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The TCP window size process appears in the modeling of the famous Transmission Control Protocol used over the Internet. This continuous time Markov process takes its values in [0, ∞), is ergodic and irreversible. It belongs to the Additive Increase Multiplicative Decrease class of processes. The sample paths are piecewise linear deter-ministic and the whole… (More)

We analyze in this paper the longest increasing contiguous sequence or maximal ascending run of random variables with common uniform distribution but not independent. Their dependence is characterized by the fact that two successive random variables cannot take the same value. Using a Markov chain approach, we study the distribution of the maximal ascending… (More)

A distributed algorithm is self-stabilizing if after faults and attacks hit the system and place it in some arbitrary global state, the system recovers from this catastrophic situation without external intervention in finite time. Unidirectional networks preclude many common techniques in self-stabilization from being used, such as preserving local… (More)

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