Mutual Exclusion

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

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

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

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

The problem (contd.)

A shared memory system solves the mutual exclusion problem when the following conditions are satisfied:Well-formednessMutual exclusionProgress

Dijkstra’s Mutual Exclusion Alg.

ConceptUse a two stage flag to indicate what stage of

processing a user is inEnsure mutual exclusion by ensuring that only

one flag at a time has a value to let it into the critical region

Dijkstra’s Mutual Exclusion Alg.

}2,1,0{)(:1,},......,1{

iflagniieveryfornturn

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

Shared Variables

Dijkstra’s Mutual Exclusion Alg.

i

i

i

i

remiflag

exit

critLgotothenjflagif

doijforiflag

iturnthenturnflagifdoiturnwhile

iflagLtry

0:)(

........

2)(

2:)(:0)(

1:)(:

Dijkstra’s Mutual Exclusion Alg.

Guarantees well-formednessPer inspection of the code

Satisfies mutual exclusionBy status of flag

Guarantees progressMore complex proof

Stronger Conditions

FairnessNo lockouts or starvationsKinds of fairness

Low level fairness High level fairness

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

PetersonNP Algorithm

ConceptThere 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

PetersonNP Algorithm

}1,........,0{)(:1,},.....1{)(

:}1,.......,1{

niflagniieveryfornkturnnkeveryfor

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

Shared variables

PetersonNP Algorithm

i

i

i

i

remiflag

exit

critikturnorkjflagijwaitfor

ikturnkiflagdontokfor

try

0:)(

......

])([])(:[:)(:)(

11

PetersonNP Algorithm

Is well formed Satisfies mutual exclusion Guarantees progress Lockout free

Alg. Using Single Writer Shared Registers (BurnsME Algorithm) Concept

Check if anyone else is trying to get a lockLay claim on the lockCheck againProceed

BurnsME Algorithm

}1,0{)(:1,

iflagniieveryfor

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

BurnsME Algorithm

i

i

i

i

remiflag

exit

critMgotojflagifdonjijforMLgotojflagif

doijjforiflag

Lgotojflagifdoijjfor

iflagLtry

0:)(

......

1)(1,:

1)(11,

1:)(1)(11,

0:)(:

BurnsME Algorithm

Is well formed Guarantees mutual exclusion Guarantees progress

Bakery Algorithm

ConceptFIFO after a wait-free doorwayDoorway is:

Everyone picks a number Waits for everyone to finish

Break ties and enter critical zone

Bakery Algorithm

)(}1,0{)(:1,

inumberichoosng

niieveryfor

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

Bakery Algorithm

i

i

i

j

i

reminumber

exit

critjjnumberiinumberorjberwaitfornum

jchoosngwaitfordoijforichoosng

jnumberinumberichoosng

try

0:)(

......

)),(()),((0)(0)(

0:)()(max1:)(

1:)(1

Bakery Algorithm

Is well formed Satisfies mutual exclusion Guarantees progress Guarantees lockout freedom

Lower bound on # registers

Cannot solve mutual exclusion with <n shared variablesSingle writer shared variablesMulti writer shared variables

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

Questions?