Scenario-driven requirement specifications are widely used to capture and represent high-level requirements. Timed Use Case Maps (TUCM) is a high-level scenario based modeling technique that can be used to capture and integrate behavioral and time-related aspects at a high level of abstraction. The Timed Use Case Maps language assumes durational semantics which introduces semantic variation points when dealing with concurrent flows. In this paper, we introduce three AsmL-based operational semantics, making the semantic variation points of TUCM concurrent behavior explicit. The proposed semantics are illustrated using an example.