We will see mutual exclusion in distributed system: - 1. Singhal’s Heuristics 2. Raymond’s Tree Based also check algorithm in detail

1. Mutual Exclusion in Distributed
Systems
Name : Ajay Kharat
ID : 2019H1030011P
BITS-Pilani

2. Mutual Exclusion Algorithms for
Distributed Systems
•Classification
•Non Token Based
•Lamport’s
•Ricart Agrawala’s
•Maekawa’s
•Token Based
•Suzuki Kasami’s Broadcast
•Singhal’s Heuristics
•Raymond’s Tree Based

3. System
SV [1…..N] : System State
SN [1…..N] : Highest Seq. No.
Token
TSV [1…..N] : System State
TSN [1…..N] : Highest Seq. No.
Singhal’s Heuristic Algorithm

4. S1
S2
S3
S4
SV [ H N N N ]
SN [ 0 0 0 0 ]
SV [ R N N N ]
SN [ 0 0 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 0 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE

5. S1
S2
S3
S4
SV [ H N N N ]
SN [ 0 0 0 0 ]
SV [ R R N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 0 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 is Requesting
Token
REQUEST Only “HRE”

6. S1
S2
S3
S4
SV [ H N N N ]
SN [ 0 0 0 0 ]
SV [ R R N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 0 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
RQ (2,1)
S2 sends Request to S1

7. S1
S2
S3
S4
SV [ H N N N ]
SN [ 0 0 0 0 ]
SV [ R R N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 0 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
RQ (2,1)
S1 updates itself and
Token(if reqd)

8. S1
S2
S3
S4
SV [ H N N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 0 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S1 updates itself and
Token(if reqd)
RQ (2,1)

9. State of System Receiving the Request
Requesting Mode R
Executing Mode E
Holding idle Token H
None of the Above N
Action
Accept the Request, Inform the
sender about its own status
Accept the Request
Accept the Request and update
the Token
Accept the Request

10. S1
S2
S3
S4
SV [ N R N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N R N N ]
TSN [ 0 1 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
Token Updated

11. S1
S2
S3
S4
SV [ N R N N ]
SN [ 0 1 0 0 ]
SV [ R E N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N R N N ]
TSN [ 0 1 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S1 completes CS
Sends Token to S2 S2 sets status to E and
Executes CS

12. S1
S2
S3
S4
SV [ N R N N ]
SN [ 0 1 0 0 ]
SV [ R N N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 1 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 comes out of CS
Sets status to N
Token
Updated

13. If System has latest information Update the
Token
Else update itself from
Token
Information : Sequence Nos. possessed by System and Token
if SN > TNS , System has latest information

14. S1
S2
S3
S4
SV [ N R N N ]
SN [ 0 1 0 0 ]
SV [ R N N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 1 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 updates itself

15. S1
S2
S3
S4
SV [ N R N N ]
SN [ 0 1 0 0 ]
SV [ N N N N ]
SN [ 0 1 0 0 ]
SV [ R R N N ]
SN [ 0 0 0 0 ]
SV [ R R R N ]
SN [ 0 0 0 0 ]
TSV [ N N N N ]
TSN [ 0 1 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 updates itself

16. S1
S2
S3
S4
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
TSV [ N N N N ]
TSN [ 0 1 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 sets its status to H
All systems are updated

17. S1
S2
S3
S4
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N H R N ]
SN [ 0 1 1 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
TSV [ N N N N ]
TSN [ 0 1 0 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
Contd.. S3 makes a REQUEST
REQUEST Only “HRE”
R(3,1)

18. S1
S2
S3
S4
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N H R N ]
SN [ 0 1 1 0 ]
SV [ N H R N ]
SN [ 0 1 1 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
TSV [ N N R N ]
TSN [ 0 1 1 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 sets S3’s status to R
S2 then updates the TOKEN for S3

19. S1
S2
S3
S4
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N N R N ]
SN [ 0 1 1 0 ]
SV [ N N E N ]
SN [ 0 1 1 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
TSV [ N N R N ]
TSN [ 0 1 1 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 sets its own status to N
Sends TOKEN to S3
S3 sets status to E
Executes CS

20. S1
S2
S3
S4
SV [ N H N N ]
SN [ 0 1 0 0 ]
SV [ N N R N ]
SN [ 0 1 1 0 ]
SV [ N H N N ]
SN [ 0 1 1 0 ]
SV [ N H N N ]
SN [ 0 1 0 0 ]
TSV [ N N R N ]
TSN [ 0 1 1 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S3 comes out of CS
Looks for any other ‘R’

