1. ITEC452 Distributed Computing Lecture 8 Distributed Snapshot
Hwajung Lee
ITEC452 Distributed Computing Lecture 8 Distributed Snapshot

2. Distributed snapshot
-- How many messages are in transit on the internet?
-- What is the global state of a distributed system of N processes?
How do we compute these?

3. One-dollar bank
Let a $1 coin circulate in a network of a million banks. How can someone count the total $ in circulation? If not counted “properly,” then one may think the total $ in circulation to be one million.

4. Importance of snapshots
Major uses in - deadlock detection - termination detection - rollback recovery - global predicate computation

5. Consistent cut If this is not true, then the cut is inconsistent
A cut is a set of events.
(a  consistent cut C)  (b happened before a)  b  C
If this is not true, then the cut is inconsistent a b c g d P1 m e f P2 P3 k i h j
Cut 1
Cut 2
(Consistent)
(Not consistent)

6. Consistent snapshot
The set of states immediately following a consistent cut forms a consistent snapshot of a distributed system.
A snapshot that is of practical interest is the most recent one. Let C1 and C2 be two consistent cuts and C1  C2. Then C2 is more recent than C1.

7. Consistent snapshot
How to record a consistent snapshot? Note that 1. The recording must be non-invasive 2. Recording must be done on-the-fly. You cannot stop the system.

8. Chandy-Lamport Algorithm
Works on a
(1) strongly connected graph
(2) each channel is FIFO.
A process called the initiator initiates the distributed snapshot algorithm by sending out a marker ( )

9. White and red processes
Initially every process is white. When a process receives a marker, it turns red if it has not already done so. Every action by a process, and every message sent by a process gets the color of that process.

10. Two steps
Step 1. In one atomic action, the initiator (a) turns red (b) records its own state (c) sends a marker along all outgoing channels
Step 2. Every other process, upon receiving a marker for the first time (and before doing anything else) (a) turns red (b) records its own state (c) sends markers along all outgoing channels
The algorithm terminates when (1) every process turns red, and (2) every process has received a marker through each incoming channel.

11. Why does it work?
Lemma 1. No red message is received by a white action.

12. Why does it work? SSS All white All red
Easy conceptualization of the snapshot state
Theorem. The Chandy-Lamport algorithm records a consistent global state. The global state recorded by Chandy-Lamport algorithm is equivalent to the ideal snapshot state SSS.
Hint. A pair of actions (a, b) can be scheduled in any order, if there is no causal order between them, so (a, b) is equivalent to (b, a)
SSS: snapshot state (page 128)

13. Why does it work? Let an observer see the following actions:
w[i] w[k] r[k] w[j] r[i] w[l] r[j] r[l] … 
w[i] w[k] w[j] r[k] r[i] w[l] r[j] r[l] … [Lemma 1]
w[i] w[k] w[j] r[k] w[l] r[i] r[j] r[l] … [Lemma 1]
w[i] w[k] w[j] w[l] r[k] r[i] r[j] r[l] … [done!]
Recorded state
Call it “break,” when a red action precedes a white action in a given run.
The idea view of the schedule has zero breaks. But in general,
The number of breaks in the recorded sequence of actions can be a positive number.
A swap reduces the number of breaks by 1.

14. Example 1. Count the tokens
Let us verify that Chandy-Lamport snapshot algorithm correctly counts the tokens circulating in the system
token C
token
no token A
no token
token
no token B A
no token
token
no token C B
Are these consistent cuts?
How to account for the channel states?
Use sent and received variables for each process.

15. Another example of distributed snapshot: Communicating State Machines

16. Something unusual
Let machine i start Chandy-lamport snapshot before it has sent M along ch1. Also, let machine j receive the marker after it sends out M’ along ch2. Observe that the snapshot state is down  up M’ Doesn’t this appear strange? This state was never reached during the computation!

17. Understanding snapshot

18. Understanding snapshot
The observed state is a feasible state that is reachable
from the initial configuration. It may not actually be visited
during a specific execution.
The final state of the original computation is always
reachable from the observed state.

19. Discussions
What good is a snapshot if that state has never been visited by the system?
- It is relevant for the detection of stable predicates.
- Useful for checkpointing.

20. Discussions What if the channels are not FIFO?
Study how Lai-Yang algorithm works. It does not use any marker
LY1. The initiator records its own state. When it needs to send a message m to another process, it sends a message (m, red).
LY2. When a process receives a message (m, red), it records its state if it has not already done so, and then accepts the message m.
Question 1. Why will it work?
Question 1 Are there any limitations of this approach?