  We develop new methods to statically bound the resources needed for the
execution of systems of concurrent, interactive threads. Our study is concerned
with a \emph{synchronous} model of interaction based on cooperative threads
whose execution proceeds in synchronous rounds called instants. Our
contribution is a system of compositional static analyses to guarantee that
each instant terminates and to bound the size of the values computed by the
system as a function of the size of its parameters at the beginning of the
instant. Our method generalises an approach designed for first-order functional
languages that relies on a combination of standard termination techniques for
term rewriting systems and an analysis of the size of the computed values based
on the notion of quasi-interpretation. We show that these two methods can be
combined to obtain an explicit polynomial bound on the resources needed for the
execution of the system during an instant. As a second contribution, we
introduce a virtual machine and a related bytecode thus producing a precise
description of the resources needed for the execution of a system. In this
context, we present a suitable control flow analysis that allows to formulte
the static analyses for resource control at byte code level.
