Toward a non-atomic era: l-exclusion as a test case
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
k-Arbiter: a safe and general scheme for h-out of-k mutual exclusion
Theoretical Computer Science
A Distributed Solution to the k-out of-M Resources Allocation Problem
ICCI '91 Proceedings of the International Conference on Computing and Information: Advances in Computing and Information
A Self-stabilizing Token-Based k-out-of-l Exclusion Algorithm
Euro-Par '02 Proceedings of the 8th International Euro-Par Conference on Parallel Processing
A New Efficient Tool for the Design of Self-Stabilizing l-Exclusion Algorithms: The Controller
WSS '01 Proceedings of the 5th International Workshop on Self-Stabilizing Systems
(h-k)-arbiter for h-out of-k Mutual Exclusion Problem
ICDCS '99 Proceedings of the 19th IEEE International Conference on Distributed Computing Systems
Self-stabilization over unreliable communication media
Distributed Computing - Special issue: Self-stabilization
Separation of Circulating Tokens
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Quorum based distributed conflict resolution algorithm for bounded capacity resources
ISPA'06 Proceedings of the 2006 international conference on Frontiers of High Performance Computing and Networking
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We present an efficient self-stabilizing solution to the k-out-of- l exclusion problem on a ring. The k-out-of-l exclusion problem is a generalization of the well-known mutual exclusion problem -- there are l units of a shared resource, any process can request at most k (1 ≤ k ≤ l) units of the shared resource, and no resource unit can be allocated to more than one process at one time. This solution is based on the circulation of l tokens around the ring. A processor requesting NEED (NEED ≤ k ≤ l) units of the resource can enter the critical section only upon receipt of NEED tokens. We propose a simple and pessimistic method to handle the deadlock problem. So, after stabilization, no mechanism is needed for the deadlock detection. Moreover, in this paper, we give a formal definition of a new efficiency property, called (k, l)-liveness, which is a desirable property of any k-out-of-l exclusion solution. This property allows as many processors as possible to execute their critical sections simultaneously without violating the safety property. We generalize the technique introduced in [6] to maintain the right number (l) tokens in the system. The tokens are counted without using any counter variable for all processors except one, called the Root. This solution improves the waiting time of an earlier solution [4] by maintaining a reasonable stabilization time. The waiting time is reduced from (l + 2)(n - 1) to 2(n - 1), where n is the size of the ring. The stabilization time is 8n instead of 4n in [4]. One nice characteristic of our algorithm is that its space requirement is independent of l for all processors except the Root.