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In a multicore system, several CPUs frequently require access to a shared memory. If this access is required to be time-predictable to enable worst-case execution time (WCET) analysis of tasks, a form of TDMA based bus arbitration is usually used. A global TDMA schedule controls when each CPU may make use of the bus. This schedule is normally static. It has been suggested that the TDMA schedule could be specialized to reduce the WCET for particular tasks. In this paper, we show that there is a hard limit to the potential of this technique within a general-purpose system. We simulate single- path tasks running within a multitask, multicore system and apply TDMA slot scheduling on the memory access traces. For medium numbers of CPU cores and low memory latencies, CPU utilization can be improved by up to 25%, but as more cores are used and memory latency increases, the bus gets saturated and the difference between a specialized schedule and a generic schedule disappears.