Self-Stabilizing ℓ-Exclusion Revisited

We consider the (deterministic) ℓ-exclusion problem, a generalization of the mutual exclusion problem which allows use of 1 ≤ ℓ < n identical copies of a non-sharable reusable resource among n processes, instead of only one, as standard mutual exclusion. This problem is defined using three properties: safety, fairness, and avoidance of ℓ-deadlock. We first show that any algorithm satisfying the three aforementioned properties has a waiting time of Ω(n − ℓ) rounds. Thus, when n is large, the gain (in terms of waiting time) of having ℓ copies of a resource, instead of one, becomes negligible. We propose to reformulate the problem by replacing the avoidance of ℓ-deadlock property by a new property, which we call fast waiting time, which requires waiting time of O(n/ℓ) rounds, which is asymptotically optimal. We call this new version of the problem fast waiting time ℓ-exclusion. We give two self-stabilizing solutions for this new problem. Our first solution works in oriented rooted ring networks. Our second solution is a generalization of the first, and works in every connected identified network.