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 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.