A Stabilizing Optimal ℓ-Exclusion Algorithm

Abstract

In this paper, we present a simple permission-based fair stabilizing solution to the [Formula: see text]-exclusion problem in tree networks. The [Formula: see text]-exclusion problem is a generalization of the mutual exclusion problem where [Formula: see text] processes, instead of 1, are allowed to use a shared resource (enter the critical section) simultaneously. The proposed algorithm is optimal in terms of waiting times of processes to enter critical sections, i.e., between two entries of a process to its critical section, no other process can enter its critical section more than once after stabilization. Since our algorithm is stabilizing, it does not require initialization and withstands transient faults. The stabilization time of the algorithm is [Formula: see text] rounds and the waiting time is [Formula: see text], where h and n are the height and the size of the tree, respectively. In addition, this algorithm satisfies all the requirements of the [Formula: see text]-exclusion problem: [Formula: see text] and liveness.