Analysis of Some Lockout Avoidance Algorithms for the k-Exclusion Problem

We analyze two algorithms for the k-exclusion problem on the asynchronous multi-writer/reader shared memory model and show their correctness. The first algorithm is a natural extension of the n-process algorithm by Peterson for the mutual exclusion algorithm to the k-exclusion problem, and the second algorithm is a combination of the first algorithm and the tournament algorithm by Peterson and Fischer for the mutual exclusion problem. These two algorithms satisfy k-exclusion, and can tolerate up to k-1 process failures of the stopping type. The running times by the first algorithm and by the second algorithm are bounded by (n-k)c+O(n(n-k)2)l and (n/k)kc+O((n/k)k+1k)l, respectively, even if there exist at most k-1 process failures of the stopping type, where n is the number of processes, l is an upper bound on the time between successive two atomic steps for any faultless process, and c is an upper bound on the time that any user spends in the critical region