- A timed CCS-like process algebra PAFAS and a testing scenario are developed for evaluating the temporal worst-case efficiency of asynchronous concurrent systems. Each action is associated with a maximal time delay, which allows components to work with arbitrary relative speeds; for simplicity, the maximal delay is 1 or 0, but time is continuous. The canonical testing preorder associated to our timed testing compares worst-case efficiency; we show that this efficiency preorder can equivalently be defined considering only discrete time, which is of course much simpler. Then we characterize the efficiency preorder with some kind of refusal traces; despite the rather weak control an asynchronous test environment has, this gives quite detailed insight into the temporal system behaviour. Since the preorder is not a precongruence for choice, we refine it to the efficiency precongruence, which is a precongruence for all operators of the algebra including recursion.