21. S1
S2
S3
S4
SV [ N N H N ]
SN [ 0 1 1 0 ]
SV [ N N H N ]
SN [ 0 1 1 0 ]
SV [ N N H N ]
SN [ 0 1 1 0 ]
SV [ N N H N ]
SN [ 0 1 1 0 ]
TSV [ N N N N ]
TSN [ 0 1 1 0 ]
STATES
R : REQUESTING A TOKEN
H : HOLDING IDLE TOKEN
E : EXECUTING IN CRITICAL SECTION
N:NONE OF THE ABOVE
S2 sets its own status to H
All sites are then updated

22. DeadLock and Starvation
Request sent to only those
systems who possess the Token or
will get Token in near future : E, R,
or H
If RQ is sent to any other system
if ‘N’ systems send
requests to each other : Deadlock
if a system sends request
to N system : Starvation
S1
S2
SV [ H N N N ]
SN [ 0 1 0 0 ]
SV [ R N N N ]
SN [ 0 1 0 0 ]
S3
SV [ R N N N ]
SN [ 0 1 0 0 ]

23. Correctness and Performance
Is the Algorithm Correct ? Will it ensure Mutual Exclusion ? YES
Presence of Token is necessary for CS to be executed
Only 1 system possesses the Token
What is the Performance metric and measure of this Algorithm ?
Less message overhead. Only few selected systems are requested
for Token
Avg/Max Message Traffic : N/2 or N (N : No. of systems)
Synchronization Delay : T (Delay between two consecutive CS
executions)
Response Time : 2T + CS execution Time (E)
Token values can be Binary {0,1} representing {R or N}

24. Raymond’s Tree Based Algorithm
All the sites have a Holder variable (pointer) to their neighbors
(parent) eventually reaching the site possessing the token
6
2 3
4 5
1
7
TOKEN
QUEUE
SITES

25. Raymond’s Tree Based Algorithm
Site 4 requests the TOKEN. Sends REQUEST to Site 2
Both sites update their queues, eventually requesting TOKEN holder
6
2 3
4 5
1
7
TOKEN
4
R4
4
2

26. Raymond’s Tree Based Algorithm
TOKEN site serves the REQUEST of site 2
6
2 3
4 5
1
7
4
R4
4

27. Raymond’s Tree Based Algorithm
6
2 3
4 5
1
7
6 7
6 7 3
Site 2 sends TOKEN to requesting Site 4, 4 executes the CS
Site 6 and 7 also REQUEST for TOKEN

28. Raymond’s Tree Based Algorithm
Each site enroute to TOKEN Site update their entries and forward the
REQUESTs, eventually reaching TOKEN site
6
2 3
4 5
1
7
2 6 7
6 7 3
3
1

29. Raymond’s Tree Based Algorithm
TOKEN site serves the REQUESTs of sites and forward the TOKEN
6
2 3
4 5
1
7
6 7
6 7 3
3
1

30. Raymond’s Tree Based Algorithm
6
2 3
4 5
1
7
6 7
6 7 3
3

31. Raymond’s Tree Based Algorithm
The requesting site gets the TOKEN and executes CS
6
2 3
4 5
1
7
7
7 3

32. Raymond’s Tree Based Algorithm
Site 3 sends the REQUEST for Site 7 to TOKEN site
6
2 3
4 5
1
7
7
7 3
R3
3

33. Raymond’s Tree Based Algorithm
Site 6 sends the TOKEN to requesting site and updates its queue
6
2 3
4 5
1
7
7 3
7

34. Raymond’s Tree Based Algorithm
Site 3 sends the TOEKN to Site 7 which then executes CS
6
2 3
4 5
1
7
3
7

35. Raymond’s Tree Based Algorithm
Site 3 sends the REQUEST for itself to TOKEN site
6
2 3
4 5
1
7
3
R3
3

36. Raymond’s Tree Based Algorithm
TOKEN site sends the TOKEN to requesting site
ALL REQUESTs are now fulfilled
6
2 3
4 5
1
7

37. Correctness and Performance
Is the Algorithm Correct ? Will it ensure Mutual Exclusion ? YES
Presence of Token is necessary for CS to be executed
Only 1 system possesses the Token
Tree has no cycles 🡪 no Deadlock
Each site receives the Token 🡪 no Starvation
What is the Performance metric and measure of this Algorithm ?
Average message complexity : O(log N) (avg distance between 2
sites)
Synchronization Delay : (T log N ) /2 (T : avg message delay)
Site can execute CS when it gets the TOKEN even if it is not its turn
On heavy loads, Synchrinozation Delay : T
Response Time : T (log N) +E (time to execute CS)

38. That’s it..
Thank You