In this paper we address the problem of schedulability analysis of distributed real-time transactions under EDF, where each transaction is a chain of precedence constrained tasks. We propose a new efficient methodology and a set of algorithms that explicitly take into account the offsets of the transactions. We show, with an extensive set of simulations, that our methodology provides improved schedulability conditions with respect to existing algorithms. Finally, we apply the methodology to an important class of systems: heterogeneous multiprocessor systems, with a general purpose processor and one or more coprocessors (DSPs).