  We address the problem of analysing the complexity of concurrent programs
written in Pi-calculus. We are interested in parallel complexity, or span,
understood as the execution time in a model with maximal parallelism. A type
system for parallel complexity has been recently proposed by Baillot and
Ghyselen but it is too imprecise for non-linear channels and cannot analyse
some concurrent processes. Aiming for a more precise analysis, we design a type
system which builds on the concepts of sized types and usages. The new variant
of usages we define accounts for the various ways a channel is employed and
relies on time annotations to track under which conditions processes can
synchronize. We prove that a type derivation for a process provides an upper
bound on its parallel complexity.
