The design of streaming (e.g. multimedia or network packet processing) applications must consider several optimizations such as the mimimization of the whole surface of the memory needed on a Chip. The minimum throughput of the output is usually fixed. In this paper, we present an original methodology to solve this problem. The application is modelled using a Marked Timed Weighted Event Graphs (in short MTWEG), which is a subclass of Petri nets. Transitions correspond to specific treatments and the places model buffers for data transfers. It is assumed that transitions are periodically fired with a fixed throughput. The problem is first mathematically modelled using an Integer Linear Program. We then study for a unique buffer the optimum throughput according to the capacity. A first polynomial simple algorithm computing the minimum surface for a fixed throughput is derived when there is no circuit in the initial MTWEG, which corresponds to a wide class of applications. We prove in this case that the capacities of every buffer may be optimized independently. For general MTWEG, the problem is NP-Hard and an original polynomial 2-approximation algorithm is presented. For practical applications, the solution computed is very close to the optimum.