1. Mutual Exclusion Presented by: Rohan Sen (Distributed Algorithms Ch. 10)

2. Topics that will be covered Overview and problem statement Dijkstra’s Mutual Exclusion Algorithm Stronger Conditions for Mutual Exclusion Algorithms Lockout-free Mutual Exclusion Algorithms Single-Writer Shared Register Algorithms The Bakery Algorithm Conclusion

3. Overview The shared memory model  Every process is a kind of state machine Set of states Three kinds of actions: input, output, internal  All communication via the shared memory  Exists a transition relation for all states System is input-enabled Not output and internal enabled  Locality restrictions  Restrictions on shared variable operations

4. The problem Allocation of single, indivisible, non-shareable resource among n users Steps by a user  Trying protocol  Critical region  Exit protocol  Remainder (non-critical region) U try crit exit rem External interface of a user

5. The problem (contd.) A shared memory system solves the mutual exclusion problem when the following conditions are satisfied:  Well-formedness  Mutual exclusion  Progress

6. Dijkstra’s Mutual Exclusion Alg. Concept  Use a two stage flag to indicate what stage of processing a user is in  Ensure mutual exclusion by ensuring that only one flag at a time has a value to let it into the critical region

7. Dijkstra’s Mutual Exclusion Alg. turn rd / wr by all processes, intially arbitrary flag(i) rd by all / wr by I, initially 0 Shared Variables

8. Dijkstra’s Mutual Exclusion Alg.

9. Guarantees well-formedness  Per inspection of the code Satisfies mutual exclusion  By status of flag Guarantees progress  More complex proof

10. Stronger Conditions Fairness  No lockouts or starvations  Kinds of fairness Low level fairness High level fairness

11. Stronger Conditions (contd.) Lockout freedom  Any user that reaches T eventually enters C  Any user that reaches E eventually enters R Time bound  If each user returns resource within time c and each step is at most l, then you enter C at most b = f(l,c) after entering T  Similarly, you enter R at most b = f(l,c) after entering E. Number of bypasses

12. PetersonNP Algorithm Concept  There are k levels At each level eliminate one user n – k processes can win at level k Only one process can win at level n – 1, yielding mutual exclusion

13. PetersonNP Algorithm turn(k) rd / wr by all, initially arbitrary flag(i) rd by all j ≠ i / wr by I, initially 0 Shared variables

14. PetersonNP Algorithm

15. Is well formed Satisfies mutual exclusion Guarantees progress Lockout free

16. Alg. Using Single Writer Shared Registers (BurnsME Algorithm) Concept  Check if anyone else is trying to get a lock  Lay claim on the lock  Check again  Proceed

17. BurnsME Algorithm Shared variables  flag(i) wr by i / rd by all j ≠ I, initially 0

18. BurnsME Algorithm

19. Is well formed Guarantees mutual exclusion Guarantees progress

20. Bakery Algorithm Concept  FIFO after a wait-free doorway  Doorway is: Everyone picks a number Waits for everyone to finish  Break ties and enter critical zone

21. Bakery Algorithm Shared variables choosng(i) wr by i / rd by all j ≠ I, initially 0 number(i) wr by i / rd by all j ≠ I, initially 0

22. Bakery Algorithm

23. Is well formed Satisfies mutual exclusion Guarantees progress Guarantees lockout freedom

24. Lower bound on # registers Cannot solve mutual exclusion with <n shared variables  Single writer shared variables  Multi writer shared variables

25. Conclusion Mutual exclusion: One at a time access to a shared resource Mutual exclusion w/o fairness Mutual exclusion w/ fairness Minimizing the number of registers

26. Questions?