1. Ordering of Events in Distributed Systems UNIVERSITY of WISCONSIN-MADISON Computer Sciences Department CS 739 Distributed Systems Andrea C. Arpaci-Dusseau Two papers: Time, Clocks, and the Ordering of Events in a Distributed System, Lamport, 1978 Distributed Snapshots: Determining Global States of Distributed Systems, Chandy and Lamport, 1985

2. Motivation: Time, Clocks, Ordering To develop distributed algorithms, want all participants see messages in same order (if want same decisions!) How can distributed nodes agree on order of messages? Process A Process B Naïve: Each process believes sent message first

3. Motivation: Time, Clocks, Ordering When does an event precede (“happen before”) another in a distributed system? Sometimes impossible to tell; sometimes it doesn’t matter –If event A occurs on machine A, and event B occurs on machine B, but there is no communication between A and B, then did event A or event B happen first??? How can a process identify which events happened before others? Logical clocks

4. Terminology Distributed system: A collection of distinct processes which are spatially separated and which communicate with one another by exchanging messages How does this differ from our previous definitions? Process: A sequence of events (instructions, sending messages, receiving messages) The events within a process have a total ordering

5. Partial Ordering Happened before: -> Rules for ordering events a and b 1) if a and b are events in same process and a comes before b, then a->b 2) if a is the sending of a message by a process and b is receiving that message, then a->b 3) if a->b and b->c then a->c a->b: It is possible for a to causally affect b Concurrent: ‡> if a ‡> b and b ‡> a, then do not know ordering of a and b It is not possible for a to causally affect b

6. Space-Time Diagram Time p1 p2 p3 p4 q1 q2 q3 q4 q5 q6 q7 r1 r2 r4 r3 What is the relationship between (q3,p3)? (p1,q3)? (p2,q3)? (q3,r4)? (r1,q6)? P QR

7. Logical Clocks Abstract view: Logical clock is a way to assign a number to an event to express ordering No relation between logical clock and physical time Clock Ci for process Pi is a function that assigns a number Ci(a) to any event a in Pi Clock condition: For any events a, b: if a->b, then C(a) < C(b) Converse condition does not hold Can’t say concurrent events have same logical time If C(a) b

8. Implementation of Logical Clocks C1. If a & b are in Pi & a before b, then Ci(a) < Ci(b) IR1. (Implementation Rule) Each process Pi increments Ci between any two successive events C2. If a is sent by Pi and b is received by Pj, then Ci(a) < Cj(b) IR2. (a) If event a is the sending of message m by process Pi, then m contains a timestamp Tm=Ci(a) (b) Upon receiving m, process Pj sets Cj greater than or equal to its presents value and greater than Tm.

9. Logical Clocks Example p1 p2 p3 p4 q1 q2 q3 q4 q5 q6 q7 r1 r2 r4 r3 What logical clock values are possible? Assume initial C(p1)=5, C(q1)=50, C(r1)=2

10. Logical Clocks Example p1 p2 p3 p4 q1 q2 q3 q4 q5 q6 q7 r1 r2 r4 r3 What logical clock values are possible? Assume initial C(p1)=5, C(q1)=50, C(r1)=2 5250 51 52 6 53 54 55 56 3 55 56 57 53 56

11. Total Ordering Use logical clocks to obtain total ordering across all processes and events a => b if and only if: 1) Ci(a) < Cj(b) OR 2) Ci(a) = Cj(b) and Pi < Pj (i.e., use process ids to break ties) Partial ordering is unique, but total ordering is not! Concurrent operations can go in any order Total ordering depends upon implementation of each Ci() Total ordering depends upon tie breaking rules

12. Distributed State Machines Each process runs same distributed algorithm Relies upon total ordering of requests Agreed upon by all participants Can be used to ensure all see events (inputs) in same order and therefore make same decisions Idea: All requests are time-stamped, responses (acks) are time-stamped too Send time-stamped request to all processes Handle next request in total order –To know next request, must have received greater timestamp from all possible participants –Problems? Example: Mutual exclusion

13. Mutual Exclusion Example A B CD 1 10 20 30 Request queue: Scenario: A and C want resource A and C each send request before see other’s (concurrent requests) C sends request out earlier in “physical time” How will all nodes agree who should get resource?

