Section: New Results

K-periodically Routed extended Event Graphs

Participants : Julien Boucaron, Anthony Coadou, Robert de Simone.

The Process Network models based on Event Graphs and varying synchronous or asynchronous interpretations allow powerful results in static scheduling and distribution allocations. Nevertheless they always postulate a uniform data flow. We tried to relax this strong assumption, while preserving the determinism/confluence of computations, as in Kahn Process Networks. Several models were inspirational (such as Boolean and CycloStatic DataFlow Graphs). But the main originality of our KRGs is to rely on two Select/Merge operator nodes only (for mux/demux effects on data streams). And, most importantly the switching patterns for these conditional nodes have to be infinitary periodic binary words, thus using exactly the same description formalisms as our previous schedule words .

We have proven a number of powerful algebraic results on such models. They may best be understood by analogy with Boolean Algebra, and the existence of normal forms (such as sum of products, or product of sums). Here, the expansion and factorization of expressions and variables amounts to sharing and unsharing of links and channels in the interconnect fabric representation of the communications across the networks.

Our main results during this year are submitted for publication, and will be published in book chpater form. We believe this model of KRGs to be an important step for the Theoretical Computer Science modeling of modern Networks-on-Chip NoCs .

Meanwhile we have also studied further issues of throughput and buffer dimensioning in the context of Latency-Independent Design (LID) [35] , [34] .