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This is fundamentally very broken The reason is that the algorithm uses a sequence of reads and writes that aren't atomic Imagine if two threads read t a ke n as 0 and, based on this information, both decide to write 1 into it Multiple threads would each think it owned the critical region, but both would be running code inside the critical region at once This is precisely the thing we're trying to avoid with the use of critical regions in the first place! Before reviewing the state of the art-that is, the techniques all modern critical regions use-we'll take a bit of a historical detour in order to better understand the evolution of solutions to mutual exclusion during the past 40+ years

This then is a weighted average of the values of X and the probabilities associated with its values In our example, we nd x = E(X) = 1 1 1 1 1 1 +2 +3 +4 +5 =3 5 5 5 5 5

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Strict Alternation We might first try to solve this problem with a technique called strict alternation, granting ownership to thread 0, which then grants ownership to thread 1 when it is done, which then grants ownership to 2 when it is done, and so on, for N threads, finally returning ownership back to after thread N 1 has been given ownership and fin ished running inside the region This might be implemented in the form of the following code snippet:

const int N = ; I I # of t h re a d s i n the system int t u r n = e; II T h read e get s i t s t u rn f i r st void EnterC r i t i c a l Region ( i nt i ) { while ( t u r n ! = i ) 1 * b u s y wa it * 1 I I Someone gave u s t h e t u rn w e own t h e region } void LeaveCrit i c a lRegion ( i nt i ) { II Give t h e t u r n to t h e next t h read ( po s s ibly wra p p i n g to e ) turn = ( i + 1 ) % N ;

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This algorithm ensures mutual exclusion inside the critical region for precisely N concurrent threads In this scheme, each thread is given a unique identifier in the range [0 N), which is passed as the argument i to E nt e r C r it i c a l Re g i o n The t u r n variable indicates which thread is cur rently permitted to run inside the critical region, and when a thread tries to enter the critical region, it must wait for its turn to be granted by another thread, in this particular example by busy spinning With this algorithm, we have to choose someone to be first, so we somewhat arbitrarily decide

In general, we have discrete uniform distribution x = E(X) =

to give thread its turn first by initializing t u r n to at the outset Upon leaving the region, each thread simply notifies the next thread that its turn has come up: it does this notification by setting t u r n , either wrapping it back around to 0, if we've reached the maximum number of threads, or by incrementing it by one otherwise There is one huge deal breaker with strict alternation: the decision to grant a thread entry to the critical region is not based in any part on the arrival of threads to the region Instead, there is a predefined ordering: 0,

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