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The use of multicores is becoming widespread in the field of embedded systems, many of which have real-time requirements. Hence, ensuring that real-time applications meet their timing constraints is a pre-requisite before deploying them on these systems. This necessitates the consideration of the impact of the contention due to shared low-level hardware resources like the front-side bus (FSB) on the Worst-Case Execution Time (WCET) of the tasks. Towards this aim, this paper proposes a method to determine an upper bound on the number of bus requests that tasks executing on a core can generate in a given time interval. We show that our method yields tighter upper bounds in comparison with the state-of-the-art. We then apply our method to compute the extra contention delay incurred by tasks, when they are co-scheduled on different cores and access the shared main memory, using a shared bus, access to which is granted using a round-robin arbitration (RR) protocol.