This paper introduces a novel (bi)simulation-based faster-than preorder which relates asynchronous processes, where the relative speeds of system components are indeterminate, with respect to their worst-case timing behavior. The study is conducted for a conservative extension of the process algebra CCS, called TACS, which permits the specification of upper time bounds on action occurrences. TACS complements work in plain process algebras which compares asynchronous processes with respect to their functional reactive behavior only, and in timed process algebras which focus on analyzing synchronous processes. The most unusual contribution is in showing that the proposed faster-than preorder coincides with several other preorders, two of which consider the absolute times at which actions occur in system runs. The paper also develops the semantic theory of TACS by studying congruence properties, equational laws, and abstractions from internal actions. Two examples, one dealing with mail delivery and one relating two implementations of a simple storage system, testify to the practical utility of the new theory.