Probabilistic self-stabilization
Information Processing Letters
Token management schemes and random walks yield self-stabilizing mutual exclusion
PODC '90 Proceedings of the ninth annual ACM symposium on Principles of distributed computing
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Probabilistic self-stabilizing mutual exclusion in uniform rings
PODC '94 Proceedings of the thirteenth annual ACM symposium on Principles of distributed computing
A more rapidly mixing Markov chain for graph colorings
proceedings of the eighth international conference on Random structures and algorithms
Self-stabilization
Self-stabilizing systems in spite of distributed control
Communications of the ACM
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Information and Computation
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FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
1983 Invited address solved problems, unsolved problems and non-problems in concurrency
PODC '84 Proceedings of the third annual ACM symposium on Principles of distributed computing
Convergence of the Iterated Prisoner's Dilemma Game
Combinatorics, Probability and Computing
On stabilization in Herman's algorithm
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Proving termination of probabilistic programs using patterns
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
A tighter bound for the self-stabilization time in Herman's algorithm
Information Processing Letters
| Hi-index | 5.23 |
In this article we investigate the expected time for Herman's probabilistic self-stabilizing algorithm in distributed systems: suppose that the number of identical processes in a unidirectional ring, say n, is odd and n ≥ 3. If the initial configuration of the ring is not "legitimate", that is, the number of tokens differs from one, then execution of the algorithm made up of synchronous probabilistic procedures with a local parameter 0 r 2-8)/8r(1-r))n2. Note that if r = ½ then it is bounded by 0.936n2. Moreover, there exists a configuration whose expected time is Θ(n2). The method of the proof is based on the analysis of coalescing random walks.