the two clocks, and a delay di, which is the total transmission time for the two messages. Strata Level 2 3 3 3 3 Strata Level 3 di=t+t’=Ti-2 – Ti-3 + Ti – Ti-1 o=oi+(t’-t)/2 oi=(Ti-2 – Ti-3 + Ti – Ti-1)/2

12. Logical Time and Logical Clocks • Lamport pointed out the issues of synchronizing clocks perfectly. • Happened-before relation (aka causal ordering or potential causal ordering). • Happened-before relation definition: • HB1: if process pi : e -> ie’, then e->e’ • HB2: For any message m, send(m)-> receive(m) where send(m) is the event of sending the message, and receive(m) is the event of receiving it. • HB3: If e,e’ and e’’ are events such that e->e’ and e’->e’’, then e->e’’

13. Logical Time and Logical Clocks • A Lamport logical clock is a monotonically increasing software counter, whose value need bear no particular relationship to any physical clock. • LC1: Li is incremented before each event is issued at process pi. • LC2: a)When a process pi sends a message m, it piggybacks on m the value t=Li b)On receiving(m,t), a process pj computes Lj:=max(Lj,t) and then applies LC1 before timestamping the event receive(m).

14. Logical Timestamps 1 2 p1 a b m1 3 4 p2 Physical Time c d m2 1 5 p3 e f

15. Vector Timestamps (1,0,0) (2,0,0) p1 a b m1 (2,1,0) (2,2,0) p2 Physical Time c d m2 (0,0,1) (2,2,2) p3 e f

16. Global States • Examples of applicability: Distributed garbage collection, distributed deadlock detection, distributed termination detection and distributed debugging. • Global states and consistent cuts: Collection of histories where history of a process is a sequence of totally ordered events at that process • A cut is consistent if, for each event it contains, it also contains all the events that happened-before that event.

17. Global state predicates, stability, safety, and liveness • Global state predicate: F(State)--->{True,false} • Stability: Once the system enters a state it never leaves it • Predicate: Safety: For an undesirable property: If S0 is the original state, then safety property w.r.t. α is the assertion that α evaluates to false for all states S reachable from S0. • Predicate: Liveness: For a desirable property (e.g. termination), liveness w.r.t. ß is the property that for any linearization L starting in S0, ß evaluates to True for some state SL reachable from S0.

18. The snapshot algorithm of Chandy and Lamport • To determine the global states of a distributed system • Goal: Record a set of process and channel states for a set of processes such that, even though the combination of recorded states may never have occurred at the same time, the recorded global state is consistent. • The algorithm assumes: • neither channels nor processes fail • channels are unidirectional and provide FIFO delivery • the graph of processes and channels is strongly connected • any process may initiate a global snapshot algorithm any time • the processes continue their execution and send and receive normal messages while the snapshot algorithm takes place

19. Snapshot Algorithm Marker receiving rule for process pi On pi’s receipt of a marker message over channel c: if ( pi has not yet recorded its state) it records its process state now; records the state of c as the empty set; turns on recording of messages arriving over other incoming channels; else Pi records the state of c as the set of messages it has received over c since it saved its state. end if Marker sending rule for process pi After pi has recorded its state, for each outgoing channel c: pi sends one marker message over c (before it sends any other message over c).

20. Example

21. Example