Mutual%20Exclusion

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Mutual Exclusion

• Presented by Rohan Sen
• (Distributed Algorithms Ch. 10)

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Topics that will be covered

• Overview and problem statement
• Dijkstras Mutual Exclusion Algorithm
• Stronger Conditions for Mutual Exclusion
  Algorithms
• Lockout-free Mutual Exclusion Algorithms
• Single-Writer Shared Register Algorithms
• The Bakery Algorithm
• Conclusion

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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

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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
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The problem (contd.)

• A shared memory system solves the mutual
  exclusion problem when the following conditions
  are satisfied
• Well-formedness
• Mutual exclusion
• Progress

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Dijkstras 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

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Dijkstras Mutual Exclusion Alg.
Shared Variables

• turn rd / wr by all processes, intially arbitrary
• flag(i) rd by all / wr by I, initially 0

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Dijkstras Mutual Exclusion Alg.
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Dijkstras Mutual Exclusion Alg.

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

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Stronger Conditions

• Fairness
• No lockouts or starvations
• Kinds of fairness
• Low level fairness
• High level fairness

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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

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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

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PetersonNP Algorithm
Shared variables

• turn(k) rd / wr by all, initially arbitrary
• flag(i) rd by all j ? i / wr by I, initially 0

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PetersonNP Algorithm
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PetersonNP Algorithm

• Is well formed
• Satisfies mutual exclusion
• Guarantees progress
• Lockout free

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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

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BurnsME Algorithm

• Shared variables
• flag(i) wr by i / rd by all j ? I, initially 0

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BurnsME Algorithm
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BurnsME Algorithm

• Is well formed
• Guarantees mutual exclusion
• Guarantees progress

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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

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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

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Bakery Algorithm
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Bakery Algorithm

• Is well formed
• Satisfies mutual exclusion
• Guarantees progress
• Guarantees lockout freedom

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Lower bound on registers

• Cannot solve mutual exclusion with ltn shared
  variables
• Single writer shared variables
• Multi writer shared variables

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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

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Questions?