Distributed Algorithms for Message-Passing Systems by Michel Raynal

Author:Michel Raynal
Language: eng
Format: epub
Publisher: Springer Berlin Heidelberg, Berlin, Heidelberg

Let us now consider (R1) to eliminate τ i and τ j and obtain conditions on ρ, η, and ϵ, which implies simultaneously (R6′) and (R7′). Taking τ i −τ j <1, and considering (R7′), we obtain the following condition (C1) which implies (R6′)

Taking τ j −τ i <1, and considering (R7′), we obtain the following condition (C2), which implies (R7′)

It follows from these conditions that the greatest pulse number r max that can be attained without problem is such that 2r max ρϵ=ρ((1−ϵ)−2−η(1+ϵ))=η(1−ϵ)−1, which is obtained for

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