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Design, implementation and verification of distributed real-time systems are acknowledged to be very hard tasks. Such systems are prone to different kinds of delay, such as execution time of actions or communication delays implied by distributed platforms. The latter increase considerably the complexity of coordinating the parallel activities of running components. Scheduling such systems must cope with those delays by proposing execution strategies  ensuring global consistency while satisfying the imposed timing constraints. In this paper, we investigate a formal model for such systems as compositions of timed automata subject to multiparty interactions, and propose a semantics aiming to overcome the communication delays problem through anticipating the execution of interactions. To be effective in a distributed context, scheduling an interaction should rely on (as much as possible) local information only, namely the state of its participating components. However, as shown in this paper these information is not always sufficient and does not guarantee a safe execution of the system as it may introduce deadlocks. Moreover, delays may also affect the satisfaction of timing constraints, which also corresponds to deadlocks in the former model. Thus, we also explore methods for analyzing such deadlock situations and for computing  deadlock-free scheduling strategies when possible.