Outline

1. Outline • Theoretical Foundations • Fundamental limitations of distributed systems • Logical clocks COP5611

2. Lamport’s Logical Clocks – review • Definitions • Happened before relation • Happened before relation () captures the causal dependencies between events • It is defined as follows • a  b, if a and b are events in the same process and a occurred before b. • a  b, if a is the event of sending a message m in a process and b is the event of receipt of the same message m by another process • If a  b and b  c, then a  c, i.e., “” is transitive COP5611

3. Lamport’s Logical Clocks – review • Definitions – continued • Causally related events • Event a causally affects event b if a  b • Concurrent events • Two distinct events a and b are said to be concurrent (denoted by a || b) if a  b and b  a • For any two events, either a  b, b  a, or a || b COP5611

4. Lamport’s Logical Clocks – review • Logical clocks • There is a clock at each process Pi in the system • Which is a function that assigns a number to any event a, called the timestamp of event a at Pi • The numbers assigned by the system of the clocks have no relation to physical time • The logical clocks take monotonically increasing values and can be implemented as counters COP5611

5. Lamport’s Logical Clocks – cont. • Conditions satisfied by the system of clocks • For any two events, if a  b, then C(a) < C(b) • [C1] For any two events a and b in a process Pi, if a occurs before b, then Ci(a) < Ci(b) • [C2] If a is the event of sending a message m in process Pi and b is the event of receiving the same message m at process Pj, then Ci(a) < Cj(b) COP5611

6. Lamport’s Logical Clocks – cont. • Implementation rules • [IR1] Clock Ci is incremented between any two successive events in process Pi Ci := Ci + d ( d > 0) • [IR2] If event a is the sending of message m by process Pi, then message m is assigned a timestamp tm = Ci(a). On receiving the same message m by process Pj, Cj is set to Cj := max(Cj, tm + d) COP5611

7. An Example COP5611

8. Total Ordering Using Lamport’s Clocks • If a is any event at process Pi and b is any event at process Pj, then a => b if and only if either • Where is any arbitrary relation that totally orders the processes to break ties COP5611

9. Example: Totally-Ordered Multicasting COP5611

10. A Limitation of Lamport’s Clocks • In Lamport’s system of logical clocks • If a  b, then C(a) < C(b) • The reverse if not necessarily true if the events have occurred on different processes COP5611

11. A Limitation of Lamport’s Clocks COP5611

12. Vector Clocks • Implementation rules • [IR1] Clock Ci is incremented between any two successive events in process Pi Ci[i] := Ci[i] + d ( d > 0) • [IR2] If event a is the sending of message m by process Pi, then message m is assigned a timestamp tm = Ci(a). On receiving the same message m by process Pj, Cj is set to Cj[k] := max(Cj[k], tm[k]) COP5611

13. Vector Clocks – cont. COP5611

14. Vector Clocks – cont. COP5611

15. Vector Clocks – cont. • Assertion • At any instant, • Events a and b are casually related if ta < tb or tb < ta. Otherwise, these events are concurrent • In a system of vector clocks, COP5611

16. Causal Ordering of Messages • The causal ordering of messages try to maintain the same causal relationship that holds among “message send” events with the corresponding “message receive” events • In other words, if Send(M1) -> Send(M2), then Receive(M1) -> Receive(M2) • This is different from causal ordering of events COP5611

17. Causal Ordering of Messages – cont. COP5611

18. Causal Ordering of Messages – cont. • The basic idea • It is very simple • Deliver a message only when no causality constraints are violated • Otherwise, the message is not delivered immediately but is buffered until all the preceding messages are delivered COP5611

19. Birman-Schiper-Stephenson Protocol COP5611

20. Schiper-Eggli-Sando Protocol COP5611

21. Schiper-Eggli-Sando Protocol – cont. COP5611

22. Schiper-Eggli-Sando Protocol – cont. COP5611