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This paper introduces a unified framework for the analysis of a class of random allocation processes thdt include: (i) the birthday paradox; (ii) the coupon collector problem* (iii) least-tecently-used (LRU) caching in memory management systems under the independent reference model; (iv) the move-to-front heuristic of self-organizing search. All analyses… (More)

We present succinctly the Arnold-Nivat's model for the synchronization of sequential preocesses, and we recall the concurrency measure defined by Beauquier, Dérard and Thimonier. We present here a new technics for the computation of this measure avoiding very often a very expensive part of the computation. We illustrate this method by the mutual exclusion… (More)

Given a set ξ = {H 1 , H 2 , · · ·} of connected non acyclic graphs, a ξ-free graph is one which does not contain any member of ξ as copy. Define the excess of a graph as the difference between its number of edges and its number of vertices. Let W k,ξ be theexponential generating function (EGF for brief) of connected ξ-free graphs of excess equal to k (k ≥… (More)

0. Abstract We show how to modelize concurrency between several processors in terms of automata and Markov chains; then, we define a concurrency measure which reflects more faithfully the behaviour of the processes and is in addition easy to compute with a symbolic manipulator like Maple (this is an improvement over a previous measure [3] whose computation… (More)

Denote by an l-component a connected graph with l edges more than vertices. We prove that the expected number of creations of (l + 1)-component, by means of adding a new edge to an l-component in a randomly growing graph with n vertices, tends to 1 as l, n tends to ∞ but with l = o(n 1/4). We also show, under the same conditions on l and n, that the… (More)