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

Abstract

Abstract-Marked Timed Weighted Event Graphs (in short MTWEG), which are a sub-class 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) applications 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 NPcomplete 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.

Periodic Schedules for Bounded Timed Weighted Event Graphs

“…Tokens model data transferred from a process to another. Some practical optimization problems and examples can be found in [10], [11], [12], [13].…”

“…From a theoretical point of view, it can be viewed as a generalization of well-known results for TEGs. For practitioners, periodic schedules for TWEGs might easily be implemented in real systems (see for example [10], [11]). Thus, even if they cannot outperform the earliest schedule with respect to the throughput, they might be used to get an easily encoded solution.…”