Hwajung Lee

-- 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?

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.

Major uses in - deadlock detection - termination detection - rollback recovery - global predicate computation

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

 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.

 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.  Analyze why certain cuts in the one-dollar bank are inconsistent.

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.

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 ( )

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.

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.

Lemma 1. No red message is received by a white action.

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 Easy conceptualization of the snapshot state All whiteAll red

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.