The drinking philosophers problem
ACM Transactions on Programming Languages and Systems (TOPLAS) - Lecture notes in computer science Vol. 174
Complexity of network synchronization
Journal of the ACM (JACM)
Asymptotic optimality of shortest path routing algorithms
IEEE Transactions on Information Theory
Concurrency in heavily loaded neighborhood-constrained systems
ACM Transactions on Programming Languages and Systems (TOPLAS)
Max-balancing weighted directed graphs and matrix scaling
Mathematics of Operations Research
Transience Bounds for Long Walks
Mathematics of Operations Research
Analysis of Distributed Algorithms based on Recurrence Relations (Preliminary Version)
WDAG '91 Proceedings of the 5th International Workshop on Distributed Algorithms
Analysis of Link Reversal Routing Algorithms
SIAM Journal on Computing
Self-Stabilizing Distributed Queuing
IEEE Transactions on Parallel and Distributed Systems
A provably starvation-free distributed directory protocol
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
Full reversal routing as a linear dynamical system
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
SIROCCO'11 Proceedings of the 18th international conference on Structural information and communication complexity
Link Reversal Algorithms
ACM SIGACT News
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A large variety of distributed systems, like some classical synchronizers, routers, or schedulers, have been shown to have a periodic behavior after an initial transient phase (Malka and Rajsbaum, WDAG 1991). In fact, each of these systems satisfies recurrence relations that turn out to be linear as soon as we consider max-plus or min-plus algebra. In this paper, we give a new proof that such systems are eventually periodic and a new upper bound on the length of the initial transient phase. Interestingly, this is the first asymptotically tight bound that is linear in the system size for various classes of systems. Another significant benefit of our approach lies in the straightforwardness of arguments: The proof is based on an easy convolution lemma borrowed from Nachtigall (Math. Method. Oper. Res. 46) instead of purely graph-theoretic arguments and involved path reductions found in all previous proofs.