14. Mutual Exclusion Example A B CD 1 10 20 30 21 22 31 2 2 2 23 32 22 Request queue: A - 2, C - 21

15. Physical Clocks Motivation: Can observe anomalous behavior if other communication channels exist between processes Useful to have physical clock with meaning in physical world Synchronize independent physical clocks, each running at slightly different rates (skew) Implementation Idea: Send timestamp with each message Receiver may update clock to timestamp+minimal network delay –Clock must always increase Lots of work in this area

16. Conclusions Distributed, replicated state machines useful for tolerating faults Need to construct total ordering of events to obtain same results everywhere Logical clocks very simple to implement Will see logical clocks used to update replicas

17. Distributed Snapshots Goal Want to record global state of distributed system (i.e., state of each process, state of each communication channel) Useful so can observe system properties –Computation terminated? –System deadlocked? –Number of tokens? Complication: Distributed system has no shared state nor shared clock Cannot record global state simultaneously everywhere Distributed snapshot: Record local state at different times and combine into meaningful picture Obtain cut in logical time, remain consistent by preserving logical ordering (if not ordering in physical time)

18. System Model Distributed system: Finite set of processes and channels; described by graph Processes Set of states, initial state, set of events Channels FIFO, error-free, infinite buffers, arbitrary but finite delay State: Sequence of messages sent but not yet received

19. Distributed Snapshot Algorithm Goal: Record local state (each process plus adjoining channels) that produces a “meaningful” global system state Idea: After local snapshot, send marker along channels Receiver records messages in channel before marker Initial: Some process decides to initiate snapshot (performed periodically)

20. Intuition with Logical Time S S1S1 S2S2 S3 Which snapshots are concurrent? How to reconcile S2 and S? How to reconcile S1 and S? How to reconcile S3 and S? m1m1 m2 B A

21. Marker Rules Marker-sending rule for p: Send marker along each channel (after recording state of p) before sending more messages Marking-receiving rule for q on channel c: if q has not recorded state yet: –record state of q –record state of c as empty if q has recorded state already: –record state of c as the msg sequence that arrived since it recorded its state Termination When state recorded of all processes and all channels Must have algorithm to collect and assemble information too

22. Banking Example Stable property? p1: $10 p2: $20p3: $30 $1 $3 $2 $5 $4

23. Banking Example p1: $10 p2: $20p3: $30 $1 $3 $2 $5 $4 p2 state: $20+1-3 = 18, empty channels

24. Banking Example p1: $10 p2: $20p3: $30 $1 $3 $2 $5 $4 p1 state: $10-1-3=6, empty channels p3 state: $30-2-5-4+3=22, empty channels Total money? 18+6+22 = $46

25. Banking Example p1: $10 p2: $20p3: $30 $1 $3 $2 $5 $4

26. Banking Example p1: $10 p2: $20p3: $30 $1 $3 $2 $5 $4 c: p2 from p1: nothing c: p2 f p3: 4 + 2 c: p3 f p1: 3 c: p1 f p3: 5 p1: 6, p2: 18, p3: 22

27. Banking Example p1: $10 p2: $20p3: $30 $1 $3 $2 $5 $4 c p2 from p3: Never $2 and $4 simultaneously

28. Properties of Recorded Global State Recorded global state, S*, may not have occurred If it bothers you that S* doesn’t actually exist... Given a permutation of the actual sequence of events S* is reachable from Sinit Sfinal is reachable from S* Stable properties will hold in S* as well How to permute sequence of events? Goal: Want snapshot to correspond to single logical cut Slide events so snapshots taken at same “logical time” Some events across processes will switch order with others –Specifically, postrecorded events and prerecorded events –prerecorded events occurred before state of p was recorded –Can’t tell ordering of concurrent pre and post events

29. Banking Example p1: $10 p2: $20p3: $30 $1 $3 $2 $5 $4 Example: Need to swap sending $4 from p3 and receiving $2 Still logically consistent; could not observe difference pre post

30. Conclusions Distributed snapshots: Allow one to reconstruct valid picture of system from snapshots taken at different points in time Record individual process states plus channels Snapshots useful for determining if stable properties hold or not Recorded state S* may not correspond to “reality”, but if stable properties hold in beginning and end states, then hold in S* too