Mutual Exclusion

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. Allocation of single, indivisible, non-shareable resource among n users Steps by a user Trying protocol Critical region Exit protocol Remainder (non-critical region) The problem 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. Shared Variables • turn rd / wr by all processes, intially arbitrary • flag(i) rd by all / wr by I, initially 0

8. Dijkstra’s Mutual Exclusion Alg.

9. Dijkstra’s Mutual Exclusion Alg. • 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 Shared variables • turn(k) rd / wr by all, initially arbitrary • flag(i) rd by all j ≠ i / wr by I, initially 0

14. PetersonNP Algorithm

15. PetersonNP Algorithm • 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. BurnsME Algorithm • 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. Bakery Algorithm • 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?