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
ACM Computing Surveys (CSUR)
Collisions among random walks on a graph
SIAM Journal on Discrete Mathematics
Randomized algorithms
Impact of local topological information on random walks on finite graphs
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Random walks, interacting particles, dynamic networks: randomness can be helpful
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Request-based token passing for self-stabilizing mutual exclusion
Information Sciences: an International Journal
Universal adaptive self-stabilizing traversal scheme: Random walk and reloading wave
Journal of Parallel and Distributed Computing
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Suppose that a distributed system is modeled by an undirected graph G = (V,E), where V and E, respectively, are the sets of processes and communication links. Israeli and Jalfon proposed a simple self-stabilizing mutual exclusion algorithm: A token is circulated among the processes (i.e., vertices) and a process can access the critical section only when it holds the token. In order to guarantee equal access chance to all processes, the token circulation is desired to be fair in the sense that all processes have the same probability of holding the token. However, the Israeli-Jalfon token circulation scheme does not meet the requirement. This paper proposes a new scheme for making it fair. We evaluate the average of the longest waiting times in terms of the cover time and show an O({\rm deg}(G)n^2) upper bound on the cover time for our scheme, where n and {\rm deg}(G) are the number of processes and the maximum degree of G, respectively. The same (tight) upper bound is known for the Israeli-Jalfon scheme.