Post on 10-Feb-2016
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Token-passing Algorithms for mutual exclusion
Suzuki-Kasami algorithmThe Main idea
Completely connected network of processes
There is one token in the network. The holder of the token has the permission to enter CS.
Any other process trying to enter CS must acquire that token. Thus the token will move from one process to another based on demand.
I want to enter CSI want to enter CS
Suzuki-Kasami Algorithm
Process i broadcasts (i, num)
Each process maintains-an array req: req[j] denotes the sequence no of the latest request from process j(Some requests will be stale soon)
Additionally, the holder of the token maintains-an array last: last[j] denotes the sequence number of the latest visit to CS from for process j.- a queue Q of waiting processes req: array[0..n-1] of integer
last: array [0..n-1] of integer
Sequence number of the request
req
req
req
req
reqlast
queue Q
Suzuki-Kasami AlgorithmWhen a process i receives a request (k, num) from process k, it sets req[k] to max(req[k], num). The holder of the token
--Completes its CS--Sets last[i]:= its own num--Updates Q by retaining each process k only if1+ last[k] = req[k] (This guarantees the freshness of the request)--Sends the token to the head of Q, along withthe array last and the tail of Q
In fact, token (Q, last)
Req: array[0..n-1] of integer
Last: Array [0..n-1] of integer
Suzuki-Kasami’s algorithm{Program of process j}Initially, i: req[i] = last[i] = 0* Entry protocol *req[j] := req[j] + 1Send (j, req[j]) to allWait until token (Q, last) arrivesCritical Section* Exit protocol *last[j] := req[j]k ≠ j: k Q req[k] = last[k] + 1 append k to Q;if Q is not empty send (tail-of-Q, last) to head-of-Q fi
* Upon receiving a request (k, num) *req[k] := max(req[k], num)
Example
0
2
1
34
req=[1,0,0,0,0]last=[0,0,0,0,0]
req=[1,0,0,0,0]
req=[1,0,0,0,0]
req=[1,0,0,0,0]
req=[1,0,0,0,0]
initial state: process 0 has sent a request to all, and grabbed the token
Example
0
2
1
34
req=[1,1,1,0,0]last=[0,0,0,0,0]
req=[1,1,1,0,0]
req=[1,1,1,0,0]
req=[1,1,1,0,0]
req=[1,1,1,0,0]
1 & 2 send requests to enter CS
Example
0
2
1
34
req=[1,1,1,0,0]last=[1,0,0,0,0]Q=(1,2)
req=[1,1,1,0,0]
req=[1,1,1,0,0]
req=[1,1,1,0,0]
req=[1,1,1,0,0]
0 prepares to exit CS
Example
0
2
1
34
req=[1,1,1,0,0]req=[1,1,1,0,0]last=[1,0,0,0,0]Q=(2)
req=[1,1,1,0,0]
req=[1,1,1,0,0]
req=[1,1,1,0,0]
0 passes token (Q and last) to 1
Example
0
2
1
34
req=[2,1,1,1,0]
req=[2,1,1,1,0]last=[1,0,0,0,0]Q=(2,0,3)
req=[2,1,1,1,0]
req=[2,1,1,1,0]
req=[2,1,1,1,0]
0 and 3 send requests
Example
0
2
1
34
req=[2,1,1,1,0]req=[2,1,1,1,0]
req=[2,1,1,1,0]last=[1,1,0,0,0]Q=(0,3)
req=[2,1,1,1,0]
req=[2,1,1,1,0]
1 sends token to 2
Raymond’s tree-based algorithm
123
45
6 7
1,4 4,7
1
1
4
1,4,7 want to enter their CS
Raymond’s Algorithm
123
45
6 71,4 4,7
1
4
2 sends the token to 6
Raymond’s Algorithm
123
45
6 7
4
4,7
4
The message complexity is O(diameter) of the tree. Extensive empirical measurements show that the average diameter of randomly chosen trees of size n is O(log n). Therefore, the authors claim that the average message complexity is O(log n)
6 forwards the token to 1
4These two directed edges will
reverse their direction
Distributed Snapshot
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?
Think about these
-- 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?
One-dollar bank
0
1
2
(0,1)
(1,2)(2,0)
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.
Importance of snapshots
Major uses in
- deadlock detection
- termination detection
- rollback recovery
- global predicate
computation
Consistent cut
(a consistent cut C) (b happened before a) b CIf this is not true, then the cut is inconsistent
a b c d g
m e f
k i h jCut 1 Cut 2
A cut is a set of events.
(Not consistent)(Consistent)
P1
P2
P3
time
Consistent snapshot
The set of states immediately following the events (actions) in 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.
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.