Section: New Results

Process Network analysis

Participants : Robert de Simone, Jean-Vivien Millo.

K-periodic routing schemes for Network-on-Chip data traffic

This year we considered more specifically the issue of exploiting the predictable routing schemes of our KRG models, expressed as infinite binary words to indicate the sucessive branching directions at merge/select switch nodes, in order to encode data traffic patterns expanded at compile time, when mapping applications expressed under the form of dataflow process networks onto processor arrays in manycore architectures based on network-on-chip interconnects. To show the potential impact of such predicatble compile-time routing patterns, we stdudied as a typical example a fulll (all-to-all) broadcast algorithm on a mesh topology, connecting mode-less computation nodes as in the theory of cellular automata. This resulted in a precise recursive definition of routing patterns, which achieve an optimal data propagation (broadcast implemented as multicast), given the availability of actual links in the NoC topology. This result was presented at the Autamata'2012 conference [30] , and an expanded version is available as technical report [44] .

A wider view of the approach, and its potential benefits, are described in a technical report [43] , submitted for publication.

Optimal data placement for process network scheduling

The topic of efficient scheduling of dataflow process network traffic to optimize both throughput and buffer queue sizing has given rise to a huge literature starting with seminal works in [49] , [47] , [56] . It has recently been given new impulse due to the advent of manycore architectures (see above). We conducted a number of theoretical works, to establish how such optimal computation scheduling can be best achieved in configurations where data are evenly distributed and streched in time across the (process) network. While this result is intuitively obvious, we formalized precisely what evenly distributed technically means, with the notion of balanced/mechanical words going a long way back in formal language theory, and we demonstrated that under such assumptions optimal schedules could be constructed in a fully analytical way, without any symbolic simulation steps or behavior expansion. The result was accepted for publication in a journal article [20] .