Round-Robin scheduling is the most popular time triggered scheduling policy, and has been widely used in communication networks for the last decades. It is an efficient scheduling technique for integration of unrelated system parts, but the worst-case timing depends on the system properties in a very complex way. The existing works on response time analysis of task scheduled under RoundRobin determine very pessimistic response time bounds, without considering in detail the interactions between tasks. This may lead to a degradation of the efficiency of Round-Robin scheduling algorithm, and becomes a practical obstacle to its application in realtime systems. In this paper we present an approach to compute much tighter best-case and worst-case response time bounds of tasks scheduled under preemptive Round-Robin, including also the effects of the scheduling algorithm. Categories and Subject Descriptors B.8 [Performance and Reliability]: Performance Analysis and Design Aids; C.3 [Special...