A polynomial algorithm for the computation of buffer capacities with throughput constraint for embedded system design

Marked timed weighted event graphs (in short MTWEG), which are a subclass of Petri nets, are widely used for modelling practical industrial problems. In this paper, a central practical problem for the design of streaming (e.g. multimedia or network packet processing) is modelled using a MTWEG. The optimization problem tackled here consists then on finding an initial marking minimizing the overall number of tokens for a minimum given throughput. If the firings of the transitions are periodic, this problem is NP-complete and can be modelled using an integer linear program. A general lower bound on the minimum overall capacity is then proved. If the initial MTWEG has a unique circuit, a polynomial time algorithm based on the resolution of a particular Diophantine equation is presented to solve it exactly. We lastly experiment it on an industrial example.